USF Libraries
USF Digital Collections

Multi-agent workload control and flexible job shop scheduling

MISSING IMAGE

Material Information

Title:
Multi-agent workload control and flexible job shop scheduling
Physical Description:
Book
Language:
English
Creator:
Wu, Zuobao
Publisher:
University of South Florida
Place of Publication:
Tampa, Fla.
Publication Date:

Subjects

Subjects / Keywords:
Due date
Multi-agent method
Make-to-order
Production planning and control
Manufacturing systems
Dissertations, Academic -- Industrial Engineering -- Doctoral -- USF   ( lcsh )
Genre:
government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

Notes

Summary:
ABSTRACT: In the make-to-order (MTO) industry, offering competitive due dates and on-time delivery for customer orders is important to the survival of MTO companies. Workload control is a production planning and control approach designed to meet the need of the MTO companies. In this dissertation, a multi-agent workload control methodology that simultaneously deals with due date setting, job release and scheduling is proposed to discourage job early or tardy completions. The earliness and tardiness objectives are consistent with the just-in-time production philosophy which has attracted significant attention in both industry and academic community. This methodology consists of the order entry agent, job release agent, job routing and sequencing agent, and information feedback agent. Two new due date setting rules are developed to establish job due dates based on two existing rules. A feedback mechanism to dynamically adjust due date setting is introduced.Both new rules are nonparametric and easy to be implemented in practice. A job release mechanism is applied to reduce job flowtimes (up to 20.3%) and work-in-process inventory (up to 33.1%), without worsening earliness and tardiness, and lead time performances. Flexible job shop scheduling problems are an important extension of the classical job shop scheduling problems and present additional complexity. A multi-agent scheduling method with job earliness and tardiness objectives in a flexible job shop environment is proposed. A new job routing and sequencing mechanism is developed. In this mechanism, different criteria for two kinds of jobs are proposed to route these jobs. Two sequencing algorithms based on existing methods are developed to deal with these two kinds of jobs.The proposed methodology is implemented in a flexible job shop environment. The computational results indicate that the proposed methodology is extremely fast.
Thesis:
Thesis (Ph.D.)--University of South Florida, 2005.
Bibliography:
Includes bibliographical references.
System Details:
System requirements: World Wide Web browser and PDF reader.
System Details:
Mode of access: World Wide Web.
Statement of Responsibility:
by Zuobao Wu.
General Note:
Includes vita.
General Note:
Title from PDF of title page.
General Note:
Document formatted into pages; contains 126 pages.

Record Information

Source Institution:
University of South Florida Library
Holding Location:
University of South Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 001670332
oclc - 62277780
usfldc doi - E14-SFE0001193
usfldc handle - e14.1193
System ID:
SFS0025514:00001


This item is only available as the following downloads:


Full Text

PAGE 1

Multi-Agent Workload Control a nd Flexible Job Shop Scheduling by Zuobao Wu A dissertation submitted in partial fulfillment of the requirements for the degree Doctor of Philosophy Department of Industrial and Ma nagement Systems Engineering College of Engineering University of South Florida Major Professor: Michael X. Weng, Ph.D. Tapas K. Das, Ph.D. Grisselle Centeno, Ph.D. Sudeep Sarkar, Ph.D. Lihua Li, Ph.D. Date of Approval: May 19, 2005 Keywords: Due Date, Multi-agent Method, Make -to-Order, Production Pl anning and Control, Manufacturing Systems Copyright 2005, Zuobao Wu

PAGE 2

Dedication To the memory of my father, Zhangxun Wu fo r his lifelong pursuit of excellence with honesty.

PAGE 3

Acknowledgments I would like to express my appreciation and gratitude to my major professor, Dr. Michael X. Weng, for his guidance throughout this research. I would al so like to thank the other committee members: Dr. Lihua Li, Dr. Tapas K. Das, Dr. Sudeep Sa rkar and Dr. Grisselle Centeno for their valuable comments and suggesti ons. I express my special thanks to Dr. Lihua Li for his support and help. I would especially like to thank my wife Hong Qiu, and my s on, Tao Wu, for their love. I would also like to thank my mother Lanxiang Li, my brother, Zuohu Wu, and my sisters: Fuxian Wu, Meixian Wu and Chunxian Wu. Without their unde rstanding and support, none of this would be possible.

PAGE 4

i Table of Contents List of Tables iii List of Figures v List of Symbols vi List of Acronyms ix Abstract xii Chapter 1 Introduction 1 1.1 Make-to-Order Industry 1 1.2 Workload Control in Make-to-Order Companies 2 1.3 Contributions 4 1.4 Dissertation Overview 5 Chapter 2 Literature Review 7 2.1 Introduction 7 2.2 Production Planning and Control 7 2.3 Due Date Setting 10 2.4 Job Release Control 15 2.5 Earliness and Tardiness Problems 18 2.6 Heuristic Scheduling 21 2.7 Flexible Job Shop Scheduling 24 2.8 Workload Control 26 2.9 Multi-Agent Systems 29 Chapter 3 Multi-Agent Scheduling Method 33 3.1 Introduction 33 3.2 Flexible Job Shop Scheduling 33 3.3 System Framework 35 3.4 Job Agent 36 3.5 Machine Agent 37 3.5.1 TOLJ Insertion Algorithm 38 3.5.2 SOLJ Sequencing Algorithm 40 3.5.3 Numerical Example 44 3.5.4 Machine Agent Protocol 46 3.6 System Coordination 47 3.7 Experimental Design 47 3.8 Analysis of Computational Results 49

PAGE 5

ii 3.8.1 WET under Different Utilizations 49 3.8.2 WT under Different Utilizations 51 3.8.3 WET under Different Numbers of Operations 52 3.8.4 WET under Different Processing Time Distributions 54 3.8.5 WET under Different Mean Processing Times 56 3.8.6 Simulation Time under Different Utilizations 58 3.9 Summary 59 Chapter 4 Dynamic Due Date Setting 61 4.1 Introduction 61 4.2 Order Entry in Make-to-Order Companies 61 4.3 DTWK and DPPW Rules 62 4.4 Order Entry Agent 64 4.5 Job Routing and Sequencing Agent 66 4.6 Information Feedback Agent 66 4.7 System Coordination 67 4.8 Analysis of Simulation Study 68 4.8.1 Comparisons among TWK, DTWK and DPPW 68 4.8.2 Comparisons among Four Rules 71 4.8.3 WET and WT Performance of Four Rules 73 4.8.4 Performance of Different Earliness and Tardine ss Weights 75 4.9 Summary 78 Chapter 5 Multi-Agent Workload Control Methodology 79 5.1 Introduction 79 5.2 Job Release Control 79 5.3 Job Release Agent 80 5.4 System Architecture 81 5.5 System Coordination 82 5.5.1 Temporal Interdependency 82 5.5.2 Sub-goal Interdependency 82 5.6 Discrete Event Simulation 83 5.7 Simulation Study 84 5.7.1 System Performance Using DFPPW 85 5.7.2 System Performance Using DFTWK 86 5.7.3 System Performance under Different Utilizations 88 5.7.4 Performance under Different Processing Time Distributions 90 5.8 Summary 95 Chapter 6 Conclusions 97 6.1 Summary of Work 97 6.2 Future Research Directions 98 References 100 About the Author E nd Page

PAGE 6

iii List of Tables Table 3.1 Numerical Values of Example 46 Table 3.2 Simulation Parameters 48 Table 3.3 WET Performance under Different Shop Utilizations 50 Table 3.4 WT Performance under Different Shop Utilizations 52 Table 3.5 WET Performance under Different Numbers of Operations 54 Table 3.6 WET Performance under Different Pro cessing Time Distributions 56 Table 3.7 WET Performance under Different Mean s of Processing Times 57 Table 3.8 Simulation Time under Different Shop Utilizations 58 Table 4.1 WET Performance under DTWK and DPPW 68 Table 4.2 WET Performance under Different Pro cessing Time Distributions 71 Table 4.3 WET Performance under Different Scheduling Methods 72 Table 4.4 WET Performance under Different Shop Utilizations 72 Table 4.5 WET Performance under Different Pro cessing Time Distributions 73 Table 4.6 WET Performance under Different Mean Pr ocessing Times 73 Table 4.7 WETs and WTs under Different Processi ng Time Distributions 74 Table 4.8 WETs and WTs under Different Mean Proce ssing Times 75 Table 4.9 WETs and WTs under Same Weights 76 Table 4.10 Performance under Different Mean Processing Times 77 Table 4.11 WETs and WTs under Different Weights 77

PAGE 7

iv Table 4.12 Performance under Different Mean Processing Times 78 Table 5.1 Performance under 90% Shop Utilization Using DFPPW 86 Table 5.2 Performance under 90% Shop Utilization Us ing DFTWK 87 Table 5.3 Performance under 85% Shop Utilization Using DFPPW 88 Table 5.4 Performance under 85% Shop Utilization Us ing DFTWK 89 Table 5.5 Performance under Normal Distribution Using DFPPW 91 Table 5.6 Performance under Normal Distribution Us ing DFTWK 92 Table 5.7 Performance under Uniform Distribution Us ing DFPPW 93 Table 5.8 Performance under Uniform Distribution Us ing DFTWK 94

PAGE 8

v List of Figures Figure 3.1. Insert New Job by TOLJ Insertion Algorithm 39 Figure 3.2. Example of SOLJ Sequencing Algorithm 45 Figure 3.3. Average WET under Different Scheduling Methods 51 Figure 3.4. Average WT under Different Scheduling Methods 53 Figure 3.5. Average WET under Different Nu mbers of Operations 55 Figure 3.6. Average WET under Different Processing Time Distributions 57 Figure 3.7. Simulation Times under Different Scheduling Methods 59 Figure 4.1. Average WET Using DTWK 69 Figure 4.2. Average WET Using DPPW 70 Figure 4.3. Average WET under 95% Utiliza tion 70 Figure 5.1. System Architecture of Multi-A gent Workload Control 81 Figure 5.2. Performance under 90% Utilization Using DFPPW 86 Figure 5.3. Performance under 90% Utilizati on Using DFTWK 87 Figure 5.4. Performance under 85% Utilization Using DFPPW 89 Figure 5.5. Performance under 85% Utilizati on Using DFTWK 90 Figure 5.6. Performance under Normal Dist ribution Using DFPPW 91 Figure 5.7. Performance under Normal Di stribution Using DFTWK 92 Figure 5.8. Performance under Uniform Di stribution Using DFPPW 94 Figure 5.9. Performance under Uniform Di stribution Using DFTWK 95

PAGE 9

vi List of Symbols WET increase jL average lateness of r ecently completed jobs when job j arrives aj earliness weight of job j j tardiness weight of job j number of waiting SOLJs in a machine queue machine/shop utilization job arrival rate average number of jobs at each machine ak available time of machine k cj due date tightness factor of job j Cj completion time of job j dj due date of job j e threshold value Ej earliness of job j f average flowtime at each machine fs average shop flowtime i index of operations Ij idle time between job j and the job that follows job j j index of jobs k index of machines

PAGE 10

viik1 planning factor k2 planning factor K number of most recently completed jobs l number of waiting jobs in a machine queue lj lead time of job j Lj lateness of job j M number of machines Mij set of machines that can process operation i of job j N number of jobs n average number of operations n j number of operations in job j Nt number of uncompleted jobs at time t oij operation i of job j p average processing time for each operation pj total processing time of job j pijk processing time for operation i of job j on machine k Qj number of jobs in queues at machines on job j’s routing R average interarrival time of jobs r average remaining processing time per job in the shop rj release/ready time of job j sij starting time of operation i of job j j njs,ˆ preferred st arting time of operation n j of job j t current time Tj tardiness of job j

PAGE 11

viiiw j waiting time per operation of job j W average shop workload WIP average WIP level

PAGE 12

ix List of Acronyms ATC apparent tardiness cost BOM bill of materials CAGG continuous aggregate loading CONWIP constant work-in-process COVERT cost over time CR critical ratio DFPPW dynamic feedback processing plus waiting DFTWK dynamic feedback total work content DPPW dynamic processing plus waiting DTWK dynamic total work content EDD earliest due date ERP enterprise resource planning ET earliness and tardiness FCFS first come first serve IDD internal due date IFA information feedback agent JA job agent JIQ jobs in queue JIS jobs in system

PAGE 13

x JIT just-in-time JRA job release agent MA machine agent MRP material requirements planning MRPII manufacturing resource planning MTO make-to-order MTS make-to-stock NOP number of operations ODD operation due date OEA order entry agent PPC production planning and control PPW processing plus waiting PR production reservation RBC repeat business customizers RSA routing and sequencing agent SOLJ single operation left job SPT shortest processing time S/OPN slack per remaining operation S/RPT slack per remaining processing time SSPR singl e step production reservation TOC theory of constrains TOLJ two or more operations left job TWK total work content VMC versatile manufacturing companies

PAGE 14

xi WET weight ed earliness and tardiness, WIP work-in-process WIQ work in queue WLC workload control XDD external due date

PAGE 15

xii Multi-Agent Workload Control a nd Flexible Job Shop Scheduling Zuobao Wu ABSTRACT In the make-to-order (MTO) industry, offe ring competitive due dates and on-time delivery for customer orders is important to the survival of MTO companies. Workload control is a production planning and control approach designed to meet the need of the MTO companies. In this dissertation, a mu lti-agent workload control methodology that simultaneously deals with due date setting, job release and scheduling is proposed to discourage job early or tardy completions. The earl iness and tardiness objectives are consistent with the just-in-time production philosophy which has attracted significa nt attention in both industry and academic community. This methodology consists of the order entry agent, job release agent, job routing a nd sequencing agent, and information feedback agent. Two new due date setting rules are develope d to establish job due dates based on two existing rules. A feedback mechanism to dynami cally adjust due date setting is introduced. Both new rules are nonparametric and easy to be implemented in practice. A job release mechanism is applied to reduce job flowtimes (up to 20.3%) and work-in-process inventory (up to 33.1%), without worsening earliness and tardin ess, and lead time performances. Flexible job shop scheduling problems are an important ex tension of the classi cal job shop scheduling problems and present additional complexit y. A multi-agent scheduling method with job earliness and tardiness objectives in a flexible job shop envi ronment is proposed. A new job

PAGE 16

xiii routing and sequencing mechanism is developed. In this mechanism, di fferent criteria for two kinds of jobs are proposed to route these j obs. Two sequencing algorithms based on existing methods are developed to deal with these two kinds of jobs. The proposed methodology is implemented in a flexible job shop environment. The computational results indicate that the proposed methodology is extremely fast. In particular, it takes less than 1.5 minutes of simulation time on a 1.6GHz PC to find a complete schedule with over 2000 jobs on 10 machines. Such computational efficiency makes the proposed method applicable in real time. Therefore, the proposed workload control methodology is very effective for the production planning and control in MTO companies.

PAGE 17

1 Chapter 1 Introduction 1.1 Make-to-Order Industry There are two kinds of manufacturing sectors of industry: make-to-stock (MTS) sector and make-to-order (MTO) sector. Production planning and control (PPC) is crucial to help meet increasing customer demands a nd expectations as markets become more competitive. The desirable objective of PPC is just-in-time (J IT) production, which products should be produced by the right quality at the right time. Most rese arch for PPC has been concentrated on the MTS industry. There has been a relativ e less attention for the MTO indus try, even though this is a sizable sector of manufacturing industry. The basic distinction between MTS and MTO is the timing of the receipt of customer orders. In th e MTS industry, the produc t is already available in stock when an order arrives and can be di spatched immediately to the customer from inventory. Enterprise resource planning or manufacturing resource planning (ERP/MRPII) systems are often applied for PPC in the MTS industry. In ERP/MRPII, the master production schedule provides the demand according to orde rs. The material requirements planning (MRP) nets demand, determines material requireme nts, and provides release dates. Capacity requirements planning checks plan feasibility. Thus orders are translated into shop jobs with associated due dates and planned release dates. In the MTO industry, some or all production takes place after the order is received. Thus MTO companies have ability to customize th eir products to meet the specific needs of

PAGE 18

2 individual customers. A customer typically makes an enquiry to several possible MTO companies. The MTO company is thus in a competitive environment in determining how to respond to a customer, especially how to determ ine due dates. Customers usually desire early due date promises and manufactur ers prefer extended due dates to ensure on-time delivery. The diverse and unpredictable nature of order arriva ls in MTO companies makes the reliable due date setting and due date guarantee as a crucia l task to improve on-time delivery performance. A trade-off has to be made between the custom er and manufacturer. This demonstrates that there is the greatest need for sophisticated PPC methods to determine due dates and ensure ontime delivery in MTO companies. 1.2 Workload Control in Make-to-Order Companies Workload control (WLC) is a sophisticated PPC approach specifically designed for the needs of MTO companies (Hendry and Ki ngsman 1989, Bertrand and Muntslag 1993). WLC consists of the three PPC levels of order entry, job release and schedulin g. At order entry level, customer enquiries are processed, and due date s are determined. To control work-in-process (WIP) inventory, a job release mechanism dete rmines when each job should enter the shop floor. After a job is released, the progress of the job on the shop floor is controlled by scheduling. Most investigations have treated order en try, job release and sc heduling separately. A few investigations focus on the interactions am ong order entry, job release and scheduling. It is challenging to coordinate order entry, job release and scheduling in real time. Simultaneously solving order entry, job release and scheduling problems by mathematical models may be quite time consuming (Kingsman 2000). No effec tive method addresses this issue.

PAGE 19

3 Shop floor configuration is a major factor fo r the applicability of PPC approaches. Job shop is an appropriate configuration for many MTO companies (Muda and Hendry 2003). Due to the existence of considerable amount of overlapping capacities with modern machines and the stochastic nature of the arrival of orders in MTO companies, flexible job shops are common in MTO companies. A flexible job shop is a ge neralization of the job shop and the parallel machine environments (Pinedo 2002). In particular, there are a set of work centers in a flexible job shop environment. Each work center has a set of parallel machines with possibly different processing efficiency (Kacem, Hammadi and Borne 2002). Flexible job shops allow an operation to be performed by any machine in a work center and thus present two issues. The first is job routing: to assign each operation to a machine. The second is job sequencing: to order the operations assi gned to a machine. Thus, flexible job shop scheduling consists of job routing and sequencing. Only a few methods su ch as tabu search, loca lization approach and neighborhood functions exist for flexible job shop scheduling. These methods require substantial computation load and are not suitabl e for large-scale scheduling problems in real time. Manufacturing environments in MTO comp anies are real-time, dynamic systems. Multi-agent method has been taken as a prom ising approach for developing advanced manufacturing systems (Cutkosky, Tenenbaum and Glicksman 1996). Such an approach provides rapid responsive and dy namic reconfigurable structures to facilitate flexible and efficient use of manufacturing re sources in a rapidly changing environment. This research focuses on the integration of order entry, job release, and flexible job shop scheduling by a multi-agent method. Minimizing job earliness and tardiness (ET) is the PPC objective. The following definitions are used throughout this research. If the shop workload exceeds some preset maximum limit, new jobs are not released to the shop floor and wait. Such

PAGE 20

4 unreleased jobs form a pre-shop pool. As jobs in MTO companies might differ significantly from each other in terms of their routings, nu mber of operations and processing times, the workload is defined as the total remaining proce ssing time of all jobs released to the shop floor. The workload norm is defined as the preset maximum limit of the workload. The waiting time in the pool is defined as the pool time of a job. The time between the release and completion of the job is defined as its shop fl owtime. Thus, the time between the arrival and the completion of a job is the sum of its pool time and shop flow time, and is commonly referred to as the manufacturing lead time. 1.3 Contributions The contributions of this research are summarized as follows. A new multi-agent WLC methodology that simulta neously deals with due date setting, job release and scheduling is proposed to di scourage job early or tardy completions. This methodology consists of the order entry agent, job release agent, job routing and sequencing agent, and information feedback agent. Two new due date setting rules are develope d to establish job due dates based on two existing rules. A feedback mechanism to dynami cally adjust due date setting is introduced. Both new rules are nonparametric and eas y to be implemented in practice. A job release mechanism is applied to re duce job flowtimes and shop WIP inventory. At the critical norm, the job release mechan ism significantly reduces job flowtimes (up to 20.3%) and WIP inventory (up to 33.1%), withou t worsening ET and lead time performances. A new multi-agent scheduling method with job earliness and tardiness objectives in a flexible job shop environment is proposed.

PAGE 21

5 A new job routing and sequencing mechanism is developed in the multi-agent scheduling method. In this mechanism, different criteria for two kinds of jobs are proposed to route these jobs. Two sequencing algorithms base d on existing methods are developed to deal with these two kinds of jobs. The proposed WLC methodology is implemented in a flexible job shop environment. The computational results show that the proposed two new due date setting rules outperform the existing DTWK and DPPW rules for ET obj ectives. The proposed multi-agent scheduling method also outperforms the existing schedu ling methods. Therefore, the proposed WLC methodology is very effective for the PPC in MTO companies. 1.4 Dissertation Overview The rest of this dissertation is organized into five chapters. Chapter 2 reviews the relevant research in eight fields. First is a review of current PPC methods and their applicability. Second, due date se tting approaches and rules are reviewed. Third, reviews of job release mechanisms are presented. Fourth, th e studies on ET problems are surveyed. Fifth, heuristic scheduling methods are discussed. Si xth, the existing flexible job shop scheduling methods are briefly described. Seventh, most ex isting research on the interactions among order entry, job release and scheduling are given. At la st, the applications of multi-agent systems in PPC are reviewed. In Chapter 3, a multi-agent scheduling method with job ET objectives in a flexible job shop environment is proposed. A new job routi ng and sequencing mechanism for flexible job shops is presented. Two heuristic algorithms fo r job sequencing are developed. The simulation results are given.

PAGE 22

6 Two new due date setting rules are described in Chapter 4. A feedback mechanism to dynamically adjust due date setting is introduced. The effectiveness of the two due date setting rules is also presented. In Chapter 5, the theory of job release control is described. A job release mechanism is discussed. The multi-agent WLC methodology for MTO companies is proposed. The computational results are also discussed. Chapter 6 concludes this research and suggests future research directions.

PAGE 23

7 Chapter 2 Literature Review 2.1 Introduction As mentioned in Chapter 1, the goal of this re search is to integrat e due date setting, job release, job routing and sequencing. This ch apter gives the relate d literature review. 2.2 Production Planning and Control The MTO industry can be classi fied into two types (Amaro et al. 1999): repeat business customizers (RBC) and versatile manufact uring companies (VMC). A RBC provides customized products on a continuous basis ov er the length of a contract. Products are customized but may be made more than once pe rmitting a small degree of predictability. The VMC market is more complex requiring more s ophisticated solutions. In VMC, a high variety of products with variable demand are manufactured in small batches with little repetition. Both RBC and VMC allow customization, but RBC is able to establish more stability by enticing customers into a more predictable and committed relationship. MTO companies produce a high variety of products in lowe r volume than MTS companies. Unstable market demand mean s a MTO philosophy would be too costly. Production does not take place un til customer orders receive, a llowing a greater degree of customization. Customization invariably lead s to nonstandard product routings on the shop floor, and lead times are naturally longer than those for MTS companies. The price and due date that a company can quote affect its succe ss in winning orders, resulting in lead times

PAGE 24

8 taking on strategic importance. It is in the MTO industry that there is the greatest need for sophisticated PPC methods. PPC methods are crucial to help meet increasingly high customer demands and expectations as markets become more competitiv e. Typical functions of a PPC system include customer enquiry and order processing, mate rial requirements planning, input and output control, and scheduling. Thus, it can be classified by three leve ls: order entry, job release and scheduling. PPC methods vary at th e three levels. Past research ha d a tendency to skip the order entry and job release levels, as these stages are of little significance in a typical MTS environment. However, the three PPC leve ls are important to the MTO industry. There are many PPC methods such as ER P/MRPII, WLC, Kanban, and theory of constrains (TOC), and constant WIP (CONWIP). Their applicabil ity is different for different production environments. A simple, effective solu tion for one company may be insufficient to solve the planning problems of another. To be successful in companies, a PPC approach should fit to the production environment. Essential el ements of the approach should correspond with the characteristics of the produc tion system. For classical methods such as MRP, these elements have become common sense. BOM (bill of materials)-explosion and constant lead times make MRP known to perform best in envir onments with high material and low capacity complexity. However, a PPC method in MTO companies must cope with many products, variable routing and numerous set ups. For exam ple, once a RBC has established a contract with a customer, it needs less control over the order entry stage, but a VMC must go through the whole process for every order. WLC is based on principles of input/outpu t control. Input control relates to both accepting orders and releasing them to the shop floor. Once released, the jobs remain on the shop floor. Scheduling will direct orders along their downstream operations. Each operation

PAGE 25

9 relates to a specific cap acity group consisting of one or mo re machines and operators. Both order entry and job release can be accompanied by output control decisions in terms of capacity adjustments. WLC uses a pre-shop pool of j obs to reduce shop floor congestion, making the shop floor more manageable. It stabilizes th e performance of the shop floor and makes it independent of variations of incoming orde rs (Bertrand and Van Oo ijen 2002). For most WLC approaches, jobs are only released onto the shop floor if the work load does not ex ceed its norm, while ensuring jobs do not stay in the pool too l ong in order to reduce lead times and meet due date objectives. While jobs remain in the pool, unexpected changes to quantity and design specifications can be accommodated at less inconvenience. A framework is proposed to explore the applicability of WLC in MTO companies (Henrich, Land and Gaalman 2004). The framework supports an initial c onsideration of WLC in the first phase of a PPC selection and impl ementation process. It is concluded that the applicability of WLC increases with raising va riability, indicat ed by increased arrival rate fluctuations, due date differen ces, processing time variabilit y, routing sequence and routing length variability. While routing flexibility has not been widely reported in literature, it can contribute to the appl icability of WLC. As discussed above, MTO companies have to react on dynamic environments: they have to cope with changes in product mix and volume, production rate changes, a high number of rush jobs, and lot of internal uncertainty. Thus, the PPC in MTO companies is rather complex and often based on insecure data. Ther efore, WLC is a sophisticated PPC approach specifically designed for the needs of MTO co mpanies (Zapfel and Missbauer 1993, Hendry, Kingsman and Cheung 1998).

PAGE 26

10 2.3 Due Date Setting A due date can be assigned to an order by first estimating its flowtime and then adding a delivery safety allowance to account for transp ortation and uncertainties Due date assignment is one of the main application areas of flowtime estimation. As it is frequently observed in literature, most research efforts directed towa rds flowtime estimation are within the context of due date assignment. There are basically two flowtime estimation approaches in literature: analytical approach and simulation approach Cheng and Gupta (1989) presen ted an extensive survey of these approaches for the due da te assignment problem. There are advantages and disadvantages associated with each approach. The analytical approach offers an exact way of determining means and variances of flowtime estimates. However, the dynamic and stochastic nature of production systems makes it difficu lt to develop realistic analyti cal models. On the other hand, simulation approach does not always produce reli able estimates. Moreover, a great number of computer runs may also be needed in the latt er case to obtain accurate and precise estimates. Since these two areas are complimentary in natu re, the literature has been developed in both directions. Due date setting methods can be dynamic or static. Dynamic methods employ job characteristics and shop congestion informati on for determining due dates. Static methods consider only job content information such as arrive time, routing, and processing time. For static methods, a job flow allowance is a fixe d amount for given job data and does not depend upon shop status when the j ob arrives (Baker 1984). The first simulation-based study in this area was conducted by Conway (1965) who compared four flowtime estimation methods: total work content (TWK), nu mber of operations (NOP), constant, random. The results of this st udy indicate that the methods which utilize the

PAGE 27

11 job information perform better than the others. Conway also observed the relationship between due date assignment methods and dispatching ru les. Later, Eilon and Chowdhury (1976) used shop congestion information in estimating flowtim es. In their work, TWK is compared with three other methods: jobs in queue (JIQ), delay in queue and m odified TWK. Results indicate that JIQ, which employs the shop congesti on information, outperforms other methods. Many studies have consistently concluded th at assigning due dates based on job content and shop congestion information could lead to better shop performance than assigning due dates based only on job content. Weeks (1979) proposed a method which combines both job and shop information. This method performs very well for the performance metrics such as mean lateness, mean earliness, and number of tar dy jobs. The results also indicate that flowtime estimation is affected by the stru ctural complexity of the shop mo re than the size of the system. Bertrand (1983a) proposed a new method of flow time estimation which exploits time-phased workload information of the shop. Two factors ar e used in analyzing th e performance of the method: minimum allowance for waiting and capacity loading limit. His results indicate that time-phased workload and capacity information significantly decrease variance of the lateness. Ragatz and Mabert (1984) compared eight different methods: TWK, NOP, TWK-NOP, JIQ, work in queue (WIQ), WEEK's method, jobs in system (JIS), and response mapping rule. Among them, the response mapping rule utilizes the response surface methodology to identify the significant factors in flowtime estimation. The results in dicate that the job and workload information are very important for predicting flowtimes. Kanet and Christy (1989) compared TWK with the processing plus waiting (PPW) rule via computer simulation in a job shop with forb idden early shipment. PPW estimates the flow allowance of a job by adding an estimate of the waiting time to the total processing time of a job. The waiting time is proportional with the numb er of operations. The results indicate that

PAGE 28

12 TWK is superior to PPW in te rms of the mean tardiness, pr oportion of tardy jobs, and mean inventory level. Fry et al. (1989) also investigated the job an d shop characteristics which affect job flowtimes in a job shop. They constructe d two linear and two mu ltiplicative nonlinear models to estimate the coefficients of the fact ors. This study shows that models using product structure and shop conditions can estimate more accurate flowtimes th an the others, linear models are superior to the multiplicative models, and the predictive ability of the models also improves as the utilization increases. Vig and Dooley (1991) proposed two flow time estimation methods: operation flowtime sampling, and congestion and operation flowtime sampling. These methods are also compared with JIQ and TWK-NOP under various shop cond itions. The results indicate that congestion and operation flowtime sampling and JIQ yield th e best performance. Vig and Dooley (1993) extended their work by combining static a nd dynamic estimates to obtain job flowtime estimates. Gee and Smith (1993) proposed an ite rative procedure for estimating flowtimes when due date dependent dispatching rules ar e used. Two flowtime estimation methods are employed, the one is based on job related information and the ot her one utilizes both job and shop related information. Their results indicate that the late method yields better estimation. They also compared the iterative approach w ith the response mapping rule of Ragatz and Mabert (1984) and found that the quality of flowtime estimation was improved by the iterative approach. As described above, TWK and PPW are parametric rules and need appropriate parameter selection based on the analysis of hist orical data which requ ires preliminary runs. TWK is a static and job characte ristic related due date setti ng method. If two jobs have the same amount of work, the same allowance will be given to them, regardless of what the current shop load is, i.e. whether heavy or moderate. Th is kind of due date assignment lacks the means

PAGE 29

13 of estimating job flowtimes dynamically. It seems that ET performance, which stress the importance of meeting job due dates as closel y as possible, can be improved if due date allowance is set to the dynamica lly estimated flowtime of each job. In another study, Bertrand (1983b) provided an analytical m odel used to establish an internal due date (IDD) for shop floor control and an external due date (XDD) quoted to the customer. It is concluded that the use of worklo ad information can contribute substantially to setting attainable due dates in jo b shops, and the due date setting rule produ ces a constant mean lateness. Delivery reliability to the customers can be controlled by making the XDD equal to the IDD plus the mean lateness plus a safety time related to the variance of lateness. Thus a small variance of lateness reduces the quoted XDD. His study also indicates that the best variance performance is obtained with an assignment rule that uses a time-phased representation of the workload in the shop. Later, Enns (1994, 1995) proposed a dynamic estimation method which employs a dynamic version of PPW (DPPW). By using the feedback of exponentially smoothed flowtime estimation error, the lateness vari ance is estimated. He also describes a method of setting due dates to achieve of the desire d percentage of tardy jobs. E nns (1998) developed a workload balancing dispatch mechanism and a dynamic version of TWK (DTWK). In his dynamic forecasting model, two different mechanisms ba sed on exponentially smoothing errors are used to set safety allowances that will result in the ta rgeted percent of tardy deliveries. If a due date independent dispatching rule is used, the opera tion lateness variance mechanism is appropriate. Otherwise, the job lateness variance mechanism is appropriate. The results indicate that a shop load balance index which considers both shop load and variability has a very strong relation with lead times. Cheng and Jiang (1998) pr oposed a similar dynamic forecasting model for DTWK and DPPW.

PAGE 30

14 DTWK and DPPW are capable of adjusting the flowtime estimation by using feedback information about current shop load conditions. Simulation results show that the dynamic due date rules are significantly better than their st atic counterparts. In addition, DTWK and DPPW are nonparametric and, therefore, are simple to implement without preliminary runs for parameter estimation. However, these models do not consider the pool time of a job in WLC situations. Recently, several artificial intelligent met hods were proposed for due date setting. Philipoom et al. (1994) investigated the feasibility of using artificial ne ural networks in flowtime estimation. The neural network models are used to forecast due dates in a simple flow shop manufacturing system. They estimated the coefficients of the methods with neural networks instead of multiple regressions. The results indicate that the neural network approach offers certain advantages ove r the conventional approaches. However, job due dates in a flow shop are stable, and the system deviation is smaller than that in a job shop. Huang et al. (1999) constructed an artificial neural network model to predict production performance for a wafer fabrication factory. They used a three-layer back-propagation neural network that allows for more accurate prediction of the WIP level and for moving volume in the next period for each wafer fabrication operation stage. There are the follo wing advantages using neural network models: neural networks can obtain a probable result even if the input data are incomplete or noisy; a welltrained neural network model can provide a real -time forecasting result; creating a neural network model does not necessitate understanding the complex relationship among the input variables. Artificial neural network models were also used for estimating lead times in a virtual wafer fabrication system (Hsu and Sha 2004). They suggest that if system information is not difficult to obtain, the artificial neural network models can perform a be tter due date prediction than conventional rules.

PAGE 31

15 A method to dynamically control the safety allowance through reinforcement learning was provided, in which job flowtimes are estimate d by parametric due date setting rules (Moses 1999). The applicability of the method to an unrestricted clas s of discrete manufacturing systems is preserved by the use of a feedback control paradigm, and control knowledge is acquired using reinforcement learning. The current s hop status is consider ed so that due date performance is improved during transient co nditions. Results of simulation experiments demonstrate the effectiveness of the method. These artificial intelligent methods are more computationally expe nsive and artificial neural network methods would require a set of training data (Sabuncuoglu and Comlekci 2002). 2.4 Job Release Control Job release has a significant effect on syst em performance. Specifically, they reduce WIP inventory and variability on the shop floor. Bergamaschi et al. (1997) provided a literature review available on efforts to optimize j ob release. Sabuncuoglu and Karapinar (1999) classified job release methods in to four types. The fi rst is job release mechanisms that do not use any information about shop status or job ch aracteristics. Examples are immediate release and interval release. The second is load-limited job rele ase mechanisms that release jobs to the shop floor according to the current workload in the shop. The third is time-phased job release mechanisms that release jobs at predetermine d release times based on flowtime estimates. They utilize information about shop capac ity and job due date. The fourth is release mechanisms that consider both the current worklo ad and job due dates. They are the extensions of load-limited release with additional considerations on due dates. There are three common load-limited job release mechanisms (Land and Gaalman 1996). The first is Bechte release mechanism bu ilds on three parameters : a release period, a

PAGE 32

16 time limit and a workload norm. The decision to release jobs is take n periodically, at the beginning of each release period. All jobs in the pool are sequen ced in order of their planned release date. The planned release date is determined by backward scheduling from the job due date. All jobs within the time limit are candidates for release. In the established sequence, jobs are released until the workload norm is exceede d. All other candidates have to wait in the job pool until the next period of release. The selection process goes on for the remaining candidates. The workload considered in this mechanism is the queue length at a machine. The second is Bertrand release mechanism does not disc uss the release sequence, but elaborates the workload norms extensively. The release decisi on is taken periodically and job release is allowed if the workload of each machine is less th an its norm. The workload considered in this mechanism differs from the workload considered by Bechte. The workload definition of Bertrand covers the processing ti me of all jobs on the shop fl oor which still have to be processed at the considered machine. The corresponding workload norm consist of two components: the planned machine output during th e release period and the planned quantity of work upstream or in the queue at the end of the release peri od. Thus, the norm depends on the average machine position within the job shop. The third is Tatsiopoulos release mechanism formalizes three ways of job release. The common push release takes place periodically. Intermediate push release can be fo rced by rush jobs or jobs with retarded material availability, and an intermediate pull release can be triggere d from the shop floor when a foreman sees his machine threatened by unplanned id leness. The periodic release de cision considers jobs in the sequence of their planned latest release dates. Job release is allowed unless a workload norm is exceeded, which applies to the interm ediate pull releases as well. When jobs are released periodically, loadlimited release mechanisms have to set the planning period length and the check period length. They greatly influence the shop

PAGE 33

17 performance, thus confirming the necessity of a careful setting of such parameters (Perona and Portioli 1998). The impact of load-limited job release in jo b shops was investigat ed by Kanet (1988), who concluded that controlling th e release of new orders should be carefully cons idered as it could result in increased idle times and thus negatively impact performances such as tardiness while making no real impact on inventory. Raman (1995) defined the notion of critical and non-critical jobs. He then used a bicriteria objective to minimi ze total tardiness and maximize the sum of release times. The former objective is app lied to critical jobs; the latter is applied to non-critical jobs. Severa l authors used cost functions to evaluate methodology performance. Tardif and Spearman (1997) used the ‘capacity feasible’ time bucket approach of MRP to determine release times. Land and Gaalman ( 1998) developed an a lternative mechanism building on the approach of Fredenhall and Melnyk (1995), whic h yields significant performance improvement. In this mechanism, a job is released when the queue at its first workstation is empty and it has th e earliest planned release time of the unreleased jobs that start at this workstation, or if no urgent jobs are in the queue and this job has the shortest processing time of all unreleased urgent jobs. Time-phased release mechanisms can be cla ssified into infinite loading and finite loading. The release time of infinite loading is calculated by subtracting the expected lead time from the due date of a job: rj = dj lj, (2.1) where rj is the release time of job j, dj job due date and lj its estimated lead time. In particular, backward infinite loading u tilizes the following methods to calculate the release time: rj = dj –k1 nj, (2.2) rj = dj k1 nj k2 Qj, (2.3)

PAGE 34

18 where k1 and k2 are the planning factors, nj number of operations in job j and Qj the number of jobs in queues at machines on job j’s routing. Finite loading considers available shop cap acity over the planning horizon and tries to match machine requirements of the jobs with the available capacity. Two types of finite loading can be identified: forward finite loading and b ackward finite loading. The first approach loads all operations of the job into available capacit y starting from the first operation. The release decision of a particular job is based on the load ing period of the last operation and the due date of a job. The job is released if the loading period of the last operation is within a preset time window about the due date. Backward finite load ing operates in the oppos ite direction. That is, each operation is placed into avai lable capacity starting with the last operation of the job and working backward from the job due date. As co mpared to forward finite loading, the release decision is based on the loading period of first operation a nd the current time. The job is released if this period is within a pres et time window from the current time. Time-phased release mechanisms focus on determining a release time for each job, regardless of current shop loa d. They often continuously rel ease jobs to the shop floor. However, load-limited release mechanisms are ba sed on current shop load. They are easier to balance and limit the shop load and therefore co ntrol WIP. On the othe r hand, job release also presents a research paradox. It has been found th at the pool time is exte nsive; therefore, the lead time to produce a jo b is not reduced (Melnyk et al. 1994). 2.5 Earliness and Tardiness Problems Even though makespan is a well-known perfor mance measure widely used in classical scheduling problems, it does not reflect the main objective concerned with some problems in practice. For example, flowtime represents a sp eed of response in manufacturing environment

PAGE 35

19 and is a good indicator of produc tion rate. Tardiness is a due da te based measure in terms of delivery performance. The JIT philosophy has been a popular ma nagement concept. Motivations for implementing JIT production are to reduce inventories and im prove response times (Zhu and Meredith 1995). One research area for JIT impl ementation that has been widely studied in recent years is to schedule jobs so as to mini mize job ET. In general, such problems are broadly called ET problems. The objective of ET problems is consistent with the JIT philosophy where an early or a late delivery of a job results in in crease of production costs. However, the majority of articles that address ET problems deal w ith scheduling problems for single machine and parallel machines (Baker and Scudder 1990, Leung 2002, Ventura and Radhakrishnan 2003, Croce and Trubian 2002). Heady and Zhu (1998) provided a heuristic algorithm for minimizing ET in a multi-machine scheduling problem. The heuristic solution procedure is based on a single machine sequencing heuristic. The singl e machine heuristic starts by forming a good initial job sequence, and then uses a proven me thod to optimally time the jobs. Luh, Chen and Thakur (1999) proposed an effective approac h, which takes into acc ount such factors as uncertain arrival times, processing times, due da tes, and job priorities. A problem formulation was presented with the goal to minimize j ob ET. Combining Lagra ngian relaxation and stochastic dynamic programmi ng, a solution methodology was also developed to obtain dual solutions. Zhu and Heady (2000) developed a mixed integer programming formulation for minimizing job ET in a multi-machine scheduling problem. Ip et al. (2000) applied a genetic algorithm in order to obtain an optimal soluti on for ET performance in a large-scale production planning and scheduling problem. Yoon and Vent ura (2002) presented linear programming formulations for minimizing the mean weighted absolute deviation from due dates to find optimal schedules in a lot streaming flow s hop. A polynomial time solution to minimize the

PAGE 36

20 maximum ET with unit processing times in a fl ow shop environment was addressed (Mosheiov 2003). An integer optimization formulation for a job shop scheduling system was developed to maximize on-time delivery, low inventory and small number of setups (Chen et al. 2003). Whether idle time between jobs should be al lowed in a schedule is an important issue for ET problems. The issue of inserting idle times depends upon the types of due dates and the workload. Clearly, it is not wise to force an unnecessarily early completion of a job when the workload is not heavy unless the machine has a larg e startup cost. In genera l, it is reasonable to insert idle times between jobs when jobs have distinct due dates and to delay the starting time when all jobs have a common due date (Alidee 1994). However, if idle time insertion is not treated properly, an ET solution procedure may fail to minimize job ET. Kutanoglu and Sabuncuoglu (1999) identified the conditions under which it may be better to keep the resource idle for a soon-to-arrive urgent job. Hodgson et al. (1998) proposed a simulation-based procedure for minimizing the maximum lateness. It is effective and efficient in providing optimal or near optimal schedules for job shop sc heduling. This procedure was also modified to provide better schedules by inserting idle time under certain conditions (Hodgson et al. 2000). A heuristic method for the ET problem on single machine with unequal due dates and ready times was presented by Mazzini and Arment ano (2001). A feasible solution is obtained through a constructive stage and th en a local search procedure is applied to update its idle times. The main feature of this approach is that idle times ar e suitably inserted during the constructive stage. When compared with EDD, the computational results have shown that the heuristic presents a good performance for the test problem instances with up to 80 jobs.

PAGE 37

21 2.6 Heuristic Scheduling Job shop scheduling is an important aspe ct of production management that has a significant effect on th e performance of a job shop. The combinatorial complexity of the scheduling problem has received co nsiderable attention in literature. Various techniques, such as mixed integer programming modeli ng (Liao and You 1993) and branch-and-bound algorithms (Balas, Lenstra and Vazacopoulos 1995) have been used to overcome the problem of this complexity. Recently, significant improve ments have been made with the development of efficient scheduling algorithm s using tabu search, simulated annealing, neural networks and genetic algorithms. In general, one of the major drawbacks of above algorithms is that the scheduling problems studied by the majority of th ese researchers were simplified to provide the conditions upon which these methods could be based (Blazewicz, Dmschke and Pesch 1996). However, analytical results obtained are usuall y for special cases, and most real-life job shop scheduling problems do not fall into this class of special cases. Furthermore, the computational complexity of a scheduling problem increases exponentially as the size of the problem increases. Thus, heuristics are appropriate me thods in large-scale scheduling problems since they create good schedules and ar e considerably faster than ot her methods (Shafaei and Brunn 1999). Dispatching rules are the most common approach in industry (Subramaniam et al. 2000). It determines the ranking of the jobs wait ing at machine queues. The information needed by dispatching rules is classified (Kutanoglu an d Sabuncuoglu 1999) by: arrival times, e.g. first come first serve (FCFS); process times, e.g. s hortest processing time (SPT); due dates: allowance based, e.g. earliest due date (EDD) ; slack based, e.g. SLACK; ratio based, e.g. critical ratio (CR); combinati on of one or more of the above e.g. operation due date (ODD).

PAGE 38

22 In many applications, meeting due date a nd avoiding delay penalty is the most important scheduling go al. Flow allowance of a job is the time between the release date and the due date. The simplest version of allowance base d priority is the EDD rule. The simplest slackbased priority rule is the SLACK rule, which give s priority to the job with the smallest slack. The ratio-based rules utilize a ki nd of ratio in their implementations. For instance, CR rule gives a priority to the job with the smallest flow allowance/remaining processing time. Other ratio-based rules are slack per remaining processing time (S/RPT) and slack per remaining operation (S/OPN). S/RPT gives a priority to the job with the longer remaining processing time, while S/OPN considers the job with more operations remaining as urgent. Some rules utilize operation due dates. The work content method is generally suggested for mean tardiness among several ways of assigning operation due dates (Baker 1984). According to this method, the in itial flow allowance of a job is allocated to the operations proportional to their processing times. The rule s such as EDD, SLACK and CR have their operation due date versions. Op eration-based rules perform better than their job-based counterparts (Kanet and Hayya 1982). Most studies have tested simple rules de signed for some extrem e shop conditions and known to be deficient with cert ain load levels. For example, EDD, SLACK, and S/RPT rules perform reasonably with light load levels but deteriorate in c ongested shops; whereas SPT rule performs well in congested shops with tight due da tes, but fails with light load levels and loose due dates. Thus, there have been attempts to co mbine two or more of these simple dispatching rules into a single rule in order to use their individual excellent perfor mance characteristics. Cost over time (COVERT) was specifically devel oped for tardiness obje ctive (Carroll 1965). The majority of above studies have been done in a uniform (or ba lanced) environment. For unbalanced systems, bottleneck dynamics was studied with the deve lopment of apparent

PAGE 39

23 tardiness cost (ATC) by Vepsalainen and Mort on (1987). ATC is very similar to COVERT with two main differences. First, the slack is local resource constrained slack which takes into account the waiting times on downstream machines. Second, the decay function for the ratio of weight/processing time is expone ntial rather than linear. The queuing time of a job in a job shop normally accounts for the major portion of its flowtime. Hence, a job flowtime cannot be acc urately determined without some knowledge regarding the expected total que uing time for its remaining ope rations. Queuing time could be influenced by many factors and are very difficu lt to estimate correctly (Chang 1997). Some of possible factors for are: scheduling heuristic; total processing time remaining; number of operations remaining; number of jobs currently in the system; number of jobs currently in the machine queues on this job’s routing; and total processing time of all jobs currently in the machine queues on this job’s routing. There are several methods to estimate que uing times. Standard estimation method calculates the queuing time of a job as proporti onal to its processing time. One issue in this method is to select a right multiplier value. In actual systems this can be done by using regression analysis with historic ally collected queuing times. L ead time iteration method is an iterative procedure which aims to improve que uing time estimation. It estimates queuing times by successive approximations using deterministi c simulation. First, a job shop is simulated using SLACK as the sequencing rule. This is a transient simulation starting from the current state of a job shop and running until the completion of all jobs. Queuing times are recorded for each job at each machine visited. A revised slack is then calculated using the queuing times observed from the simulation. The simulation is then rerun usi ng the revised slack from the previous iteration. The process is repeated until the estimations of the queuing times stabilize.

PAGE 40

24 On small problems, the procedure may converg e exactly. Usually, queu ing estimates tend to stabilize after 3 to 10 iterations (Zozom et al. 2003). 2.7 Flexible Job Shop Scheduling Numerically controlled multi-purpose machin es in job shops have a considerable amount of overlapping cap abilities. They can be easily reconfigured to perform a variety of operations. In order to maximize job shop perfor mances, management should make use of the flexibility while operating job shops. Otherwise, the advantag e of having very capable machines might disappear. On the other hand, consideration of flexibility in job shop scheduling will dramatically increase the complexity of the problem, which is already very hard to solve. This will certainly in crease the cost of the solution. The classical modeling of a job shop scheduling problem does not reflect the requirements of modern job shops. Modeling su ch scheduling problems without considering overlapping capabilities does not reflect the rea lity of modern job shops. Classical job shop scheduling methods are generally incapable of addressi ng such capac ity overlapping. There is a need to model and solve flexib le job shop scheduling problems. Flexible job shops allow an operation to be performed by any machine in a work center. The corresponding flexible job shop scheduling problems are an important ex tension of the classi cal job shop scheduling problems. Although there is a huge amount of literature on classical job shop scheduling problems, flexible job shop scheduling problems do not have much literature. A tabu search algorithm for flexible j ob shop scheduling problems was developed (Chambers 1996). In this algorithm, the feasible in itial solution with the smallest makespan is obtained by selecting from the 12 priority dispatching solutions. Then, two move neighborhoods are implemented, corresponding to job routing and sequen cing in flexible job

PAGE 41

25 shop scheduling. A sequencing move is defined by the exchange of adjacent critical operation pairs. Each machine is scanned successively fo r candidate exchange pair s. A routing move is also defined by the relocation of a critical ope ration to a feasible alternate machine position. For a given solution, every each relocation of ever y reroutable critical operation is considered. The contemplated move that yields a smaller makespan can override a move’s tabu status. Local search techniques and two neighbor hood functions for flexible job shop scheduling problems were proposed (Mastrolilli and Gambardella 2000). Local search employs the idea that a given solution may be improv ed by making small changes. A local search algorithm starts off with an initial solution and then continually tries to find better solutions by searching neighborhoods. In orde r to minimize the makespan, two neighborhood functions are used in local search methods for the flexible job shop scheduling problems. The computational experiments found 120 new better upper bo unds and 116 optimal solutions over 221 benchmark problems. A linguistic based meta-heurist ic modeling and solution appr oach for solving flexible job shop scheduling problems was presented (Ba ykasoglu 2002). Makespan is considered as the main performance criteria to evaluate the goodness of the gene rated solutions. Mean flowtime, number of tardy jobs, and maximum ta rdiness are also considered. This approach makes use of linguistics, simulated annealing a nd priority rule-based heuristic. The main contribution is to show how the grammars of li nguistics can be utilized in modeling and solving flexible job shop scheduling proble ms. In his work, the flexible job shop scheduling problem is presented as a grammar and the productions in the grammar are defined as controls. Employing the grammars simplify the model formation. This simplification has enabled the development of meta-heuristic optimization procedures such as simulated annealing for the solution of the

PAGE 42

26 problem. Thus, use these controls and the priority rule-based heuristic, a simulated annealing algorithm is developed to solve flex ible job shop scheduling problems. A localization approach and an evolutiona ry approach were pr esented for jointly solving job routing and sequenci ng problems with total or partia l flexibility (Kacem, Hammadi and Borne 2002). The considered objective is to minimize makespan and the total processing time of the machines. The localization approach makes it possible to solve the problem of resource allocation and build an ideal assignm ent model. When each operation is assigned to the suitable machine, this loca lization approach takes into acc ount the workloads of machines on which the operations have already been assigne d. In the evolutionary approach controlled by the assignment model, advanced genetic manipul ations are applied in order to enhance the solution quality. The initial population is construc ted starting from the set of assignments found in the localization approach. This study also e xplains some of the practical and theoretical considerations in the construction of a more robust encodi ng to solve the flexible job shop problem by applying genetic algorith ms. It is worth noting that the scheduling uses different dispatching rules. In general, one of the major drawbacks of a bove methods is that they require substantial computation load and are not suitable for solv ing practical large-scale scheduling problems. 2.8 Workload Control WLC encapsulates the three planning and cont rol levels of order entry, job release and scheduling. Routing and sequencing are usually studied separately. It can result in many problems due to factors such as conflicting obj ectives and an inability to communicate in dynamic situations. To overcome these problems, researchers (Nasr and Elsayed 1990, Huang, Zhang and Smith 1995) stressed the need to in tegrate job routing and scheduling. By taking

PAGE 43

27 into account shop status information, it is possi ble to increase the effectiveness of routing decisions at scheduling level. Weintraub et al. (1999) presented a procedure for scheduling jobs with alternative processes in job shops. The objec tive of this procedure is to minimize manufacturing costs while satisfying job due dates. Process plans with alternatives job routes, operations, and sequences are selected according to current shop conditions. The results show that there are substantial differences in scheduling performa nce between scheduling with alternatives and scheduling without alternatives. Scheduling with a lternatives can greatly improve the ability to satisfy due dates under various shop conditions. An integration model of concurrent planning and scheduling was realized through a multi-agent approach (Wu, Fuh and Nee 2002). It provides a practical approach for software integration in a distributed environment. Many investigations have been done in th e interactions among due date setting, job release and scheduling. Melnyk and Ragatz (1989) used simulation to investigate the impact of due date tightness, release mechanism, and shop dispatching rules on a number of performance measures. Their results show that job releas e mechanisms have a significant impact on performance and the impact is dependent upon the specific mechanism. Wein and Chevalier (1992) defined a broade r scheduling problem that considers three dynamic decisions: assigning due-dates to exogenous ly arriving jobs, releas ing jobs from a job pool to the shop floor, and sequencing jobs at each of two machines in the shop. The job shop is modeled as a multiclass queuing network, a nd the objective is to minimize both shop WIP and job lead times, subject to an upper bound constraint on the propor tion of tardy jobs. Tagawa (1996) proposed a new concept of job shop scheduling system, which consists of the following five decision systems. Orde r entry system has the function of screening arrived orders and setting the due dates of accepted orders. Master scheduling system makes a

PAGE 44

28 broad schedule of design, fabrication, and asse mbly. Once a customer or der is accepted, it is changed into a planned job and is turned over to the master sche duling system. Master schedule consists of detailed design schedule, fabricat ion schedule, and assembly schedule. Firstly, detailed design schedule is made by forward scheduling method. Secondly, assembly schedule is made by backward scheduling method starti ng from job due dates. Lastly, fabrication schedule is made so as to be inserted between assembly schedule and detailed design schedule. Job scheduling system makes a schedule on job basis and work center basis. In the job scheduling system, the master schedule is broken down into a schedule with possible start day and finish day. Operation scheduling system has the function of making a feasible schedule, which is on operation, machine and work day basis. Th e main criterion of this system is to keep the due date given by the job scheduling system The subcriterion is the utilization of the machine. Dispatching system de termines the sequence of operati ons to be done on the specified work day on each machine. In this dispatching system, dispatch is done periodically, such as once half a day, every two days, or others. The cr iteria of the dispatching system are keeping due dates, elevating the utilization of a machine and easiness of the operation. A framework to integrate job release, r outing, and sequencing was proposed (Shafaei and Brunn 2000). This system consists of an inte ger programming model that is concerned with job release and routing decisions and a dispatching rule that pr ovides the detailed scheduling. Two heuristics that integrate job release and scheduling were proposed, which are effective at lowering WIP and satisfying due dates (Zozom 2003). However, a practical problem in MTO companies is that the due date setting for possi ble orders from customer enquiries, job release and scheduling should be coordina ted in real time. A more eff ective method should be explored to meet this need.

PAGE 45

29 2.9 Multi-Agent Systems The technological advances of distributed information syst ems have greatly inspired and supported the development of multi-agent systems in production planning, scheduling and control. Shaw (1988) proposed a multi-ag ent manufacturing scheduling and control mechanism. He pointed out that a manufacturing cell could subc ontract work to other cells through a bidding mechanism. A mu lti-agent virtual manufacturi ng system was implemented in a simulated form using the MetaMorph mediatorcentric federation archit ecture on a distributed computing platform (Maturana and Norrie 1996). It interfaces with the multi-agent concurrent design environment system. Therefore, desi gn, process planning, routing and scheduling activities are coordinated concu rrently across a simulated exte nded enterprise. In MetaMorph, mediator is a distributing deci sion-making support system for c oordinating the activities of a multi-agent system. This coordination involves thr ee main phase: subtasking, creation of virtual communities of agents, and execution of the processes imposed by the tasks. Sikora and Shaw (1997) presented a multi-agent framework for achieving system integration. Within this framework, they develo ped coordination mechanisms for the agents on three levels: the decision leve l, where several functional modul es collaborate on the underlying decision processes; the process level, where agents interact to complete the processes based on their task expertise and mutual interdependence; and, finally, the system level, where different stages coordinate their functioning to achieve desirable system level performance. Sikora and Shaw (1998) also provided a re presentational formalism, coordination mechanisms, and control schemes necessary for integrated different units of an information system while meeting such performance criteria as overall effectiveness, efficiency, responsiveness, and robustness. Saad, Kawamura and Biswas (1997) made use of a cont ract-net approach for heterarchical scheduling of flexible manufacturing sy stems. Their system employed a production reservation (PR)

PAGE 46

30 approach where a job agent schedules all the operations prior to its release to the shop. A problem with the PR approach is that it does not handle the n eed to reschedule jobs when machine breakdowns occur or there is a need to modify a job. To solve the problem, they also proposed a single step production re servation (SSPR) approach that schedules one operation at a time as a job moves through the system. In term s of average tardiness, they found that SSPR outperformed PR. Cavalieri et al. (2000) compared two multi-agent models: a market-like multi-agent architecture and a multi-agent architecture with supervisor. The former model can be referred as representative of pure heterarchical archite cture. The latter, due to the presence of a supervisor agent, is a reference of architect ures with a slight degree of hierarchy. The experiments show that the market-like architect ure results more robust than the architecture with supervisor. In this market-like model, an agent with a high decision-making autonomy represents each manufacturing entity. In partic ular, two main typologies of agents, the part agent and the resource agent, are available. The part agent is the control module of a production batch or a single manufacturing job. It contains all manuf acturing data regarding the job, the main information and the decision-making rules for carrying out nego tiation processes and controlling on-line production. On th e other hand, a resource agent is the logical representation of any of the production resources in a shop floor Like a part agent, a resource agent collects all the information related to the negotiation tasks. The control strategy is carried out through a contract-net protocol. A part agent activates task announcement when triggered events arrive, these events include part arrival, near comp letion of an operation, resource breakdown after commitment, etc. The resource agents that recei ve the announcement construct bids based on their status and system states, and submit bids if they desire. Parts may receive many bids.

PAGE 47

31 They will evaluate the bids and prepare an offe r to the chosen resources When a resource gets an offer, it has the opportunity to accept or deny based on certain circumstances. The negotiation is completed when both part and resource are committed. In the multi-agent architectur e with supervisor, the schedul ing phase is distinguished from the real-time control phase. In first phase, a supervisor agent selects resources according to technological and operational criteria. In real-time contro l phase, it is accomplished by the part agent, since it is the user of the serv ice supplied by all the machines assigned during the scheduling phase. It can solve locally and autonomously unexpected situations due to breakdowns or operation delays. However, if the problem ca nnot be solved locally, the intervention of the supervisor is requested. In the model, the supervisor can modify the assignments built up during the scheduling phase. Ren (2000) presented a multi-agent scheduling architecture. In his architecture, every machine, job and control system has its own scheduling agent to dete rmine local scheduling priorities for jobs. Each agen t is assigned a weight called a cooperation we ight, and the final priority of a job is a weighted sum of these local priorities. The job with the highest final priority is processed first. To show the effectiveness, the architecture is applied to solve three job shop scheduling problems. One is to schedule so as to minimize the mean tardiness of all jobs. The second is to schedule so as to mini mize the mean ET of all jobs. The third is a generalization of the second problem, which repl aces single-point due dates with job due windows. The exhaustive search and simulated ann ealing are used to find the beast cooperation weights. Lu and Yih (2001) proposed a framework that util izes autonomous agent and weighted functions for distributed decisi on-making while all agents work in active and collaborative ways to help their decisions. This collaborative control framework is ca pable of realizing and

PAGE 48

32 seeking balances among heterogeneous obj ectives of the producti on entities within a collaborative manufacturing system. Simple index values, instead of deta iled data, were used for information exchange among agents. This can greatly reduce the communication and computation load of the control system and ke ep detailed production information confidential while the agents in the system coul d belong to different companies. Usher (2003) explored two methods of enha ncing the negotiation process employed by a multi-agent system to support performance improve ments in real-time routing of jobs in a job shop environment. The first method takes ad vantage of an extende d negotiation period to provide a more complete picture of the shop conditions in order to enhance the validity of the decisions made by individual agents. The second a pproach explores the po ssibility of process model data to increase the accuracy of time estimates used in the negotiation process. Maione and Naso (2003) applied geneti c algorithms to adapt the decisions strategies of autonomous agents in a heterarchical manuf acturing system. Yen and Wu (2004) presented a multi-agent scheduling paradigm to transform existing standalone scheduling systems to Internet scheduling agents that can communicate with each ot her and solve problems beyond individual capabilities. Subbu and Sanderson (2004) proposed an evolutionary multi-agent planning framework particularly suited to di stributed design and manufacturing systems. This framework combines a multi-age nt architecture and distributed coevolutionary algorithms.

PAGE 49

33 Chapter 3 Multi-Agent Scheduling Method 3.1 Introduction Flexible job shop scheduling problems are an important extension of the classical job shop scheduling problems and present additional issues. A multi-agent scheduling method with job ET objectives in a flexible job shop environment is discu ssed in this chapter. The ET objectives are consistent with the just-intime production philosophy which has attracted significant attention in both industry and academic community. 3.2 Flexible Job Shop Scheduling In this research, scheduling consists of job routing and sequencing and is a decisionmaking process with the objectiv es of minimizing job ET. Job routing and sequencing is to organize the execution of N jobs on M machines. Each job j consists of nj operations that need to be done in a given order on predetermined work centers. Let Oij denote operation i in job j. The execution of Oij requires one machine selected from a wo rk center that consists of a set of machines MijM. Job routing is to assign each operation Oij to machine k (k Mij). Job sequencing is to determine the starting time sij of Oij on machine k. Defining dj as the due date and Cj as the completion time of job j, job earliness is given by Ej= max(0, dj Cj), (3.1)

PAGE 50

34 and job lateness and tardiness are defined by Lj =Cj dj, (3.2) Tj =max(0, Lj). (3.3) The scheduling objectives are to minimize th e total weighted earliness and tardiness (WET), which is given by n j j j j jT E WET1) ( (3.4) where j is the earliness weight and j is the tardiness weight. When j= j =1 for all j, this reduces to the special case of mi nimizing the total unweighted ET. To minimize the WET, it may be necessary to insert idle times. This means holding a job that may be completed too early. One way to accomplish this is to examine the slack of a job. It is obvious that a job should be held fr om processing if it has a large positive slack, especially when it only has a sing le operation left. However, the d ecision can be quite difficult if a job still has many operations left. Under th ese two situations, jobs are distinguished (Ren 2000) and defined as the following: If a job only has a single operatio n left, it is called a SOLJ (single operation left job); otherwise it is calle d a TOLJ (two or more operations left job). Intuitively, the completion time of a SOLJ can be determined accurately once it starts processing. If the earliest po ssible completion time of any SOLJ is greater than its due date, it is tardy, even if the SOLJ is processed immediatel y when the machine becomes available. In this case, SOLJ j is preferred to start as ea rly as the machine is availa ble. On the other hand, SOLJ j may have a lot of positive slack. This allows the j ob to start at an appropriate starting time such that it can be completed exactly at its due date We define such starting times as preferred starting times. For a job with nj operations, when the job is a SOLJ, (nj-1) operations have been finished and the remaining operation of the SOLJ is the last operation nj, and the starting time

PAGE 51

35 of SOLJ j can be expressed as j njs,. Let j njs,ˆ denote the preferred starting time of SOLJ j, pijk the processing time of Oij on machine k, and ak the available time of machine k. Then j njs,ˆ can be computed by ; ˆ,otherwise p d d p a if a sijk j j ijk k k j nj (3.5) If machine k is idle, ak is the current time t; otherwise it is equal to the completion time cj hC,of operation h of current job jc being processed on k. So ak is given by ; ,,otherwise C idle is k if t acj h k (3.6) Ideally, a SOLJ should be scheduled by making its starting timej njs,equal to j njs,ˆ. Practically, however, tardiness is usually worse th an earliness. This is because tardiness leads to unsatisfied customers, while earliness just means some inventory holding. Therefore, it may be better to set preferred starting times earlier. In particular, we consider reducing the preferred starting times by a threshold value e as given in (3.7). ; ˆ,otherwise e p d d p a if a sijk j j ijk k k j nj (3.7) 3.3 System Framework The proposed multi-agent method consists of job agents (JAs) and machine agents (MAs). Each agent has its goals and includes three components: a knowledge base, a functional component, and a control unit (Sikora and Shaw 1997). The knowledge base consists of the domain knowledge/data. The functional component consists of computational procedures for decision-making. The control unit consists of protocols that pr ovide the mechanism for agents

PAGE 52

36 to communicate with each other. The protocols of all agents together constitute the system coordination approach. 3.4 Job Agent A JA communicates with MAs and makes r outing decision by selecting a machine for each operation. A JA is created whenever a job is released to the shop. When the job finishes its processing, the JA is destroyed. A JA maintains a list of machines for each operation. It also has the following knowledge to formulate a bid in the MA: the number of uncomplet ed operations, the remaining processing time of an operation that is cu rrently processing on the machine, and the uncompleted processing time of a job. The data c ontained in JA knowledge base consists of the job ID, due date, release time, earliness cost, ta rdiness cost and process planning of each job. A process planning contains an operation sequence, the work center and processing time for each operation. The functional component of a JA is for job routing. Job r outing selects a machine for the next operation of a job when the current operation is completed. When a job is a TOLJ, TOLJ routing selects the machine with the earliest completion time. If at least two alternatives are tied for the criterion of the earliest completio n time, the machine with fewer queuing jobs is selected for shop load balancing. However, when a new SOLJ selects a machin e for its next operation, the machine with the smallest total WET of SOLJs from existing j obs in the machine queue and the new SOLJ is selected. If there is a tie, the machine with fewer waiting SOLJs is selected. The motivation is that fewer waiting SOLJs can reduce the overl apping chance between SOLJs, which means the

PAGE 53

37 SOLJs can start most likely at th eir preferred starting times and, t hus, results in a smaller total WET of SOLJs. If there is still a tie, the criteria of TOLJ routing are applied. For each operation of any job, the JA requests bids from the machines that can process the operation. For a TOLJ, a bid includes the co mpletion time of the operation and the queue size on a machine. For a SOLJ, a bid includes the total WET of all SOLJs, SOLJ size, completion time of the operation and queue size on a machine. The JA evaluates all the bids and selects a machine. The JA repeats this proc edure until all the processing is completed. The JA protocol is given as follows. JA protocol 1) Send a bid request to MAs. 2) Evaluate the bids from MAs. 3) Select a machine. 4) If all operations of a job are co mpleted, stop; otherwise go to step 1. 3.5 Machine Agent An MA is responsible for the decisions re lated to job sequencing. Each machine is represented by an MA. An MA has the knowledge of its status (idle or busy), queuing jobs, number of finished tasks and total machine busy time. The da ta contained in MA knowledge base consists of the machine ID, machine type, machine capabilities and co st of each machine. The functional component of an MA is fo r job sequencing. To minimize the WET, job sequencing should try to make SOLJs fini shed on time. When a new job (say job v) is scheduled in a machine queue, there are two possibilities: a SOLJ or a TOLJ.

PAGE 54

38 In the case 1, job v is a TOLJ. In this case, schedule job v, without interrupting the current schedule of the existing jobs, to be completed as early as possible. In the case 2, job v is a SOLJ. First reschedule v and all existing SOLJs. Then insert existing TOLJs one at a time us ing the algorithm for case 1. The insertion order of existing TOLJs can be determined using some dispatching rules. We tested 5 rules: FIFO, SPT, EDD, SLACK and COVERT (Kutanoglu and Sabuncuogl u 1999), and found that COVERT generally gave significant better results. The COVERT prio rity index of a job re presents the expected tardiness cost per unit of imminent processing ti me. If a job has zero or negative slack, it is projected to be tardy and its priority index is 1/pijk. If the slack exceeds the worst case waiting time, the priority index is zero. If the slack is between these two extremes, the priority changes linearly as the slack changes. Two heuristic algorithms are presented to sc hedule jobs: TOLJ insertion algorithm is used for case 1 and SOLJ sequencin g algorithm is proposed for case 2. 3.5.1 TOLJ Insertion Algorithm TOLJ insertion algorithm determines the starting and completion times of the new TOLJ v. It is modified based on the PR approach (Saad, Kawamura and Biswas 1997). In the insertion process of TOLJ v, the current schedule is kept unchanged. There are three possibilities: v is inserted at the head, inside or at the end of the queue to get the earliest completion time. When TOLJ v is inserted at the head, let job j1 as the first job in the queue to be processed. If the starting time 1,j hsof operation h of j1 is equal to or greater than the sum of the available time ak of machine k and the processing time pivk of TOLJ v, v can finish its

PAGE 55

39 processing before j1 starts. Therefore, v should be scheduled at th e head of the queue as depicted in Figure 3.1(a). The completion time Civ is given by Civ = ak + pivk. (3.8) In Figure 3.1(a), as ak is greater than current time t, machine k is busy at time t. When TOLJ v is inserted inside, an MA searches forward through the current schedule to determine the earliest idle time period that the machine can accommodate the processing of TOLJ v. Let Ij as the idle time between job j and the job that follows j in the current schedule. If Ij is equal to or great than pivk, TOLJ v can be inserted into the id le time period as depicted in Figure 3.1(b). Civ is given by Civ = Chj + pivk. (3.9) t v j1 ak Time (a) j v ak = t Ij (b) t jr v ak (c) Figure 3.1. Insert New Job by TOLJ Insertion Algorithm

PAGE 56

40 When TOLJ v is inserted at the end, let job jr be the last job in the queue to be processed. TOLJ v is then scheduled following job jr, as depicted in Figure 3.1(c). Civ is given by Civ = rj hC,+ pivk. (3.10) Let l be the number of existing jobs. The TO LJ insertion algorithm is presented as follows. TOLJ insertion algorithm 1) Set u =1. 2) If 1,j hs ak + pivk, Civ = ak + pivk, stop; otherwise go to step 3. 3) If u = l, Civ = rj hC,+ pivk, stop; otherwise go to step 4. 4) If Ij pivk, go to step 5; otherwise go to step 6. 5) Civ = Chj + pivk, stop. 6) u = u +1, go to step 3. In this algorithm the complexity of steps 1 and 2 is O(1). Steps 3-6 constitute a loop that is repeated at most n times. There are O(1) operations in steps 3-6. The resulting complexity for the loop is O(n). So the complexity of TOLJ insertion algorithm is O(n). 3.5.2 SOLJ Sequencing Algorithm SOLJ sequencing algorithm determines the starting and completion times by rescheduling all jobs including new SOLJ v. It first reschedules all SOLJs including v to minimize the total WET and then inserts the existing TOLJs.

PAGE 57

41 Let l be the number of waiting jobs and be the number of waiting SOLJs. Then there are (l) waiting TOLJs. SOLJ sequencing algorith m calculates the preferred starting time j njs,ˆ of SOLJ v and updates j njs,ˆ for the existing SOLJs by (3.5). If 1, there are at least two SOLJs including v. SOLJ sequencing algorithm reschedules all SOLJs by the MA algorithm (M azzini and Armentano 2001), which consists of the ordering procedure, feasib ility procedure, updating procedure and local search procedure. As the local search procedure has little effect on the solutions, it is not implemented in this research. The ordering, feasibility and updating pr ocedures in a flexible job shop environment are restated briefly as follows. The ordering procedure sequences a ll SOLJs in non-decreasing values of j njs,ˆ. The feasibility procedure then schedules one of the SOLJs at a time by attempting to make their j njs, equal to j njs,ˆ. If there is no overlapping between j and any other job al ready in the partial schedule, the procedure schedules another job. Otherwise, it is necessary to eliminate the overlapping. Let j* be the first job with which j overlaps. The following four possible moves are considered in order to el iminate the overlapping. In the first move, j remains in its current position and j* shifts to the right. The new completion time ,* *j njCof j* is the sum of the completion time j njC, of j and the processing time k j njp, ,* of j*. The WET increase for j* is given by 1=max{*j '*jE, *j '*jT}-max{*j *jE, *j *jT}, (3.11) where'*jE is new weighted earliness, '*jTis new weighted tardiness, *jEis old weighted earliness and *jTis old weighted tardiness.

PAGE 58

42 In the second move, j* remains in its current position and j shifts to the right. The new completion time j njCof job j is the sum of the completion time *, j njCof j* and the processing time k j njp, ,of j. The WET increase for j is computed as 2=max{j' jE, j' jT}-max{jEj, jT j}. (3.12) In the third move, j* shifts to the right and j shifts to the left. It is necessary to determine the appropriate amount of left and right shifts. In order to keep the WET increase to the minimum, one can compute the latest starting time ', j j nsof job j by ', j j ns=max{* * *,j njC, ak, *,j njs-k j njp, ,}, (3.13) where j** is the job before job j* and (* *,j njs-k j njp, ,) is the minimum shift of j to the left to eliminate the overlapping between j* and j. Note that the job is ready to be processed when a job is routed to a machine in a flexible job s hop environment. However, if the machine is busy, the job has to wait. So the ready time of a job in the MA algorithm is replaced by ak in (3.13). The completion times of j and j* in the new partia l schedule are ,j njC= ', j j ns+k j njp, ,. (3.14) ,* *j njC=' j njC+k j njp, ,* *. (3.15) The WET increase for j and j* is given by 3=max{*j '*jE, *j '*jT}-max{*j *jE, *j *jT} +max{j' jE, j' jT}-max{jEj, jT j}. (3.16) In the fourth move, j* shifts to the left and j shifts to the right. This move is similar to Move 3 and the appropriate starting time '* *j j nsfor j* is computed as

PAGE 59

43'* *j j ns=max{* * *, j njC, ak, j njs,-k j njp, ,* *}. (3.17) The new completion times of j and j* are ,* *j njC= '* *j j ns+k j njp, ,* *. (3.18) j njC=' ,* *j njC+k j njp, ,. (3.19) The WET increase 4 is computed by (3.16), using the completion times given by (3.18) and (3.19). Of the above 4 moves, the move with the minimum WET increase (i.e., move argmin{ i | i=1,2,3,4}) is selected to eliminate the ove rlapping. The procedure repeats until all infeasibilities are eliminated. The updating procedure aims to reduce the total WET and consists of two phases: shifting the jobs to the left and shifting the jobs to the right. Once the SOLJs are scheduled, if there are TOLJs (i.e., l > ), TOLJ insertion algorithm inserts one of the TOLJs at a time in the order determined by the CoverT rule. SOLJ sequencing algorithm is formally stated as follows. SOLJ sequencing algorithm 1) Calculate j njs,ˆfor each SOLJ. 2) If =0, go to step 8; otherwise go to step 3. 3) Order SOLJs in nondecreasing values of j njs,ˆ. 4) Set u=1. 5) Insert a SOLJ by f easibility procedure. 6) Update idle times by updating procedure.

PAGE 60

44 7) If u= +1, go to step 8; otherwise u=u +1, go to step 5. 8) Calculate the total WET of SOLJs. 9) If l> go to step 10 ; otherwise stop. 10) Calculate the CoverT priority index for each TOLJ. 11) Sequence existing TOLJs by the CoverT rule. 12) Set u=1. 13) Insert a TOLJ by TO LJ insertion algorithm. 14) If u=l-, stop; otherwise go to step 15. 15) u=u +1, go to step 13. In this sequencing algorithm, the values of j njs,ˆ in step 1 and CoverT priority index in step 10 are computed with complexity O(n). The ordering in step 3 and the sequencing in step 11 are implemented to run in O(n log(n)) time. The complexity of th e loop in steps 5-7 is O(n3). The complexity of the computation in step 8 is O( 1). Steps 13-15 form a l oop that is repeated at most (n-1) times and at each repetition there are O(n) operations in step 13. The complexity of this loop is O(n2). Thus, the complexity of SOLJ sequencing algorithm is O(n3). 3.5.3 Numerical Example This example is provided to demonstrat e SOLJ sequencing algorithm. The current schedule on machine k is shown in Figure 3.2(a). There ar e 2 SOLJs (S1 and S2) and 3 TOLJs (T1, T2 and T3). A new SOLJ v is to be scheduled. The current time t is 52 and the available time ak is 60. The values of pijk, dj, j and j corresponding the ex isting jobs and v are shown in Table 3.1.

PAGE 61

45 t = 52 S1 T1 S2 T2 T3 80 90 95 120 136 148 Time ak=60 (a) v S1 S2 60 80 95 106 120 124 (b) v S1 S2 60 80 106 124 149 (c) v S1 S2 60 80 95 120 138 (d) v S1 S2 60 80 98 123 (e) v S1 S2 60 80 81 106 124 (f) S1 v S2 T2 T1 T3 60 80 98 123 139 149 161 (g) Figure 3.2. Example of SO LJ Sequencing Algorithm By (3.5), v nvs,ˆ =106 and the preferred starting times of S1 and S2 do not changed. Let the SOLJs start at their preferred starting times. The partia l schedule of SO LJs depicted in

PAGE 62

46 Figure 3.2(b) is infeasible. In particularly, SOLJ v overlaps with S2. The four moves 1-4 are depicted in Figure 3.2(c-f) respectively with 1= 116, 2=42, 3=38 and 4=42. Therefore, move 3 is selected because it gives the minimum WET increase. Table 3.1 Numerical Values of Example Job pijk dj j j S1 20 68 2 5 S2 25 120 3 4 T1 10 176 5 2 T2 16 157 2 1 T3 12 198 5 1 v 18 124 1 3 Since there is no idle time in the partial schedule by move 3, the updating procedure does not change it. The total WET of SOLJs is 98 by (3.4). The CoverT ru le gives the order of (T2, T1, and T3) for the TOLJs. TOLJ insertion algorithm inserts one of the three TOLJs at a time in the order and the final schedu le is depicted in Figure 3.2(g). 3.5.4 Machine Agent Protocol An MA receives the bid reque st from a JA. The MA formulates and submits a bid. Once a machine is selected, the job is added to the machine queue. When a machine is idle and there are waiting jobs in the machine queue, the mach ine processes the jobs by the schedule. The MA protocol is described as follows. MA Protocol 1) Receive a bid request from a JA. 2) Formulate a bid. 3) Submit the bid to the JA.

PAGE 63

47 4) Add a job to the machine queue. 5) Process jobs by the schedule. 3.6 System Coordination There is a temporal interdependency among th e activities of JAs and MAs. There is also a sub-goal interdependency. A JA needs to kn ow the completion time of the operation of a TOLJ or the total WET of SOLJs, which can be determined by the MA. Thus, each agent is dependent on the others, resulting in a circular interdependency. The system coordination begins when a jo b is released to the shop. When an MA receives the bid request from a JA, it formulates a bid. Then the JA eval uates all bids from the MAs and selects a machine. Once a machine is selected, the job is moved to the machine. Finally, the machine processes jobs according to the schedule. The coordination activities for a job continue with one operation at a time until th e job is finished. It is assumed that the coordination time can be ignored in comparison with the processing time So a JA initiates coordination for next operation of the job wh en the current operation is completed. 3.7 Experimental Design To test the performance of the proposed multi-agent method, we consider the following flexible job shop. It has five work centers. Each work center ha s two parallel machines with different speeds. Specifically, the processing tim e of a job on one machine is 10% longer than that on the other machine. Different operations of a job are performed in different work centers. The operation sequence for a job is randomly ge nerated among five work centers. However, there are 5 alternative sequences. No job preempti on is allowed. Job reentr ance is not allowed. The total work content rule is used to set job due dates. That is,

PAGE 64

48 dj = rj +c pj, (3.20) where rj is the release time of job j, c is the due date tightness factor and pj is the total processing time of job j. The shop load is determined by a jo b arrival rate. The job arrivals are generated using an expone ntial distribution for interarrival times. The average interarrival time R can be expressed as ) /( M pn R (3.21) where p is the average processing time for each operation, n the average number of operations and the shop utilization. The simulation parameters are shown in Table 3.2. Table 3.2 Simulation Parameters Parameter Values 80%, 85%, 90%, 95% c 2, 4, 6, 8, 10, 12 pijk uniform(1, 30) j uniform(1, 5) j uniform(1, 5) nj 3, 4, 5, uniform(3, 5) Each simulation experiment consists of twen ty replications. As mentioned earlier, job tardiness is generally worse than job earliness. Ther efore, it may be better to start jobs before their preferred starting times by some threshol d. In our experiments, we considered two threshold values ( e =0 and e =2 p ). In each replication, the shop is continuously loaded with jobs numbered on their arrivals. The simulation continues until 2200 j obs are completed per run. We are interested in system behavi or in steady state. To eliminat e the system warm-up effect, the first 200 completed jobs are not recorded. Pleas e note that when each simulation terminates, there are still jobs in the system.

PAGE 65

49 The entire system is implemented using an object-oriented progr amming approach and C++, which is run on a 1.6GHz PC with 512MB RAM. The PR and SSPR approaches are also implemented as a benchmark for comparing the relative performances of the proposed multiagent approach. These two approaches are better than a number of co mmon dispatching rules and well-known existing multi-agent methods to route jobs dynamically. 3.8 Analysis of Computational Results This section reports the results of computa tional experiments. We analyze these results in detail and provide our findings. In addition to the WET performance, we also report the weighted tardiness (WT) performance to show the robustness of our proposed method, since WT has been used as a primary performance me asure against job due da tes in literature. 3.8.1 WET under Different Utilizations When each job has 5 operations, Table 3.3 pr esents the means and standard deviations (s.d.) of the WETs. When the utilization leve l is 90%, Figure 3.3 gives the average WETs under different scheduling methods. From Table 3.3 and Figure 3.3, the proposed multi-agent method significantly outperforms PR and SSPR for all utilization levels and due date settings. Under the proposed scheduling method, as the due date tightness factor increases, the average WET decreases. This trend also maintain s as the shop utilization level decreases. This should be expected as in low utilization shops and with loose due date settings, one can get better schedules to complete jobs closer to thei r due dates. As a matter of fact, for large due date setting factors and low shop utilization levels (80% and 85%), the proposed multi-agent method found schedules in which jo bs are completed very close to their due dates. At high shop

PAGE 66

50 utilization levels (90% and 95%), the propos ed multi-agent method performs very well by using a threshold value e= 2 p However, at 80% and 85% shop utilization levels, the method performs better when e =0 unless for very tight due date settings. Table 3.3 WET Performance under Different Shop Utilizations Agent ( e =0) Agent1 ( e =2 p ) SSPR PR c mean s. d. mean s. d.mean s. d. mean s. d. = 95% 2 1958.76 564.15 1920.74550.822237.29604.87 3207.28867.67 4 1590.75 519.39 1462.09516.181813.09588.84 2764.53863.77 6 1257.24 398.73 1030.06435.331444.20547.13 2353.98837.15 8 1010.04 366.26 653.56426.561164.32466.39 2000.70780.61 10 792.07 320.28 474.30365.241013.47319.53 1722.19693.61 12 641.82 257.22 291.88293.32992.14190.20 1533.58568.50 = 90% 2 777.54 246.10 749.58239.92849.18262.94 1508.90489.84 4 516.21 202.38 377.49189.76532.58206.18 1096.35470.49 6 365.29 159.91 190.56116.29492.1078.68 816.91378.45 8 260.17 170.25 105.9772.85688.77135.64 733.25209.96 10 125.62 71.64 53.5723.631029.36213.58 831.2493.50 12 55.74 47.79 33.235.281434.71252.14 1062.66198.81 = 85% 2 330.14 60.27 291.9669.67332.5982.40 639.92125.99 4 165.55 62.44 98.3934.68320.9433.24 403.7094.06 6 83.25 53.59 49.7313.69637.8966.67 508.2255.52 8 50.03 61.60 38.594.531057.2488.09 815.0473.17 10 15.67 14.18 37.403.261499.0597.88 1207.63102.60 12 6.51 1.06 36.922.121946.45103.31 1634.61121.66 = 80% 2 183.97 43.24 159.9433.53184.8335.51 343.1151.10 4 61.21 26.81 54.989.48381.8725.63 312.7422.24 6 17.69 11.85 43.471.83796.9047.10 627.1637.44 8 7.41 5.43 42.552.231241.2654.67 1044.1154.59 10 4.87 1.12 43.001.841689.6659.58 1484.7363.64 12 4.56 0.48 43.022.212138.9063.76 1931.6269.15 As for SSPR and PR, SSPR outperforms PR fo r tight due date settings and high shop utilization levels, and underperfo rms PR for other due date settings and shop utilization levels.

PAGE 67

51 WET Note that the performan ce pattern of these methods in terms of standard deviation is similar to the performances of these methods with respect to the mean WET. Figure 3.3. Average WET under Different Scheduling Methods 3.8.2 WT under Different Utilizations When each job has 5 operations, the simulation results of the WTs are presented in Table 3.4. When the utilization level is 90%, Fi gure 3.4 gives the average WTs under different scheduling methods. From Table 3. 4 and Figure 3.4, one can see that as the due date tightness factor increases or shop utiliza tion level decreases, the average WT decreases. This trend holds for all the implemented methods. For all utilization levels and due date settings, the proposed multi-agent method performs better by usin g a threshold value e= 2 p than when e= 0. In addition, the proposed multi-agent method significantly outperforms PR except for 80% utilization and due date setting c= 2, and mostly outperforms SSPR except for loose due date settings and low shop utilization levels. 0 200 400 600 800 1000 1200 1400 1600 2 4 6 8 10 12 A gent A gent1 SSPR PR Tightness factor

PAGE 68

52 Table 3.4 WT Performance under Different Shop Utilizations Agent ( e =0) Agent1 ( e =2 p ) SSPR PR c mean s. d. mean s. d. mean s. d. mean s. d. = 95% 2 1958.76 564.15 1920.63550.892237.12605.033207.27867.67 4 1590.73 519.40 1460.39517.321800.36597.452761.33866.42 6 1257.17 398.77 1026.17437.751391.22574.222331.39853.52 8 1009.81 366.42 646.81430.201026.53526.801929.94824.33 10 791.70 320.50 465.67369.82726.30440.081565.80777.43 12 641.19 257.51 282.06298.92491.09334.021246.93709.56 = 90% 2 777.53 246.10 748.63240.36846.84263.971508.56490.09 4 516.13 202.41 368.36194.05464.12234.371077.98480.68 6 365.02 159.96 174.63121.92219.11154.05713.53432.98 8 259.65 170.35 85.7077.3792.5676.74446.75342.77 10 124.81 71.89 30.5228.3338.3234.47270.55242.68 12 54.51 48.27 7.517.5316.5915.44161.28161.12 = 85% 2 330.12 60.27 284.8971.36317.4085.13636.44126.66 4 165.30 62.47 73.8338.1587.0350.45293.96109.77 6 82.65 53.63 18.9215.8720.5017.71121.4576.42 8 48.99 61.77 6.526.175.375.6749.9946.26 10 14.35 14.38 3.563.551.481.7821.4126.09 12 4.96 1.30 1.700.260.490.6510.1314.43 = 80% 2 183.92 43.26 144.8035.98146.9941.41330.3452.86 4 60.78 26.81 18.3111.1020.5714.2190.4033.55 6 16.87 11.89 3.332.123.183.0422.6814.41 8 6.31 5.49 1.710.620.570.726.325.29 10 3.51 1.29 1.430.230.060.081.911.75 12 2.99 0.25 1.580.200.010.020.670.65 3.8.3 WET under Different Numbers of Operations When jobs have different numbers of opera tions, Table 3.5 shows the WETs with 90% shop utilization. In Table 3.5, there are 4 scenarios. When nj = 5, 4, or 3, all jobs have the same number of operations. For the 4th scenario each job can have 3-5 operations (i.e., nj ~ uniform(3,5)).

PAGE 69

53 Figure 3.4. Average WT under Different Scheduling Methods When the multi-agent method is applied and e= 0, Figure 3.5 gives the average WET under different numbers of operations. For job j with nj operations, TOLJ j has no more than ( nj-1) operations remaining and SOLJ j has only one operation to be finished. When the number of operations of a job is decreased from 5 to 3, the operation number ratio of SOLJ/TOLJ is increased on the average and there should be increasing overlapping conflicts and hence decreasing possibilities to sche dule SOLJs at their preferred starting times. However, from Table 3.5 and Figure 3.5, the WET performance by the proposed method changes slightly as the number of operations changes. This observation also holds when jobs have various numbers of operations from the uniform distribution in the range 3-5. 0 200 400 600 800 1000 1200 1400 1600 2 4 6 8 10 12 A gent A gent1 SSPR PR WT Tightness factor

PAGE 70

54 Table 3.5 WET Performance under Di fferent Numbers of Operations Agent ( e =0) Agent1( e =2 p ) SSPR PR c mean s. d. means. d.means. d. mean s. d. nj = 5 2 777.54 246.10 749.58239.92849.18262.94 1508.90489.84 4 516.21 202.38 377.49189.76532.58206.18 1096.35470.49 6 365.29 159.91 190.56116.29492.1078.68 816.91378.45 8 260.17 170.25 105.9772.85688.77135.64 733.25209.96 10 125.62 71.64 53.5723.631029.36213.58 831.2493.50 12 55.74 47.79 33.235.281434.71252.14 1062.66198.81 nj = 4 2 677.84 359.28 658.64375.96843.70496.50 1123.83545.80 4 485.29 337.42 371.03300.69589.98406.79 817.83489.61 6 360.74 297.81 219.08246.16522.16256.55 645.06357.43 8 229.51 247.71 121.21160.41616.23167.28 628.51210.94 10 143.30 182.47 71.55100.17818.32221.18 737.39168.49 12 90.18 135.09 47.2956.421084.85308.23 937.10247.61 nj = 3 2 698.93 183.51 644.06190.89927.42307.63 1075.95343.18 4 572.42 178.07 441.98186.55696.48287.81 832.78330.75 6 475.44 166.67 312.29150.86554.21224.03 659.28284.17 8 376.13 158.26 209.09121.36516.66131.88 580.55200.61 10 292.11 127.66 137.0693.51574.1467.04 594.02107.62 12 229.45 126.28 91.2973.57703.0696.82 683.4564.77 nj = uniform(3,5) 2 725.08 210.96 681.13212.08866.89296.03 1100.28308.38 4 507.16 181.32 379.86166.43586.58224.80 783.09268.51 6 360.18 154.66 204.56111.06478.5391.75 591.16161.70 8 253.38 125.76 99.3950.05543.62106.56 558.6965.15 10 172.79 102.18 53.8220.93742.82184.85 668.80126.08 12 106.52 64.35 33.806.941022.35230.24 885.91193.09 3.8.4 WET under Different Processing Time Distri butions This Section reports the computational re sults when job processing times follow a different distribution. In par ticular, we consider uniform, ex ponential and normal distributions. These computational experiments may reveal the impact of pro cessing time distribution on the ET performance for the proposed method, Ta ble 3.6 shows the WETs with 90% shop utilization.

PAGE 71

55 WET Figure 3.5. Average WET under Diffe rent Numbers of Operations When processing time distribution follows an exponential distribution, we truncate the random number to be a value between 1 and 45. This truncation will assure that the mean operation processing time is roughly 15, the sa me as the uniform distribution U (1, 30). Similarly, we truncate the random number from a normal distribut ion N (15, 75). Again, this truncation guarantees that the processing time is at least 1 and the mean is about 15. From Table 3.6, the proposed multi-agent method significantly outperforms PR and SSPR for all due date settings. When the multi-agent method is applied and e= 0, Figure 3.6 gives the average WETs under different proc essing time distributions Under the proposed scheduling method, as the due date tightness f actor increases, the average WET decreases. When the processing time distributions are expon ential and due date setti ng factors are large (6, 8, 10 and 12), the proposed multi-agent method found schedules in which jobs are completed very close to their due dates. In addition, fo r uniform distribution and normal distribution, the proposed multi-agent method performs very well by using a threshold value e= 2 p However, 0 100 200 300 400 500 600 700 800 900 2 4 6 8 10 12 nj = 5 nj = 4 nj = 3 nj = uniform(3,5) Tightness factor

PAGE 72

56 for exponential distribution, the pr oposed method performs better when e =0 unless for extremely tight due date settings. Table 3.6 WET Performance under Differe nt Processing Time Distributions Agent ( e =0) Agent1( e =2 p ) SSPR PR c mean s. d. means. d.means. d. mean s. d. pijk = uniform(1,30) 2 777.54 246.10 749.58239.92849.18262.94 1508.90489.84 4 516.21 202.38 377.49189.76532.58206.18 1096.35470.49 6 365.29 159.91 190.56116.29492.1078.68 816.91378.45 8 260.17 170.25 105.9772.85688.77135.64 733.25209.96 10 125.62 71.64 53.5723.631029.36213.58 831.2493.50 12 55.74 47.79 33.235.281434.71252.14 1062.66198.81 pijk = exponential(15) 2 244.14 51.85 139.6624.76175.6333.08 301.0738.05 4 92.46 30.70 59.299.38326.5516.14 286.8714.72 6 35.25 18.65 48.952.80659.6636.58 544.5322.08 8 16.89 9.82 47.172.311026.7246.23 884.4437.57 10 10.33 7.04 46.941.301400.6952.52 1247.9146.72 12 6.83 3.93 47.132.681776.9257.28 1616.3053.24 pijk = normal(15,75) 2 507.77 193.31 479.53194.70537.18216.51 985.97329.34 4 283.27 152.43 186.87124.02350.56122.63 642.47260.09 6 176.38 107.57 83.7473.19509.3892.08 531.28131.89 8 102.76 93.40 47.6336.65846.45138.39 651.38106.07 10 66.11 71.59 36.5812.691248.96172.32 925.60178.34 12 41.69 48.40 33.655.231672.71190.23 1281.97234.07 3.8.5 WET under Different Mean Processing Times When the multi-agent method is used and the mean of the processing time is increased from 15 to 35, Table 3.7 shows the average WE Ts. For the exponential distribution, processing times are truncated with a mean of 35, a maximu m of 65, and a minimum of 20. This truncation assures that the average operation processing time generated is about 35. For the uniform distribution and normal distributio n, processing times are truncated with a mean of 35, a maximum of 50, and a minimum of 20.

PAGE 73

57 WET 0 100 200 300 400 500 600 700 800 90024681012 uniform[1,30] exponential[15] normal[15,75] Figure 3.6. Average WET under Differe nt Processing Time Distributions For every processing time distribution, the average WETs almost increase when the mean of the processing time increases. However, when the mean of the processing time is 15, exponential distribution produces th e best results. When the mean of the processing time is 35, uniform distribution produces the best results. Table 3.7 WET Performance under Di fferent Mean Processing Times Multi-agent c 2 4 6 8 10 12 Uniform(1,30) 777.54516.21365.29260.17125.62 55.74 Uniform(20,50) 625.72525.66409.46229.04168.27 111.15 Exponential(15) 244.1492.4635.2516.8910.33 6.83 Exponential(35) 1307.44837.25627.13447.42342.54 261.37 Normal(15,75) 507.77283.27176.38102.7666.11 41.69 Normal(35,75) 918.82716.44686.60454.66237.77 190.99 Tightness factor

PAGE 74

583.8.6 Simulation Time under Different Utilizations Table 3.8 presents the simulation times to find a complete schedule with over 2000 jobs on 10 machines when each job has 5 operations. When the utilization level is 90%, Figure 3.7 gives the simulation times under different scheduling methods. Table 3.8 Simulation Time under Different Shop Utilizations (seconds) Agent ( e =0) Agent1 ( e =2 p ) SSPR PR c mean s. d. max means. d. max means. d.max mean s. d.max = 95% 2 22.73 5.85 34.4422.415.7733.450.960.021.00 0.93 0.010.94 4 27.00 7.74 42.5924.056.6037.560.980.041.09 0.93 0.010.94 6 35.43 9.49 55.2627.507.4843.470.970.051.09 0.92 0.020.94 8 46.40 14.08 76.3832.609.6453.841.010.111.34 0.93 0.020.97 10 52.41 16.34 87.5335.479.8155.500.990.041.09 0.93 0.010.94 12 63.21 15.36 94.7840.5511.2963.390.970.031.03 0.94 0.020.97 = 90% 2 10.90 2.69 17.6410.502.2215.270.960.031.03 0.93 0.010.94 4 15.02 4.35 27.1611.512.5817.040.960.010.97 0.93 0.010.94 6 21.78 6.73 38.3913.772.8420.930.970.031.06 0.92 0.020.95 8 28.79 11.79 62.3917.503.2426.341.010.051.12 0.92 0.020.94 10 33.45 10.68 62.5322.073.8532.900.990.041.06 0.93 0.010.94 12 40.73 10.48 67.7624.355.1338.480.960.010.97 0.93 0.010.94 = 85% 2 6.13 0.64 7.635.860.867.690.960.021.00 0.93 0.010.94 4 9.38 1.10 12.237.160.588.470.970.021.00 0.93 0.010.94 6 13.53 2.21 19.6110.020.6310.941.000.041.06 0.94 0.020.96 8 18.22 3.83 29.1313.450.8814.850.970.021.00 0.93 0.010.95 10 22.50 3.03 30.2216.611.1819.070.960.021.00 0.93 0.010.94 12 27.21 4.33 38.5620.371.4222.931.060.091.29 0.91 0.020.93 = 80% 2 4.83 0.82 7.054.660.926.941.070.081.22 0.93 0.010.94 4 7.56 0.63 8.925.660.236.050.960.031.03 0.93 0.010.94 6 10.68 0.50 11.808.030.288.600.960.021.00 0.94 0.020.96 8 13.94 1.00 15.7710.640.4311.610.980.091.25 0.93 0.010.94 10 17.33 1.09 19.0812.980.4413.910.950.010.97 0.94 0.030.98 12 21.15 1.06 22.9515.440.6816.600.960.021.00 0.93 0.010.95

PAGE 75

59 Seconds Figure 3.7. Simulation Times unde r Different Scheduling Methods From Table 3.8, as the due date tightness factor increases or shop utilization level increases, the simulation time of the proposed method increases. For loose due date settings under all shop utiliz ation levels, the proposed method is faster when e= 2 p than e= 0. The largest computer time for all simulation instan ces is 94.78 seconds. This indicates that the proposed method is computati onally efficient from the pr actical point of view. One can also see that both PR and SSPR can find schedules for our simulation settings within about 2 seconds. In ge neral, 5 minutes would be a reasonable threshold value for industrial scheduling practice, a nd thus the propose method can be implemented in real time. 3.9 Summary A flexible job shop with five work centers is considered to test the proposed method against the existing methods in literature. The computational e xperiments show that the new 0 5 10 15 20 25 30 35 40 45 2 4 6 8 10 12 A gent A gent1 SSPR PR Tightness factor

PAGE 76

60 method significantly outperforms the existing me thods for WET performance, and the proposed method is insensitive to the number of operations. In general, the new method also outperforms the implemented methods in terms of WT which has been the primary performance measure ag ainst job due dates. This indicates that the proposed method is robust. In addition, the propos ed method is very efficient computationally. In particular, it takes less than 1.5 minutes of simulation time on a 1.6GHz PC to find a complete schedule with over 2000 jobs on 10 mach ines. Such computational efficiency makes the proposed method applicable in real time. The computational experiments indicate that the due date tightness factor significantly affects the performance of the proposed method for all considered shop load levels. Quick response to customers requires small due date tightness factors. But this can lead to unsatisfactory large tardiness. On the other ha nd, most jobs can be completed on time with large due date tightness factors. Thus, to set a proper due date tightness factor is a challenging research issue.

PAGE 77

61 Chapter 4 Dynamic Due Date Setting 4.1 Introduction A multi-agent job routing and sequencing me thod with ET objectives is discussed in Chapter 3. The method significantly outperf orms the existing job routing and sequencing methods. However, the ET performance under high s hop utilizations is st ill not desired and a lot of jobs will be tardy. The reason is that th e poor ET performance is not necessary due to bad scheduling. The origin may be wrong commitmen ts of due dates. This chapter discusses dynamic due date setting to address this issue. 4.2 Order Entry in Make -To-Order Companies In MTO companies, the arrival of customer enquiries cannot be pr edicted in advance. Whether an enquiry turns into an order de pends upon the bid the company gives and how it compares with bids from competitors. Each enquiry from a customer tends to be unique. An enquiry may come with a desired delivery date a nd merely ask for a price. In this case, MTO companies should check whether the possible orde r from the enquiry can be manufactured to meet the given due date. If an enquiry request s both a delivery date and a price to be quoted, MTO companies should determine what alternative due dates are feasible and what extra costs in providing extra capacity will be incurred for shorter due dates. It is preferable to select one which best meets the company objectives. This research does not consider price quotation and

PAGE 78

62 just focuses on due date setting. Th e due date of the corresponding job j for a possible order can be determined by dj rj +lj, (4.1) where rj is the time when job j is received and lj its estimated lead time. 4.3 DTWK and DPPW Rules The TWK and PPW rules are commonly us ed to set due dates and expressed respectively as dj = rj +TWKc pj, (4.2) dj = rj + pj + PPWc nj, (4.3) where pj is the total processing time of job j, nj the number of operations TWKc the due date tightness factor for TWK, and PPWc the due date tightness factor for PPW. The due dates may be tight or loose, depending on the value of the parameters TWKc and PPWc set to be small or large. To eliminate the effect of the due date tig htness factor, a dynamic forecasting model to establish IDDs and XDDs is proposed (Bertran d 1983 and Enns 1995). The authors assume that the operation processing times at all machines follow the same distribution and all machines are utilized at the same level. Such a job shop is generall y referred to as a un iform shop. Then the average workload W in the shop can be computed by W = M r, (4.4) where r is the average total remaining processing time per job in the shop, M the number of machines in the shop, and the average number of jobs at each machine. According to Little’s law,

PAGE 79

63 = f, (4.5) where f is the average flowtim e at each machine and is the arrival rate of jobs at each machine. The steady-state utilization of each machine can be expressed as = p, (4.6) where p is the expected processing time per operation. Combining (4.4), (4.5) and (4.6) yields W =p Mrf / (4.7) A dynamic version of (4.7) can be expressed as Wt =p f Mrt t/ (4.8) If no assembly operations are involved, tr can be expressed as /t t tN W r (4.9) where Nt is the number of uncompleted jobs in the shop at time t Combining (4.8) and (4.9) yields ). /( M p N ft t (4.10) Thus the waiting time wj per operation of job j can be estimated as follows. wj = ft p (4.11) Now, the flowtime of job j can be estimated as nj ft = nj) /( M p Nt= ) /( M N pt j. Setting the flowtime as the estimated lead time for job j leads to the DTWK rule. dj = rj + pj ) /( M Nt. (4.12) Similarly, we can set the DPPW rule as follows. dj = rj + pj + nj p M Nt) 1 ) /( ( (4.13) Both (4.12) and (4.13) are IDD. The corresponding XDD is obtained by adding a delivery safety allowance.

PAGE 80

64 As pointed out by Enns (1995) when the shop is lightly loaded under DPPW, it is possible that 1 ) /( M Nt. This means that the flow allowance of a job may be less than its total processing time, which is clearly unreasona ble. Therefore, a modified DPPW rule is proposed as follows. dj = rj + pj + nj p M Nt} 1 ) /( 0 max{ (4.14) On the other hand, the DTWK and DPPW rules can produce a constant average lateness of jobs (Bertrand 1983). To reduce the consta nt average lateness, a new due date setting method based on a dynamic feedback mechanism is proposed. It consists of order entry agent (OEA), job routing and sequencing agent (RSA), and information feedback agent (IFA). 4.4 Order Entry Agent The OEA is responsible for customer enquir ies and due date settings for the possible orders. The OEA has the information such as order number and order specification. The OEA determines job due date by (4.1). The estimated flowtime defined in (4.12) is a good starting point for estimating the lead time of a job. As mentioned earlier, due dates set by (4.12) may be systematically leading to a c onstant lateness. If the constant lateness is positive, such due dates are set generally too tight. On the other hand, if the constant lateness is negative, such due dates are loose. This motivat es to modify (4.12) by introducing a feedback. Consequently a dynamic feedback TWK (DFT WK) rule is obtained as follows. dj = rj + pj ) /( M Nt+ jL (4.15) where jL is the average lateness of recently completed jobs at the time when job j is received. jL can be considered as the system feedback in the following sense. If jL< 0 jL (> 0), jobs recently completed are early (tardy), which i ndicates due dates are loos e (tight). Therefore,

PAGE 81

65 it is reasonable to adjust due date setting according to (4.15). In addition, DFTWK dose not explicitly include th e job pool time, and jL should be considered to re flect the estimate of the job pool time. For DPPW, we si milarly propose a dynamic fee dback PPW (DFPPW) rule to assign due dates as follows. dj = rj + pj + nj p M Nt} 1 ) /( 0 max{ + jL. (4.16) The due dates set by (4.15) or (4.16) ar e job IDDs and job XDDs are obtained by adding some delivery safety allowance. While the original rules (4.2) and (4.3) are parametric, the new rules (4.15) and (4.16) are nonparametric. This is pretty signifi cant in the sense that there is no need to determine a parameter and, therefore, they are easy to be implemented in practice. An OEA communicates with the RSA and IFA. In particular, when an MTO company receives an enquiry, the OEA re quests current shop status and jL from the RSA and IFA, respectively. It then determines the job due da te and releases the job. The OEA protocol is given as follows. OEA protocol 1) Send the RSA a request to get current shop status. 2) Receive the shop status from the RSA. 3) Send the IFA a request to get jL 4) Receive jL from the IFA. 5) Set the job due date. 6) Release the job.

PAGE 82

664.5 Job Routing and Sequencing Agent The function of job routing and sequencing ag ent (RSA) is to rout e and sequence jobs. It has current shop status information such as number of jobs in the pool and on the shop floor, shop utilization, and the total remaining pro cessing time of all jobs at each machine. The RSA consists of two subagents: job agen ts (JAs) and machine agents (MAs), which have been discussed in Chapter 3. The RSA protocol is given as follows. RSA protocol 1) Receive the request of current shop status from the OEA. 2) Send the shop status to the OEA. 3) Receive a job from the OEA. 4) Select a machine for an operation by the JA. 5) Sequence jobs by the MA. 6) Process an operation by the MA. 7) If a job is not completed, go to step 4. 4.6 Information Feedback Agent The Information Feedback Agent (IFA) provi des a mechanism to estimate the average lateness jL used in (4.15) and (4.16). It maintains the information of recently completed jobs. In this research, jL is determined based on the K most recently completed jobs. In particular, a simple moving averag e is used as the estimate of jL That is, /1K L LK i i j (4.17)

PAGE 83

67 The motivation of using the job feedback information is that the average lateness from recently completed jobs reasonably predicts the ti ghtness of job due date setting. The remaining question is to determine what K value to use. Observe that so me time elapses between a job’s arrival and its completion. During this elapsed ti me, some new jobs may arrive. We define the number of new jobs arrived between the arrival and completion of a job as its lag. Evidently, any job may have an impact on other jobs only when it is in the system. Therefore, it is reasonable to set K to be the average lag of all jobs. This can be computed fr om historical data. Once K is determined over a reasonable period of time, it remains stable unless job lags change dramatically. When the IFA receives a request from th e OEA, the IFA determines the average lateness of recently completed jobs and sends it to the OEA. The IFA protocol is given as follows. IFA protocol 1) Receive a request form the OEA. 2) Determine the average lateness. 3) Send the average lateness to the OEA. 4.7 System Coordination When a WTO company receives an enquiry for a possible order, the OEA determines the IDD and XDD of the corresponding job of the order, which uses the information from the RSA and IFA. For each operation of any job, a JA requests bids from the machines that can process the operation. When an MA receives the bi d request from a JA, it formulates a bid. The JA evaluates all bids from the MAs and selects a machine. Once a machine is selected, the job

PAGE 84

68 is moved to the machine. The machine then se quences and processes th e jobs. The coordination activities for a job continue with one opera tion at a time until the job is finished. 4.8 Analysis of Simulation Study This section reports the results of computational experiments. 4.8.1 Comparisons among TWK, DTWK and DPPW The experimental design is considered as th e same as in Chapter 3. Each job has 5 operations. Processing times are sampled from a uniform distribu tion in the range 1-30. When IDDs are determined by (4.12) and (4.14), the m eans and standard deviations of the WETs are given in Table 4.1. Table 4.1 WET Performance under DTWK and DPPW Multi-agent SSPR PR mean s. d.means. d. means. d. = 95% DTWK 107.94 26.95481.96131.29809.13210.77 DPPW 48.68 17.11211.5035.81554.32133.85 = 90% DTWK 38.24 7.19257.7059.94454.78116.14 DPPW 20.59 3.67163.9327.49333.5867.70 = 85% DTWK 15.11 4.53164.4723.25278.6038.86 DPPW 8.32 1.86127.6415.78227.7329.27 = 80% DTWK 11.86 3.29129.5013.75207.9019.79 DPPW 7.30 0.77111.6610.93180.4316.57 From Figure 4.1 and Figure 4.2, the multi-agent method is the best for the WET performance. SSPR significantly outperform s PR under various u tilization levels.

PAGE 85

69 From Table 3.3, when due dates are determined by TWK, The computational experiments indicate that the du e date tightness factor significan tly affects the performances of the multi-agent method, PR and SSPR for all utilizat ion levels. From Table 4.1, when due dates are determined by DTWK and DPPW, they do not select the due da te tightness factor. Furthermore, DTWK and DPPW significantly outperform TWK for all considered situations under PR and SSPR. When the multi-agent met hod is used, DTWK and DPPW outperform TWK except for TWK under loose due date settings and low utilization levels. 0 100 200 300 400 500 600 700 800 900 85%87%89%91%93%95% Utilization WET Agent SSPR PR Figure 4.1. Average WET Using DTWK One can see that DPPW significantly outperf orms DTWK for WET performance. When the utilization level is 95%, Figure 4.3 gives the aver age WETs under DPPW and DTWK. If the multi-agent method is applied, the averag e WET by DPPW is only 45.1% of that by DTWK. Similarly, under SSPR and PR, the average WETs by DPPW are only 43.9% and 68.5% of those of by DTWK, respectively. This tr end can also be observed when the utilization levels are 90%, 85%, and 80%.

PAGE 86

70 0 100 200 300 400 500 600 85%87%89%91%93%95% Utilization WET Agent SSPR PR Figure 4.2. Average WET Using DPPW Agent SSPR PR 0 100 200 300 400 500 600 700 800 900 123 Scheduling Methods WET DTWK DPPW Figure 4.3. Average WET under 95% Utilization When jobs have different processing time distributions, Table 4.2 shows the WETs with 90% shop utilization. In Table 4.2, there are 3 scenarios. First, processing times are sampled from a uniform distribution in the range 1-30. Second, processing times are randomly generated from a truncated exponential dist ribution with a mean of 15, a maximum of 45, and a minimum of 1. This truncation assures that the average operation processing time generated is about 15.

PAGE 87

71 Third, processing times are sampled from a trun cated normal distribution with a mean of 15, a variance of 75, a maximum of 30, and a minimum of 1. From Table 4.2, one can also observe that DPPW significantly outperforms DTWK for WET performance for all different processing time distributions and scheduling methods tested. Table 4.2 WET Performance under Differe nt Processing Time Distributions Multi-agent SSPR PR mean s. d.means. d. means. d. pijk = uniform(1,30) DTWK 38.24 7.19257.7059.94454.78116.14 DPPW 20.59 3.67163.9327.49333.5867.70 pijk = exponential(15) DTWK 74.68 6.54186.0519.48292.5127.08 DPPW 26.26 9.69121.569.13208.8015.10 pijk = normal(15,75) DTWK 44.11 6.44130.6417.17221.4028.84 DPPW 22.38 4.98100.689.39184.0416.57 When processing time distributions are uniform, the proposed multi-agent method produces the best results. Mean while, normal distribution is bette r than exponentia l distribution for proposed multi-agent method. For PR and SSPR, normal distribution is the be st. Exponential distribution is better than uniform distribution. 4.8.2 Comparisons among Four Rules This section presents the effectiveness of the proposed DFTWK and DFPPW versus DTWK and DPPW. When processing times ar e randomly generated from a truncated exponential distribution with a m ean of 15, a maximum of 45, and a minimum of 1, Table 4.3 shows the average WETs with 90% shop utilization.

PAGE 88

72 Table 4.3 WET Performance under Different Scheduling Methods Methods DTWK DFTW K DPPWDFPPW Multi-agent 74.68 48.48 26.2617.78 SSPR 105.84 99.8282.7586.01 PR 162.98 156.38136.31139.73 From Table 4.3, when the proposed multi-ag ent scheduling method is applied, DFPPW and DFTWK significantly outperform DPPW and DTWK, respectively. However, for PR and SSPR, there is no significant difference betw een DTWK and DFTWK, DPPW and DFPPW. For the proposed scheduling method, the average WETs are given in Table 4.4 under different shop utilizations. From Table 4.4, it can be seen that under all shop utilizations, DFPPW and DFTWK significantly outperform DPPW and DTWK, respectively. This means introducing the job completion feedback jL into due date setting works extremely well. Of the 4 due date setting rules cons idered, DFPPW is the best for WET performance. It is worth noting that DPPW significantly outperforms DTWK for WET performance under all 4 utilization levels tested. Table 4.4 WET Performance under Different Shop Utilizations DTWK DFTW K DPP W DFPPW 95% 83.79 52.4031.6720.18 90% 74.68 48.48 26.2617.78 85% 61.52 39.5825.6216.56 80% 53.59 34.9921.9015.12 When jobs have different processing time distributions, Table 4.5 shows the WETs with 90% shop utilization. Under different processi ng time distributions, D FPPW and DFTWK also significantly outperf orm DPPW and DTWK, respectively. When the processing time distributions are uniform, the proposed multi-agent method produces the best WET performance. Normal distribution is be tter than exponential

PAGE 89

73 distribution. In addition, DFPPW produces th e least average WET for all processing time distributions and due date setting rules. Table 4.5 WET Performance under Differe nt Processing Time Distributions pijk DTWKDFTW K DPPW DFPPW Uniform(1,30) 38.2426.6520.5914.70 Exponential(15) 74.6848.48 26.2617.78 Normal(15,75) 44.1130.6122.3815.39 When the mean of the processing time is incr eased from 15 to 35, Table 4.6 shows the average WETs. For the exponential distribution, processing times ar e truncated with a mean of 35, a maximum of 65, and a minimum of 20. This truncation assures that the average operation processing time generated is about 35. For th e uniform distribution an d normal distribution, processing times are truncated with a mean of 35, a maximum of 50, and a minimum of 20. From Table 4.6, uniform distribution produces the best results in the three processing time distributions. Table 4.6 WET Performance under Di fferent Mean Processing Times pijk DTWKDFTW K DPPW DFPPW Uniform(20,50) 56.2138.1443.59 28.53 Exponential(35) 91.3460.80 52.19 35.26 Normal(35,75) 67.5844.9852.07 35.63 4.8.3 WET and WT Performance of Four Rules From (4.12), when 1 ) /( M Nt, the flow allowance of a job may be less than its total processing time, which is clearly unreasonable. Therefore, a DTWK rule is proposed as follows. dj = rj + pj max{1 ,) /( M Nt}. (4.18)

PAGE 90

74 Similarly, we can set the DFTWK rule as follows. dj = rj + pj max{1 ,) /( M Nt} + jL (4.19) When jobs have different processing time distributions, Table 4.7 shows the WETs and WTs with 90% shop utilization. In Table 4.7, cj = ( dj rj ) / pj, (4.20) where cj is the due date tightness factor. Under different processing time distributi ons, DFPPW and DFTWK also significantly outperform DPPW and DTWK, re spectively. When the processing time distributions are uniform, the proposed multi-agent method produces the best WET performance. In addition, DFPPW produces the least average WET for all processing time distributions and due date setting rules. From Tables 4.5 and 4.7, there is no signi ficant different results between (4.12) and (4.18), (4.15) and (4.19). Table 4.7 WETs and WTs under Differe nt Processing Time Distributions pijk DTW K DFTW K DPP W DFPPW WET Uniform(1,30) 38.1526.0520.59 14.70 Exponential(15) 75.1349.9526.26 17.78 Normal(15,75) 44.0230.3422.38 15.39 WT 34.2021.5317.74 11.55 72.2946.2323.48 14.71 Uniform(1,30) Exponential(15) Normal(15,75) 40.5726.2419.65 12.40 cj Uniform(1,30) 4.935.416.47 7.06 Exponential(15) 3.274.046.77 7.65 Normal(15,75) 3.624.085.43 6.05

PAGE 91

75 When the mean of the processing time is incr eased from 15 to 35, Table 4.8 shows the average WETs. From Table 4.8, uniform distribu tion produces the best results in the three processing time distributions. Table 4.8 WETs and WTs under Diffe rent Mean Processing Times pijk DTW K DFTW K DPP W DFPPW WET Uniform(20,50) 56.0438.9743.59 28.53 Exponential(35) 91.1560.71 52.19 35.26 Normal(35,75) 67.5646.8452.07 35.63 WT 50.6833.0240.07 24.73 86.2255.0448.17 30.98 Uniform(20,50) Exponential(35) Normal(35,75) 62.5341.1748.88 32.07 cj Uniform(20,50) 5.586.106.29 6.85 Exponential(35) 5.776.377.05 7.62 Normal(35,75) 5.476.016.03 6.76 4.8.4 Performance of Different Earliness and Tardiness Weights The above computational experi ments use the earliness and tardiness weights in (3.4) independently sampled from the uniform distributi on in the range of 1-5. In practice, however, tardiness penalty should not be smaller than earliness penalty, since tardiness can lead to customer dissatisfaction. Theref ore, it is of interest to c onsider such scenarios that ,j j for all j In particular, two cases are considered in this section: j j and j j 2. When j j j is sampled from integer uniform distribut ion in the range of 1-5. Tables 4.9 and 4.10 report the computa tional results. When j j 2 j is sampled from integer uniform distribution in the range of 1-3. Tables 4.11 and 4.12 repor t the computational results. When j j from Table 4.9, DFPPW and DF TWK also significantly outperform DPPW and DTWK respectively under different processing time distributions. When the

PAGE 92

76 processing time distributions are uniform, th e proposed multi-agent method produces the best WET and WT performance. Norm al distribution is better th an exponential distribution. Table 4.9 WETs and WTs under Same Weights pijk DTW K DFTW K DPP W DFPPW WET Uniform(1,30) 38.0526.2120.42 14.83 Exponential(15) 75.2749.1127.60 17.77 Normal(15,75) 44.7530.1522.28 15.42 WT 33.9221.6417.44 11.70 72.3345.3924.74 14.65 Uniform(1,30) Exponential(15) Normal(15,75) 41.1825.9019.45 12.40 cj Uniform(1,30) 3.295.416.53 7.07 Exponential(15) 3.243.996.84 7.68 Normal(15,75) 3.644.095.46 6.11 From Tables 4.7 and 4.9, there is no significant different results between j j and when j and j are independently sampled. When the mean of the processing time is in creased from 15 to 35, Table 4.10 shows the average WETs and WTs. From Table 4.10, uniform distribution produces the best results in the three processing time distributions. When j j 2, from Table 4.11, DFPPW and DFTW K also significantly outperform DPPW and DTWK respectively under different processing time distributions. When the processing time distributions are uniform, th e proposed multi-agent method produces the best WET and WT performance. Normal distribution is better than exponential distribution. In addition, DFPPW produces the least average WET for all processing time distributions and due date setting rules.

PAGE 93

77 Table 4.10 Performance under Different Processing Time Distributions pijk DTW K DFTW K DPP W DFPPW WET Uniform(20,50) 55.0639.8142.30 27.60 Exponential(35) 90.1961.5854.93 35.08 Normal(35,75) 69.6545.5354.34 36.91 WT 49.5833.6538.65 23.82 85.1255.7350.93 30.92 Uniform(20,50) Exponential(35) Normal(35,75) 64.3139.7850.99 33.42 cj Uniform(20,50) 5.526.096.30 6.74 Exponential(35) 5.736.457.06 7.65 Normal(35,75) 5.546.006.09 6.65 From Tables 4.9 and 4.11, compared with j j WETs and WTs are increased when j j 2. For cj, there is no significant difference. Table 4.11 WETs and WTs under Different Weights pijk DTW K DFTW K DPP W DFPPW WET Uniform(1,30) 49.8633.6225.79 19.18 Exponential(15) 98.1664.9036.60 24.49 Normal(15,75) 58.9240.2229.09 20.12 WT 46.4629.7923.01 16.24 95.7361.8433.80 21.42 Uniform(1,30) Exponential(15) Normal(15,75) 56.1336.8526.51 17.29 cj Uniform(1,30) 4.895.306.37 6.94 Exponential(15) 3.243.946.64 7.38 Normal(15,75) 3.604.085.35 5.90 When the mean of the processing time is in creased from 15 to 35, Table 4.12 shows the average WETs and WTs. From Table 4.12, uniform distribution produces the best results in the three processing time distributions.

PAGE 94

78 Table 4.12 Performance under Different Mean Processing Times pijk DTW K DFTW K DPP W DFPPW WET Uniform(20,50) 71.5050.1154.08 38.67 Exponential(35) 117.2381.3570.17 50.05 Normal(35,75) 91.9863.2073.88 49.14 WT 66.4644.4650.38 34.58 112.5475.9265.82 45.18 Uniform(20,50) Exponential(35) Normal(35,75) 87.3357.9070.57 45.39 cj Uniform(20,50) 5.485.916.13 6.63 Exponential(35) 5.686.406.90 7.62 Normal(35,75) 5.485.946.01 6.58 4.9 Summary The ET performances of SSPR, PR and the proposed scheduling method under various shop utilizations are significantly affected by the tightness factor when due dates are determined by TWK. However, DTWK and DPPW do not select the ti ghtness factor and use dynamic shop load information for due date setti ng. The computational experiments show that DTWK and DPPW outperform TW K. DPPW produces the best WET performance in these three rules. DTWK and DPPW can produce a constant average lateness. The DFTWK and DFPPW rules do not need to select the tightness factor They also use the feedback information of recently completed jobs. The simulation results indicate that for WET performance, DFTWK and DFPPW significantly outperform the ex isting DTWK and DPPW, respectively, and DFPPW performs much better than DFTWK. The strong perf ormance of DFTWK and DFPPW suggests that the job completion feedback mechanis m introduced in due da te setting works very well.

PAGE 95

79 Chapter 5 Multi-Agent Workload Control Methodology 5.1 Introduction Job release control has a significant effect on system performance in the PPC of MTO companies. Specifically, they can reduce WIP inventory and job flowtimes. This chapter discusses job release control and then pr oposes a multi-agent WLC methodology that simultaneously deals with due date setting, job release and scheduli ng in MTO companies. 5.2 Job Release Control The arrival of orders in MTO companies is a stochastic process over time. As each order tends to be different and requires varying routings and processing times, the number of jobs does not characterize the total work on th e shop floor very well. Instead, we define workload as the total remaining processing time of all jobs on the shop, and workload norm as the maximum amount of workload allowed on th e shop floor. Evidently, as the workload norm changes, WIP will also change. According to Little’s law, the relationship among WIP, shop flowtime and throughput rate can be expressed as WIP = sf, (5.1) where WIP is the average WI P level on the shop, fs the average job flowtime and the throughput rate. At low WIP, a considerable th roughput reduction can be expected. However,

PAGE 96

80 when WIP rises to a certain point, the throughput ceases to increase (Bergamaschi et al. 1997). On the other hand, the flowtime con tinues to rise. This means that a critical WIP level exists for a good system performance. This phenomenon may also exist between WIP and other performance measures such as WET. The work load norm corresponding to the critical WIP level is called the critical norm. The critical norm may be determined empirically. The purpose of job release control is to fix WIP at the critical level. 5.3 Job Release Agent The job release agent (JRA) provides a job re lease mechanism to control WIP. In this research, continuous aggregate lo ading (CAGG) is used as the job release mechanism. CAGG performs well for the flowtime and tardines s related criteria (Sa buncuoglu and Karapinar 1999). By CAGG, if current workload falls belo w the workload norm, jobs are continuously released from the job pool to the shop until the workload reaches its norm. On the other hand, if the workload exceeds its norm when a new job arrives, it will wait in the job pool. Consequently, one can restrain the WIP level while maintaining certain system performance. The JRA receives jobs from the OEA a nd puts the jobs in the pool. It also communicates with the RSA and determines curr ent workload. The JRA continuously monitors current workload. If the pool is not empty and the workload is less th an its norm, the JRA releases jobs from the pool to the shop. In this research, jobs are releas ed in EDD order (i.e., the job with the earliest due date in the job pool is re leased first). The JRA protocol is given as follows.

PAGE 97

81 JRA protocol 1) Receive a job from the OEA. 2) Put the job in the pool. 3) If the pool is not empty, send the RSA a request to get current shop status, and go to step 4; otherwise wait until a new job arrives, and go to step 1. 4) Receive current shop status from the RSA. 5) Calculate current workload. 6) If current workload is less than its norm, release a job in EDD order. Go to step 3. 5.4 System Architecture To integrate due date setting, job release, and scheduling, a multi-agent WLC methodology is developed. The system arch itecture is sketched in Figure 5.1. There are four types of agents in the me thodology: OEA, JRA, RSA, and IFA, as defined earlier. All agents consist of three modul es. The first is the data module, which carries certain information for the use of the agent. The communication module c onsists of protocols for the agent to communicate with each other. Finally, the decision module makes decisions using the information from the da ta module and communication module. Figure 5.1. System Architecture of Multi-Agent Workload Control jL Completed jobs Enquiry + OEA JRA RSA (JAs and MAs) IFA Workload norm

PAGE 98

825.5 System Coordination One challenging issue faced by multi-agent systems is the agent coordination that arises due to the interdependencies and interactions among agents. Individual agents in a multi-agent system have their individual sub-goals. A coor dination mechanism integrates the individual sub-goals of agents into the sy stem goal through message-passing. Three types of interdependencies are id entified (Sikora and Shaw 1998). However, there are only two valid interdepende ncies in multi-agent WLC systems. 5.5.1 Temporal Interdependency The activities of agents may be interdependent due to the fact that an activity of one agent may be restricted by the activities of othe r agents. For example, certain activities cannot be started until other activities ar e finished. In WLC systems, only after the due date of an order is set, the corresponding job can be released, and then the job can be processed on the shop floor. 5.5.2 Sub-goal Interdependency The sub-goals of agents resulting from task decomposition may be overlapping or interdependent. Agents have to exchange info rmation during the process of decision making. For instance, to determine the due date of a j ob by (4.14) or (4.15), an OEA needs to know the average job lateness that is dete rmined by the IFA. For job rel ease, the JRA should get current workload that can only be determined by the RSA. The coordination process in the multi-agent WLC methodology is as follows. When an MTO company receives an enquiry from a cust omer, the OEA determines the job due date using the information from the RSA and IFA. Then the job is put in the job pool. If the pool is

PAGE 99

83 not empty and current workload falls below its norm, the JRA releases a job to the shop floor. After a job is released, a JA for the job is created. The JA requests bids from the machines that can process the next operation. When an MA rece ives the bid request from the JA, it formulates a bid. The JA then evaluates all bids from th e MAs and selects a machine. After a machine is selected, the job is moved to the machine. The MA sequences the jobs and the machine processes the job. The routing and sequencing process is repeated unt il a job is finished. 5.6 Discrete Event Simulation The WLC simulation system is implemente d using an object-oriented approach and C++. The simulation begins by setting the simu lation clock to zero, initializing cumulative statistics to zero, generating any initial events, and defining the system st ate at time zero. The simulation program then cycles, repeatedly passing the current least-time event to the appropriate event subroutines until the simula tion is over. At each step, after finding the imminent event but before calling the event subrou tine, the simulation clock is advanced to the time of the imminent event. Next, the appropria te event subroutine is called to execute the imminent event, update cumula tive statistics, and generate future events. Executing the imminent event means that the system states and entity attributes are changed to reflect the fact that the event has occurred. The simu lation algorithm is given as follows. Simulation algorithm 1) Set CLOCK=0 and cumulative statistics=0. 2) Generate initial system state. 3) Call time advance algorithm to find imminent event. 4) Call appropriate event subroutine.

PAGE 100

84 5) Advance COLOCK to imminent event time. 6) If the simulation is not over, go to step 3; otherwise go to step 7. 7) Generate the simulation report. Time advance algorithm 1) If a job arrives, go to st ep 2; otherwise go to step 5. 2) Set its operation sequence, work center s, processing times, earliness and tardiness weights. 3) Call the OEA algorithm to get its due date. 4) Put the job in the job pool. 5) Call the RSA algorithm to get current workload. 6) If current workload is not greater than its norm, go to step 7; otherwise go to step 8. 7) Call the JRA algorithm to re lease a job to the shop floor. 8) If a job is not completed, call the RSA algorithm to schedule an operation. 5.7 Simulation Study In order to evaluate the effectiveness of the proposed methodology, we provide an extensive simulation study based on randomly generated problem instances. The shop environment will be similar to the one used in Chapter 3. Each job has 5 operations. However, processing times are randomly generated from a truncated exponential dist ribution with a mean of 15, a maximum of 30, and a minimum of 1. In addition, results of pr evious studies indicate that the choice of job release mechanisms is the most critical in the range of 85% to 90% (Ragatz and Mabert 1988). Therefore, 85% a nd 90% utilizations ar e considered in the simulation of job release control.

PAGE 101

85 This section presents simulation experiments to investigate the pe rformance of the job release control. The performance measure of WET is important but do not capture all the impact of job release control. Flowtime and maximum WIP in term s of number of jobs provide some indication of shop congestion, and lead tim e reflects responsiveness to customer orders. Therefore, the average lead time (LT), aver age flowtime (FT) and maximum WIP are also reported. Immediate release or no job release control is used to compare the performance of CAGG. Tables 5.1 and 5.2 present the computational results when the shop utilization is 90%, and Tables 5.3 and 5.4 report the computational results at 85% utilization. When the shop utilization is 90%, Tables 5.55.8 report the computa tional results under di fferent processing time distributions. Note that in all 8 tables, the norm of means no release cont rol. In addition, we only implement the two proposed due date setting rules. 5.7.1 System Performance Using DFPPW From Table 5.1 and Figure 5.2, we can see that using DFPPW, the average WET and LT almost remains constant when the norm decreases from to 1000. As the lead time is the sum of the pool time and the flowtime, it means that for a job, the increase in its pool time offsets the reduction in its waiting time on the shop floor for any norm no smaller than 1000. When the norm further decreases from 1000, the average WET and LT increase quickly. On the other hand, the average FT and maximum WIP continue to decrease as the norm decreases, and both decrease more rapidly as the norm is below 1000. Therefore, 1000 should be considered as the critical norm. Unde r the critical norm, the average WET and LT are little changed, but the average FT and ma ximum WIP are reduced by 10.5% and 20.1%, respectively, compared w ith no release control.

PAGE 102

86 Table 5.1 Performance under 90% Shop Utilization Using DFPPW Norm WETLTFTMax WIP 18.13272.89272.8960.55 1700 18.41271.83271.4659.80 1600 18.23271.65270.9159.20 1500 18.35271.85270.2458.90 1400 18.31272.91269.8858.05 1300 18.40270.57264.8056.80 1200 18.06271.49261.9054.95 1100 18.22270.25253.1052.65 1000 18.04272.84244.1448.40 900 18.84278.06230.2744.35 800 20.39295.33212.9039.25 700 24.12357.12194.2934.00 Figure 5.2. Performance under 90% Utilization Using DFPPW 5.7.2 System Performance Using DFTWK When DFTWK is used for due date setting, one can observe from Table 5.2 and Figure 5.3 that 1000 is also the crit ical norm at 90% utilization. As the norm is reduced from to the critical norm, the average WET and LT remain roughly constant, but the average FT and maximum WIP are reduced by 3.7% and 18.0%, respectively. 0 50 100 150 200 250 300 350 400 700 900 1100 1300 1500 1700 Workload norm WET LT FT Max WIP

PAGE 103

87 Table 5.2 Performance under 90% Shop Utilization Using DFTWK Norm WETLTFTMax WIP 44.62171.77171.7741.15 1700 45.00172.00171.9542.55 1600 44.92172.58172.4741.45 1500 44.47171.23171.0041.45 1400 44.41170.93170.4140.55 1300 44.67171.53170.4938.95 1200 44.82172.03170.2837.80 1100 44.64172.76169.2635.90 1000 44.35171.15165.3733.75 900 45.15174.29163.1531.75 800 47.56181.34157.9528.80 700 49.99191.83149.8025.85 Under both proposed due date setting rules, the job release contro l reduces flowtime and maximum WIP at no expense of worse WET and lead time performances Shorter job flowtime and smaller maximum WIP may lead to less shop c ongestion. This indicate s that the job release control is effective. Figure 5.3. Performance under 90% Utilization Using DFTWK 0 50 100 150 200 250 700 900 1100 1300 1500 1700 Workload norm WET LT FT Max WIP

PAGE 104

88 As seen in Chapter 4, DFPPW significantl y outperforms its counterpart DFTWK in terms of WET performance, when there is no job release control. From Tables 5.1 and 5.2, the same conclusion holds when there is job release control. For example, when the norm is set equal to the critical norm of 1000, the aver age WET by DFPPW is onl y 59.3% of that by DFTWK. However, DFTWK significantly outpe rforms DFPPW for average LT, FT and maximum WIP performance measures. While le ss WET means better JIT production, smaller LT and FT indicates quicker cu stomer response and less s hop congestion, respectively. Therefore, there is a trade-off between DFPP W and DFTWK, in terms of multiple system performance measures. 5.7.3 System Performance under Different Utilizations From Tables 5.3 and 5.4, and Figures 5.4 and 5.5, one can see similar observations. However, the critical norm decreases to 800 from 1000 at 90% utilization. The critical norm is affected by shop utilization leve ls. When the shop uti lization is reduced from 90% to 85%, all the average WET, LT, FT and maximum WIP al so decrease. This would be expected. Table 5.3 Performance under 85% Shop Utilization Using DFPPW Norm WETLTFTMax WIP 16.56255.90255.9056.05 1600 16.60255.52255.3855.90 1500 16.64252.66252.2655.35 1400 16.67256.40255.1755.55 1300 16.60253.54251.2854.40 1200 16.58254.14249.5953.40 1100 16.35252.58244.3450.95 1000 16.63247.62235.1948.40 900 16.33254.38231.5746.50 800 17.01252.07215.6641.85 700 17.74273.50201.0836.15 600 20.87311.71178.7830.30

PAGE 105

89 When the utilization is decreased from 90% to 85%, the advantage of job release control increases. As the workload norm decreases from to the critical norm, the average WET and LT are almost unchanged at both utilizations. However, the reductions of average FT and maximum WIP increase from 10.5% to 15.7% and 20.1% to 25.3%, respectively, under DFPPW. Similarly, such reductions in average FT and maximum WIP incr ease from 3.7% to 5.4% and from 18.0% to 20.7%, respectively, under DFTWK. Figure 5.4. Performance under 85 % Utilization Using DFPPW Table 5.4 Performance under 85% Shop Utilization Using DFTWK Norm WETLTFTMax WIP 39.58155.00155.0036.15 1600 39.58155.10155.0936.30 1500 39.56154.85154.8236.10 1400 39.19153.70153.6036.40 1300 38.90153.75153.5136.25 1200 38.96153.62153.1735.65 1100 38.92153.70152.6134.00 1000 38.73154.01152.0733.20 900 39.23153.86150.0430.55 800 39.07153.96146.5628.65 700 40.92159.62142.9226.05 600 44.04170.81136.1123.55 0 50 100 150 200 250 300 350 600 800 1000 1200 1400 1600 Workload norm WET LT FT Max WIP

PAGE 106

90 Figure 5.5. Performance under 85 % Utilization Using DFTWK 5.7.4 Performance under Different Pro cessing Time Distributions The above sections report the results when processing times are randomly generated from a truncated exponential dist ribution with a mean of 15, a maximum of 30, and a minimum of 1. This section reports th e simulation results when jobs have different processing time distributions. When the shop utilization is 90% and pro cessing times are sampled from a truncated normal distribution with a mean of 15, a varian ce of 75, a maximum of 30, and a minimum of 1, Tables 5.5 and 5.6 give the WETs using DF PPW and DFTWK, respectively. When the shop utilization is 90% and processi ng times are sampled from a unif orm distribution in the range 130, Tables 5.7 and 5.8 give the WETs using DFPPW and DFTWK, respectively. From Table 5.5 and Figure 5.6, 1700 should be considered as the critical norm. Under the critical norm, compared wi th no release control, the average WET and LT are little changed, but the average FT and maxi mum WIP are reduced by 20.3% and 33.1%, respectively. 0 20 40 60 80 100 120 140 160 180 600 800 1000 1200 1400 1600 Workload norm WET LT FT Max WIP

PAGE 107

91 Compare with Table 5.1, when the proce ssing time distributions are changed from exponential to normal, the critical norm is in creased from 1000 to 1700. At the critical norm, average WET is reduced from 18.04 to 15.32. The reduction of average FT increases from 10.5% to 20.3% and the reduction of maximum WI P increases from 20.1% to 33.1%. However, the average LT is also incr eased from 272.84 to 449.51. Table 5.5 Performance under Normal Distribution Using DFPPW Norm WETLTFTMax WIP 15.39454.32454.3293.60 3500 15.32454.16453.5093.30 3000 15.42454.92451.4393.40 2500 15.46452.14437.3688.80 2200 15.34452.74418.9680.90 2000 15.00450.58402.2075.50 1700 15.32449.51362.2262.60 1500 16.59456.56333.6853.80 1400 16.84463.01315.9050.00 1300 17.95468.18298.0746.20 1200 21.32492.11278.5842.70 Figure 5.6. Performance under No rmal Distribution Using DFPPW 0 100 200 300 400 500 600 1200 1700 2200 2700 3200 3700 Workload norm WET LT FT Max WIP

PAGE 108

92 When DFTWK is applied, form Table 5. 6 and Figure 5.7, one can see similar observations. From Tables 5.6 and Figure 5.7, 1700 is also the critical no rm. Under the critical norm, compared with no release control, the average WET and LT are little changed, but the average FT and maximum WIP are reduced by 15.5% and 31.4%, respectively. Table 5.6 Performance under Norm al Distribution Using DFTWK Norm WETLTFTMax WIP 30.61346.55346.5574.80 3500 30.38345.44344.8973.70 3000 30.25344.43341.5872.30 2500 30.33343.81336.2969.00 2200 29.48335.89321.3963.00 2000 30.10338.91314.4358.90 1700 30.40340.93292.8451.30 1500 32.19346.62277.0446.50 1400 33.40351.25267.2144.20 1300 35.03358.41256.5541.00 1200 39.46387.64245.4637.90 Figure 5.7. Performance under No rmal Distribution Using DFTWK 0 50 100 150 200 250 300 350 400 450 1200 1700 2200 2700 3200 3700 Workload norm WET LT FT Max WIP

PAGE 109

93 Compare with Table 5.2, when the proce ssing time distributions are changed from exponential to normal, the critical norm is al so increased from 1000 to 1700. At the critical norm, average WET is reduced from 44.35 to 30.40. The reduction of average FT increases from 3.7% to 15.5% and the reduction of maximum WIP increases from 18.0% to 31.4%. However, the average LT is also increased from 171.15 to 340.93. When processing times are sampled from a uniform distribution in the range 1-30, Tables 5.7 gives the WETs using DFPPW. Table 5.7 Performance under Unif orm Distribution Using DFPPW Norm WETLTFTMax WIP 14.70536.49536.4999.60 5000 14.62536.45536.4599.60 4500 14.63536.38536.1899.40 4000 14.52535.70534.4099.30 3500 14.10533.97530.1497.40 3000 14.59535.47521.5092.90 2500 14.09531.72497.9881.40 2200 14.41536.74468.1175.30 2000 14.47534.36437.3766.60 1700 16.14546.14385.6156.40 1500 21.08572.23342.6150.40 From Tables 5.7 and Figure 5.8, 2000 should be considered as the critical norm. Under the critical norm, compared wi th no release control, the average WET and LT are little changed, but the average FT and maxi mum WIP are reduced by 18.5% and 33.1%, respectively. Compare with Table 5.1, when the proce ssing time distributions are changed from exponential to uniform, the critical norm is in creased from 1000 to 2000. At the critical norm, average WET is reduced from 18.04 to 14.47. The reduction of average FT increases from

PAGE 110

94 10.5% to 18.5% and the reduction of maximum WI P increases from 20.1% to 33.1%. However, the average LT is also incr eased from 272.84 to 534.36. When DFTWK is applied, one can see simila r observations from Ta ble 5.8 and Figure 5.9. 2000 is also the critical norm. Under the cr itical norm, compared w ith no release control, the average WET and LT are little changed, but the average FT and maximum WIP are reduced by 16.0% and 31.9%, respectively. Figure 5.8. Performance under Un iform Distributi on Using DFPPW Table 5.8 Performance under Unif orm Distribution Using DFTWK Norm WETLTFTMax WIP 26.49451.73451.7388.60 5000 26.49451.73451.7388.60 4500 26.34451.11450.9888.60 4000 26.10448.91447.9287.70 3500 26.21463.99460.2586.88 3000 25.22443.80435.4680.90 2500 24.61438.88416.2572.20 2200 25.26436.95395.3465.20 2000 25.63440.77379.3860.30 1700 28.38453.66344.6752.30 1500 33.97481.96315.0847.00 0 100 200 300 400 500 600 700 1500 2500 3500 4500 5500 Workload norm WET LT FT Max WIP

PAGE 111

95 Compare with Table 5.2, when the proce ssing time distributions are changed from exponential to normal, the critical norm is al so increased from 1000 to 2000. At the critical norm, average WET is reduced from 44.35 to 25.63. The reduction of average FT increases from 3.7% to 16.0% and the reduction of maximum WIP increases from 18.0% to 31.9%. However, the average LT is also increased from 171.15 to 379.38. Figure 5.9. Performance under Un iform Distribution Using DFTWK In addition, there is only a little differe nce between the uniform distributions and normal distributions of pro cessing times for all performance under DFPPW and DFTWK. 5.8 Summary This new multi-agent WLC methodology simulta neously deals with due date setting, job release and scheduling in real time. Unde r job release control, DFTWK and DFPPW can consider job pool times and thus eliminate the need to estimate job pool times in due date setting. 0 100 200 300 400 500 600 1500 2500 3500 4500 5500 Workload norm WET LT FT Max WIP

PAGE 112

96 The computational results show that the proposed WLC methodology reduces job flowtimes and shop WIP pretty significantl y, without worsening ET and lead time performances. As should be exp ected, the critical workload norm decreases as shop utilization decreases. However, under the same utilizat ion and processing time distributions, both DFTWK and DFPPW result in the same critical nor m. This may indicate that the critical norm is not affected by how due dates are set. Under the considered utilization levels, D FPPW leads to better WET performance but longer lead times and more cong estion than DFTWK. If a compa ny attempts to complete jobs as close to their due dates as possible, DFPPW is much better than DFTWK. However, if the priority is customer response, DFTWK produces better results.

PAGE 113

97 Chapter 6 Conclusions 6.1 Summary of Work This dissertation has proposed a multi-a gent WLC methodology with earliness and tardiness objectives. This methodology simultaneously deals with due date setting, job release and scheduling. It can be used as a PPC method in real time for MTO companies. Two new due date setting rules, DFTWK a nd DFPPW, are developed to establish job due dates. They do not need to select the ti ghtness factor and use a feedback mechanism to dynamically adjust due date setting. Both new rules are nonparametric and easy to be implemented in practice. Unde r job release control, DFTWK and DFPPW can consider job pool times and, thus, eliminate the need to esti mate job pool times in due date setting. The simulation results indicate that DFPPW leads to better WET performance but longer lead times and more congestion than DFTWK. According to different performance requirements, MTO companies can choose a suitable one from thes e two due date setting rules. If a company attempts to complete jobs as close to their due dates as poss ible, DFPPW is much better than DFTWK. However, if the prio rity is customer response, DFTWK produces better results. The job release control significantly redu ces job flowtimes and shop WIP inventory, without worsening ET and lead time performances. An important task for job release control is to determine critical workload norm. This res earch concludes that the critical workload norm

PAGE 114

98 decreases as shop utilization decreases. Unde r the same utilization and processing time distributions, both DFTWK and DFPPW re sult in the same critical norm. A multi-agent scheduling method with job ea rliness and tardiness objectives in a flexible job shop environment is proposed. A new job routing and sequencing mechanism is developed. In this mechanism, different criteri a for two kinds of jobs are proposed to route these jobs. Job sequencing enables to hold a job that may be completed too early. Two sequencing algorithms based on exis ting methods are developed to d eal with these two kinds of jobs. The computational experiments show that the multi-agent scheduling method significantly outperforms PR and SSPR for WET performance, and the propos ed method is insensitive to the number of operations. The proposed method also outperforms PR and SSPR in terms of WT performance which has been the primary perfor mance measure against job due dates. This indicates that this proposed method is robust. In addition, the proposed me thod is very efficient computationally. Such computational efficiency makes the proposed method applicable in real time. The proposed methodology is implemented in a flexible job shop environment. The computational experiments show that the propos ed WLC methodology is very effective for the PPC in MTO companies. In addition, the com putational results indi cate that the proposed methodology is extremely fast and can be implemented in real time. 6.2 Future Research Directions In the proposed multi-agent job routing and sequencing method, SOLJ sequencing algorithm reschedules all SOLJs by the MA algorithm (Mazzini and Armentano 2001). However, the MA algorithm results in more tardiness and less earliness. In practice, however, tardiness penalty should not be smaller than earliness penalty, since tardiness can lead to

PAGE 115

99 customer dissatisfaction. Further research wi ll investigate more effective single machine sequencing algorithm to reduce tardiness. DFPPW usually leads to better ET perfor mance but longer lead times and more congestion than DFTWK. The performance meas ure for the selection of DFPPW and DFTWK is a very interesting future research dir ection. The use of econom ic objectives can be considered. For the workload control, under the same utilization and processing time distributions, both DFTWK and DFPPW result in the same critical norm. This may indicate that the critical norm is not affected by how due dates are set. Furt her investigation is necessary to confirm this observation. On the other hand, it is observed that the critic al norm decreases as the shop utilization decreases. A future research w ould be to further inve stigate this effect.

PAGE 116

100 References Alidee, B. (1994). Minimizing absolute and squa red deviation of completion times from due dates. Production and Operations Management, 3, 133-147. Amaro, G. M., Hendry, L. C. and Kingsman, B. G. ( 1999). Competitive advantage, customization and a new taxonomy for non make-to-stock companies. International Journal of Operations and Production Management, 19, 349371. Anderson, E. J. and Nyirenda, J. C. (1990). Two new rules to minimize tardiness in a job shop. International Journal of Production Research, 28, 22772292. Aydin, M. E. and Oztemel, E. (2000). Dyna mic job-shop scheduling using reinforcement learning agents. Robotics and Autonomous Systems, 33, 169-178. Baker, K. R. (1984). Sequencing rules a nd due date assignments in a job shop. Management Science, 30, 1093-1104. Baker, K. R. and Bertrand, J. W. M. (1982). A dynamic priority rule fo r sequencing against due dates. Journal of Operations Management, 3, 37-42. Baker, K. R. and Kanet, J. J. (1983). Job shop scheduling with modified due dates. Journal of Operations Management, 4, 11-22. Baker, K. R. and Scudder, G. D. (1990). Sequenc ing with earliness and ta rdiness penalties: a review. Operations Research, 38, 22-36. Baykasoglu, A. (2002). Linguistic-based meta-heu ristic optimization m odel for flexible job shop scheduling. International Journal of Production Research, 40, 4523-4543. Balas, E., Lenstra, J. K. and Vazacopoulos, A. (1995). One machine scheduling with delayed precedence constraints. Management Science, 41, 94-109. Bergamaschi, D., Cigolini, R., Perona, M. and Portioli, A. (1997). Orde r review and release strategies in a job shop environm ent: a review and a classification. International Journal of Production Research, 35, 399–420. Bertrand, J. W. M. (1983a). The effect of workload dependent due dates on job shop performance. Management Science, 29, 799–816.

PAGE 117

101 Bertrand, J. W. M. (1983b). The use of worklo ad information to control job lateness in controlled and uncontrolled release production systems. Journal of Operations Management, 3, 79-92. Bertrand, J. W. M. and Muntslag, D. R. ( 1993). Production control in engineering-to-order firms. International Journal of Production Research, 30/31, 3-22. Bertrand, J. W. M. and Van Ooijen, H. P. G. (2002). Workload based order release and productivity: a missing link. Production Planning and Control, 13, 665-678. Blazewicz, J., Dmschke, W. and Pesch, E. (1996). The job shop scheduling problem: conventional and new solution techniques. European Journal of Operational Research, 93, 1-33. Carroll, D. C. (1965). Heuristic sequencing of jobs w ith single and multiple components. Ph. D dissertation, MIT. Cavalieri, S., Garetti, M., Macchi, M. and Taisch, M. (2000). An experimental benchmarking of two multi-agent architectures for production scheduling and control. Computers in Industry. 43, 139-152. Chambers, J. B. (1996). Classical and flexible job s hop scheduling by tabu search. Ph.D. dissertation, University of Texas at Austin, Austin, Texas. Chang, F. C. R. (1997). Heuristics for dynami c job shop scheduling with real-time updated queueing time estimates. International Journal of Production Research, 35, 651-665. Chen, D., Luh, P. B., Thakur, L. S. a nd Moreno Jr., J. (2003). Optimization-based manufacturing scheduling with multiple resources, setup requirements, and transfer lots. IIE Transactions, 35, 973-985. Cheng, T. C. E. and Gupta, M. C. (1989). Survey of scheduli ng research involving due date determination decisions. European Journal of Operational Research, 38, 156-166. Cheng, T. C. E. and Jiang, J. (1998). Job shop scheduling for missed due-date performance. Computers & Industrial Engineering, 34, 297-307. Conway, R. W. and Maxwell, W. L. (1962). Ne twork dispatching by the shortest operation discipline. Operations Research, 10, 51-73. Conway, R.W. (1965). Priority dispatch ing and job lateness in a job shop. Journal of Industrial Engineering, 16, 228–237. Conway, R. W., Maxwell, W. L. and Miller, L. W. (1967). Theory of scheduling. AddisonWesley Inc., Reading, MA.

PAGE 118

102 Croce, F. D. and Trubian, M. (2002). Optimal idle time insertion in early-tardy parallel machines scheduling with precedence constraints. Production Planning and Control. 13, 133-142. Cutkosky, M. R., Tenenbaum, J. M. and Glic ksman, J. (1996). Ma defast: collaborative engineering over the Internet. Communication of the ACM, 39, 78-87. Das, T. K., Gosavi, A., Mahadevan, S. and Marchalleck, N. (1999). Solving semi-markov decision problems using average reward reinforcement learning. Management Science, 45, 560-574. Eilon, S. and Chowdhury, I.G. (1976). Due dates in job shop scheduling. International Journal of Production Research, 14, 223–237. Enns, S.T. (1994). Job shop lead time requireme nts under conditions of controlled delivery performance. European Journal of Operational Research, 77, 429–439. Enns, S. T. (1995). A dynamic forecasting m odel for job shop flowtime prediction and tardiness control. International Journal of Production Research, 33, 1295-1312. Enns, S. T. (1998). Lead time selection and the behavior of work flow in job shops. European Journal of Operational Research, 109, 122-136. Fredenhall, L. D. and Melnyk, S. A. (1995). Assessing the impact of reducing demand variance through improved planning on the performance of a dual resource c onstrained job shop. International Journal of Production Research, 33, 1521–1534. Fry, T.D., Philipoom, P.R. and Markland, R.E. ( 1989). Due date assignment in a multistage job shop. IIE Transactions, 21, 153–161. Gee, E. S. and Smith, C. H. (1993). Sele cting allowance policies for improved job shop performance. International Journal of Production Research, 31, 1839–1852. Heady, R. B. and Zhu Z. (1998). Minimizing the sum of job earliness and tardiness in a multimachine system. International Journal of Production Research, 36, 1619–1632. Hendry, L. C. and Kingsman, B. G. (1989). Prod uction planning systems a nd their applicability to make to order companies, European Journal of Operational Research, 40, 1-15. Hendry, L. C., Kingsman, B. G. and Cheung, P. (1998). The effect of workload control (WLC) on performance in make-to-order companies. Journal of Operations Management, 16, 63-75. Henrich, P., Land, M. and Gaalman G. (2004). E xploring applicability of the workload control concept. International Journal of Production Economics, 90, 187–198. Hodgson, T. J., Cormier, D., Weintraub, A. J. and Zozom, Jr. A. (1998 ). Note. satisfying due dates in large job shops. Management Science, 44, 1442-1446.

PAGE 119

103 Hodgson, T. J., King, R. E., Thoney, K., Stanisla w, N., Weintraub, A. J. and Zozom, Jr. A. (2000). On satisfying due dates in larg e job shops: idle time insertion. IIE Transactions, 32, 177-180. Hong, J. and Prabhu, V.V. (2004). Distribu ted reinforcement learning control for batch sequencing and sizing in just -in-time manufacturing systems. Applied Intelligence, 20, 71–87. Hsu, S. Y. and Sha, D. Y. (2004). Due date as signment using artificial neural networks under different shop floor control strategies. International Journal of Production Research, 42, 1727-1745. Huang, S. H., Zhang, H. and Smith, M. L. (1995). A progressive approach for the integration of process planning and scheduling. IIE Transactions, 27, 456-464. Huang, C. L., Huang, Y. H., Chang, T. Y., Chang, S. H., Chung, C. H., Huang, D. T. and Li, R. K. (1999). The construction of productio n performance prediction system for semiconductor manufacturing with artificial neural networks. International Journal of Production Research, 37, 1387–1402. Ip, W.H., Li, Y., Man, K.F. and Tang, K.S. (2000). Multi-product planning and scheduling using genetic algorithm approach. Computers and Industrial Engineering, 38, 283-296. Jayamohan, M. S. and Rajendran, C. (2004) Development and analysis of cost-based dispatching rules for job shop scheduling. European Journal of Operational Research, 157, 307-321. Kacem, I., Hammadi, S. and Borne, P. (2002) Approach by localization and multiobjective evolutionary optimization for flex ible job-shop scheduling problems. IEEE Transactions on Systems, Man and Cybernetic s, Part C: Applic ations and Reviews, 31, 1-13. Kanet, J. J. (1988). Load-limited order release in job shop scheduling systems. Journal of Operations Management, 7, 44–58. Kanet, J. J. and Christy, D.P. (1989). Manufact uring systems with forb idden early shipment: implications for setting manufacturing lead times. International Journal of Production Research, 27, 783–792. Kanet, J. J. and Hayya, J. C. (1982). Priority di spatching with operation due dates in a job shop. Journal of Operations Management, 2, 155-163. Kanet, J. J. and Zhou, Z. (1993). A decision theo ry approach to prior ity dispatching for job shop scheduling. Production and Operations Management, 2, 2-14.

PAGE 120

104 Kingsman, B. G. (2000). Mode lling input-output workload control for dynamic capacity planning in production planning systems. International Journal of Production Economics, 68, 73–93. Krothapalli, N. K. C. and Deshmukh, A.V. (1999). Design of negotiation protocols for multiagent manufacturing systems. International Journal of Production Research, 37, 16011624. Kutanoglu, E. and Sabuncuoglu I. (1999). An analysis of heuristi cs in a dynamic job shop with weighted tardiness objectives. International Journal of Production Research, 37, 165187. Land, M. J. and Gaalman, G. (1996). Worklo ad control concepts in job shops: a critical assessment. International Journal of Production Economics, 46–47, 535–548. Land, M. J. and Gaalman, G. (1998). The perfor mance of workload cont rol concepts in job shops: improving the release method. International Journal of Production Economics, 56–57, 347–364. Leung, Joseph Y.-T. (2002). A dual criteria sequencing problem with earliness and tardiness penalties. Naval Research Logistics, 49, 422-431. Li, L., Tang, H., Wu, Z., Gong, J ., Gruidl, M., Zou, J. Tockman, M. and Clark, R. A. (2004). Data mining techniques for cancer detec tion using serum proteomic profiling. Artificial Intelligence in Medicine, 32, 71-83. Liao, C. J. and You, C. T. (1993). An improved formulation for the job shop scheduling problem. Journal of Production Research Society, 43, 1047-1054. Lu, T. P. and Yih, Y. (2001). An agent-based production control framework for multiple-line collaborative manufacturing. International Journal of Production Research, 39, 21552176. Luh, P. B., Chen, D. and Thakur, L. S. (1999). Effective approach for job-shop scheduling with uncertain processing requirements. IEEE Transactions on Robotics and Automation, 15, 328-339. Maione, G. and Naso, D. (2003). A genetic a pproach for adaptive multiagent control in heterarchical manufacturing systems. IEEE Transactions on Systems, Man and Cybernetics, Part A, 33, 573-588. Mastrolilli, M. and Gambardella, L. M. ( 2000). Effective neighborhood functions for the flexible job shop problem. Journal of Scheduling, 3, 3-20. Maturana, F. and Norrie, D. H. (1996). Multi-a gent mediator archit ecture for distributed manufacturing. Journal of Intelligent Manufacturing, 7, 257-270.

PAGE 121

105 Mazzini, R. and Armentano, V. A. (2001). A heuristic for single machine scheduling with early and tardy costs. European Journal of Operational Research, 128, 129-146. Melnyk, S. A. and Ragatz, G. L. (1989). Order review/release systems: research issues and perspectives. International Journal of Production Research, 27, 1081–1096. Melnyk, S. A., Tan, K. C., Denzler, D. R. and Fredendall, L. (1994). Evaluating variance control, order review/release and di spatching: a regression analysis. International Journal of Production Research, 32, 1045–1061. Moses, S. A. (1999). Due date assignment using feedback control with reinforcement learning. IIE Transactions, 31, 989-999. Morton, T. E. and Ramnath, P. (1992). Guided forward tabu/beam search for scheduling very large dynamic job shops. Technical Report 1992-47, Gra duate School of Industrial Administration, Carnegie-Mellon University. Mosheiov, G. (2003). Scheduling unit proces sing time jobs on an m-machine flow-shop. Journal of the Operational Research Society, 54, 437-44. Muda, M. S. and Hendry, L. C. (2003). The SHEN model for MTO SM E’s: a performance improvement tool. International Journal of Oper ations and Production Management, 23, 470-486. Nagendra Prasad, M.V., Lesser, V.R., and Lander, S.E. (1998). Learning Organizational Roles for Negotiated Search in a Multi-agent System. International Journal of HumanComputer Studies, 48, 51-67. Nasr, N. and Elsayed, E. (1990). Job s hop scheduling with alternative machines. International Journal of Production Research, 28, 1595-1609. Perona, M. and Portioli, A. ( 1998). The impact of paramete rs setting in load oriented manufacturing control. International Journal of Production Economics, 55, 133-142. Philipoom, P. R., Rees, L. R. and Wiegmann, L. (1994). Using artificial neural networks to determine internally-set due-date assignments for shop scheduling. Decision Sciences, 25, 825-847. Pinedo, M. (2002). Scheduling Theory, Algorithms and Systems. Prentice Hall. Pontrandolfo, P., Gosavi, A., Okogbaa, O. G. and Das, T. K. (2002) Global supply chain management: a reinforcement learning approach. International Jour nal of Production Research, 40, 1299-1317. Ragatz, G. L. and Mabert, V. A. (1984). A simulation an alysis of due date assignment rules. Journal of Operations Management, 5, 27-39.

PAGE 122

106 Ragatz, G. L. and Mabert, V. A. (1988). An ev aluation of order releas e mechanisms in a jobshop environment. Decision Science, 19, 167-189. Raman, N. (1995). Input control in job shops. IIE Transactions, 27, 201–209. Ren, H. (2000). Multi-agent scheduling and its applications in job shops with due date related objectives. Ph.D. dissertation, University of South Florida, Tampa, Florida. Ronald, R. and Uzsoy, R. (2001). Experimental evaluation of heuristic optimization algorithms: a tutorial. Journal of Heuristics, 7, 261-304. Russell, R. S., Dar-el, E.M. and Taylor II, B.W. (1987). A comparative analysis of the COVERT job sequencing rule using va rious shop performance measures. International Journal of Production Research, 25, 1523-1539. Saad, A., Kawamura, K. and Biswas, G. (1997). Performance evaluation of contract net-based heterarchical scheduling for flex ible manufacturing systems. Intelligent Automation and Soft Computing, 3, 229-248. Sabuncuoglu, I. and Comlekci, A. (2002). Oper ation-based flowtime estimation in a dynamic job shop. Omega, 30, 423-442. Sabuncuoglu, I. and Karapinar, H. Y. (1999). Analysis of or der review/release problems in production systems. International Journal of Production Economics, 62, 259-279. Shafaei, R. and Brunn, P. (1999). Workshop schedulin g using practical (inacc urate) data-Part 1: The performance of heuristics scheduling rules in a dynamic job shop environment using a rolling time horizon approach. International Journal of Production Research, 37, 3913-3925. Shafaei, R. and Brunn, P. (2000). Workshop schedulin g using practical (inacc urate) data-Part 3: A framework to integrate job release, rou ting and scheduling functions to create a robust predictive schedule. International Journal of Production Research, 38, 85-99. Shaw, M. J. (1988). Dynamic scheduling in cel lular flexible manufacturing systems: a framework for networked decision making. Journal of Manufacturing Systems, 7, 8394. Shen W. and Barthes J.P. ( 1997). An experimental environment for exchanging engineering design knowledge by cognitive agents. In Ma ntyla M., Finger S. and Tomiyama, T., (Eds.), Knowledge Intensive CAD-2, Chapman and Hall, 19-38. Shen, W., Maturana, F. and Norrie D. H. (1 998). Learning in Agent-Based Manufacturing Systems. Proceedings of AI and Manufacturing Research Planning Workshop, Albuquerque, NM, AAAI Press, 177-183. Shultz, C. R. (1989). An expediting heuristic fo r the shortest processing time dispatching rule. International Journal of Production Research, 27, 31-41.

PAGE 123

107 Sikora, R. and Shaw, M.J. (1997). Coordinati on mechanisms for multi-agent manufacturing systems: applications to integr ated manufacturing scheduling. IEEE Transactions on Engineering Management, 44, 175-187. Sikora, R. and Shaw, M.J. (1998). A multiagent framework for the coordination and integration of information systems. Management Science, 44, 65-78. Subbu, R. and Sanderson, A. C. (2004). Ne twork-based distributed planning using coevolutionary agents: architecture and evaluation. IEEE Transactions on Systems, Man and Cybernetics, Part A, 34, 257-269. Subramaniam, V., Lee, G. K., Hong, Y. S., Wong, Y. S. and Ramesh, T. (2000). Dynamic selection of dispatching ru les for job shop scheduling. Production Planning & Control, 11, 73-81. Sun, D. and Lin, L. (1994). A dynamic job s hop scheduling framework: a backward approach. International Journal of Production Research, 32, 967-985. Tagawa, S. (1996). A new concept of job shop scheduling system –– hierarchical decision model. International Journal of Production Economics, 44, 17-26. Tardif, V. and Spearman, M. L. (1997). Diagnos tic scheduling in a finite capacity environment. Computers and Industrial Engineering, 32, 867–878. Thomalla, C. S. (2001). Job shop schedul ing with alternative process plans. International Journal of Production Economics, 74, 125-134. Usher, J. M. (2003). Negotiation-based routi ng in job shops via collaborative agents. Journal of Intelligent Manufacturing, 14, 485-499. Ventura, J. A. and Radhakrishnan, S. (2003) Single machine scheduling with symmetric earliness and tardiness penalties. European Journal of Operational Research, 144, 598612. Vepsalainen, A. P. J. and Morton, T. E. (1987) Priority rules for jo b shops with weighted tardiness costs. Management Science, 33, 1035-1047. Vepsalainen, A. P. J. and Morton, T. E. (1988) Improving local priority rules with global leadtime estimates: A simulation study. Journal of Manufacturi ng and Operations Management, 1, 102-118. Vig, M. M. and Dooley, K. J. (1991). Dynamic rules for due date assignment. International Journal of Production Research, 29, 1361–1377. Vig, M. M. and Dooley, K. J. (1993). Mixing static and dynamic estimates for due date assignment. Journal of Operations Management, 11, 67–79.

PAGE 124

108 Wang, D., Fang, S.-C. and Hodgson,T. J. (1998). A fuzzy due-date bargainer for the make-toorder manufacturing systems. IEEE Transactions on Systems, Man and Cybernetics, Part C, 28, 492-497. Wang, D., Fang, S.-C. and Nuttle, H. L. W. ( 1999). Soft computing for multicustomer due-date bargaining. IEEE Transactions on Systems, Man and Cybernetics, Part C, 29, 566-575. Weeks, J.K. (1979). A simulation study of predictable due dates. Management Science, 25, 363–373. Wein, L. M. and Chevalier P. B. (1992). A broa der view of the job-shop scheduling problem. Management Science, 38, 1018-1033. Weintraub, A. J., Cormier, D., Hodgson, T. J ., King, R. E., Wilson, J. and Zozom, Jr. A. (1999). Scheduling with alternatives: a link between process planning and scheduling. IIE Transactions, 31, 1093-1102. Weiss, G. and Sen, S. (1995). Adaptation and Learning in Multi-Agent Systems. Lecture Notes in Artificial Intelligence, 1042, Springer-Verlag. Wu, S. H., Fuh, J. Y. H. and Nee, A. Y. C. (2002). C oncurrent process planning and scheduling in distributed virtual manufacturing. IIE Transactions, 34, 77-89. Wu, Z. and Li, L. (2003). Case-based reason ing for breast cancer prognosis: a web-based multiagent scheme. Proceedings of the World Congress on Medical Physics and Biomedical Engineering. Sydney, Australia. Wu, Z., Weng, M. and Ren, H. (2003). A fuzz y analytic hierarchy pr ocess based scheduling and control system. Proceedings of the 13th Intern ational Conference on Flexible Automation & Intelligent Manufacturing. Tampa, Florida, 62-68. Wu, Z. and Weng, M. (2005). Multiagent sche duling method with earliness and tardiness objectives in flexible job shops. IEEE Transactions on Systems, Man and Cybernetics, Part B, 35, 293-301. Wu, Z. and Weng, M. (2005). Dynamic due date setting and shop scheduling for make-to-order companies. Proceedings of the 2005 Industrial Engineering Research Conference, Atlanta, Georgia. Wu, Z. and Weng, M. (2005). Multiagent-bas ed workload control for make-to-order manufacturing. International Journal of Production Research, submitted. Yen, B. P.-C. and Wu, O. Q. (2004). Internet scheduling environment with market-driven agents. IEEE Transactions on Systems, Man and Cybernetics, Part A, 34, 281-289. Yoon, S. H. and Ventura, J. A. (2002). Minimizi ng the mean weighted absolute deviation from due dates in lot-streami ng flow shop scheduling. Computers and Operations Research, 29, 1301-1315.

PAGE 125

109 Zapfel, G. and Missbauer, H. (1993). New c oncepts for production planning and control. European Journal of Operational Research, 67, 297-320. Zhao, X., Nakashima, K. and Zhang, Z. G. ( 2002). Allocating kanbans for a production system in a general configuration with a new control strategy. IEEE Transactions on Systems, Man and Cybernetics, Part A, 32, 446-452. Zhu Z. and Heady, R. B. (2000). Minimizing th e sum of earliness/tard iness in multi-machine scheduling: a mixed integer programming approach. Computers and Industrial Engineering, 38, 297-305. Zhu, Z., and Meredith, P. H. (1995). Defining critical elements in JIT implementation: a survey. Industrial Management and Data Systems, 95, 21-28. Zozom, Jr. A., Hodgson, T. J., Ki ng, R. E., Weintraub, A. J. a nd Cormier, D. (2003). Integrated job release and shop-floor scheduling to minimize WIP and meet due-dates. International Journal of Production Research, 41, 31-45.

PAGE 126

About the Author Zuobao Wu received the Bachelor’s and Master’s degrees from Nanjing University of Science and Technology, Nanjing, China, in 198 5 and 1987, respectively, and the Ph.D. degree in mechanical engineering from Zhejiang Univ ersity, Hangzhou, China, in 1995. From 1995 to 2000, he was with the National CIMS Engineer ing Research Center, Tsinghua University, Beijing, China, as an Associate Professor. From 2000 to 2001, he was with the Department of Industrial Engineering at Texas Tech Universi ty, Lubbock, TX, as a Research Associate. He has published over 40 refereed journal a nd conference papers in production planning and control, scheduling, multi-agent systems, c oncurrent engineering and computer integrated manufacturing. He is also the author of one book and two book chapters. He is a member of IIE.


xml version 1.0 encoding UTF-8 standalone no
record xmlns http:www.loc.govMARC21slim xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.loc.govstandardsmarcxmlschemaMARC21slim.xsd
leader nam Ka
controlfield tag 001 001670332
003 fts
005 20051216093254.0
006 m||||e|||d||||||||
007 cr mnu|||uuuuu
008 051115s2005 flu sbm s000 0 eng d
datafield ind1 8 ind2 024
subfield code a E14-SFE0001193
035
(OCoLC)62277780
SFE0001193
040
FHM
c FHM
049
FHMM
090
T56 (Online)
1 100
Wu, Zuobao.
0 245
Multi-agent workload control and flexible job shop scheduling
h [electronic resource] /
by Zuobao Wu.
260
[Tampa, Fla.] :
b University of South Florida,
2005.
502
Thesis (Ph.D.)--University of South Florida, 2005.
500
Includes vita.
504
Includes bibliographical references.
516
Text (Electronic thesis) in PDF format.
538
System requirements: World Wide Web browser and PDF reader.
Mode of access: World Wide Web.
Title from PDF of title page.
Document formatted into pages; contains 126 pages.
520
ABSTRACT: In the make-to-order (MTO) industry, offering competitive due dates and on-time delivery for customer orders is important to the survival of MTO companies. Workload control is a production planning and control approach designed to meet the need of the MTO companies. In this dissertation, a multi-agent workload control methodology that simultaneously deals with due date setting, job release and scheduling is proposed to discourage job early or tardy completions. The earliness and tardiness objectives are consistent with the just-in-time production philosophy which has attracted significant attention in both industry and academic community. This methodology consists of the order entry agent, job release agent, job routing and sequencing agent, and information feedback agent. Two new due date setting rules are developed to establish job due dates based on two existing rules. A feedback mechanism to dynamically adjust due date setting is introduced.Both new rules are nonparametric and easy to be implemented in practice. A job release mechanism is applied to reduce job flowtimes (up to 20.3%) and work-in-process inventory (up to 33.1%), without worsening earliness and tardiness, and lead time performances. Flexible job shop scheduling problems are an important extension of the classical job shop scheduling problems and present additional complexity. A multi-agent scheduling method with job earliness and tardiness objectives in a flexible job shop environment is proposed. A new job routing and sequencing mechanism is developed. In this mechanism, different criteria for two kinds of jobs are proposed to route these jobs. Two sequencing algorithms based on existing methods are developed to deal with these two kinds of jobs.The proposed methodology is implemented in a flexible job shop environment. The computational results indicate that the proposed methodology is extremely fast.
590
Adviser: Michael X. Weng.
653
Due date.
Multi-agent method.
Make-to-order.
Production planning and control.
Manufacturing systems.
690
Dissertations, Academic
z USF
x Industrial Engineering
Doctoral.
773
t USF Electronic Theses and Dissertations.
4 856
u http://digital.lib.usf.edu/?e14.1193