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Multi-criteria decision making in outpatient scheduling

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Title:
Multi-criteria decision making in outpatient scheduling
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English
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Iezzi, Jana
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University of South Florida
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Tampa, Fla
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Subjects / Keywords:
Healthcare
Clinic
Waiting time
Eigenvector method
Simulation
Dissertations, Academic -- Engineering Management -- Masters -- USF   ( lcsh )
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bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

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Abstract:
ABSTRACT: Hospital ambulatory patients are seen in outpatient departments (OPDs) located in the hospital. 83.3 million visits were made to these departments in 2002. Many sources of patient waiting time exist including: poor coordination of information, inefficient scheduling, inaccurate time estimation and others. Well-designed and executed patient scheduling has the potential to remedy some of these problems. To properly schedule patients, variability in demand must be addressed. Patients may cancel appointments, arrive late and arrive without appointments. We address this problem based on a Multi-attribute Decision Making (MADM) approach. Decision models are developed using the Simple Additive Weighting (SAW) method to address scheduling decisions for late-arrival and walk-in patients and the operational decision of calling back patients from the waiting room.The models are developed as part of a case study at H.^ Lee Moffitt Cancer Center and tested in a single-clinic computer simulation against the current clinic system decision process with respect to various performance measures.The proposed decision models successfully made walk-in and late patient scheduling decisions. The contributions of this research include identifying, defining and weighting of relevant decision making criteria at H. Lee Moffitt. Our decision models guaranteed all of the defined criteria are included every time a walk-in or late patient decision must be made. Based on the findings, implementation of the models with no reduction in number of patients would improve scheduling and operational decisions while not affecting clinic output measures.Using criteria to restrict the number of late and walk-in patients, on average, the clinic closed between 36.20 minutes and 47.95 minutes earlier. However, practitioner and room utilization suffered.^ ^The tradeoff among number of patients seen, resource utilization, waiting time and clinic close time should be considered but cannot be fully assessed solely on the information gathered in this research. As a case study of H. Lee Moffitt Cancer Center, the decision models successfully incorporated all relevant patient criteria without adversely affecting the clinic system. Future research is needed to better understand what factors will impact system measures and expand the decision models to other outpatient clinic settings.
Thesis:
Thesis (M.S.E.M.)--University of South Florida, 2006.
Bibliography:
Includes bibliographical references.
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Mode of access: World Wide Web.
Statement of Responsibility:
by Jana Iezzi.
General Note:
Title from PDF of title page.
General Note:
Document formatted into pages; contains 126 pages.

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aleph - 001919597
oclc - 184903355
usfldc doi - E14-SFE0001817
usfldc handle - e14.1817
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ABSTRACT: Hospital ambulatory patients are seen in outpatient departments (OPDs) located in the hospital. 83.3 million visits were made to these departments in 2002. Many sources of patient waiting time exist including: poor coordination of information, inefficient scheduling, inaccurate time estimation and others. Well-designed and executed patient scheduling has the potential to remedy some of these problems. To properly schedule patients, variability in demand must be addressed. Patients may cancel appointments, arrive late and arrive without appointments. We address this problem based on a Multi-attribute Decision Making (MADM) approach. Decision models are developed using the Simple Additive Weighting (SAW) method to address scheduling decisions for late-arrival and walk-in patients and the operational decision of calling back patients from the waiting room.The models are developed as part of a case study at H.^ Lee Moffitt Cancer Center and tested in a single-clinic computer simulation against the current clinic system decision process with respect to various performance measures.The proposed decision models successfully made walk-in and late patient scheduling decisions. The contributions of this research include identifying, defining and weighting of relevant decision making criteria at H. Lee Moffitt. Our decision models guaranteed all of the defined criteria are included every time a walk-in or late patient decision must be made. Based on the findings, implementation of the models with no reduction in number of patients would improve scheduling and operational decisions while not affecting clinic output measures.Using criteria to restrict the number of late and walk-in patients, on average, the clinic closed between 36.20 minutes and 47.95 minutes earlier. However, practitioner and room utilization suffered.^ ^The tradeoff among number of patients seen, resource utilization, waiting time and clinic close time should be considered but cannot be fully assessed solely on the information gathered in this research. As a case study of H. Lee Moffitt Cancer Center, the decision models successfully incorporated all relevant patient criteria without adversely affecting the clinic system. Future research is needed to better understand what factors will impact system measures and expand the decision models to other outpatient clinic settings.
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PAGE 1

Multi-Criteria Decision Making in Outpatient Scheduling by Jana Iezzi A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Engineering Management Department of Industrial and Ma nagement Systems Engineering College of Engineering University of South Florida Major Professor: Jos L. Zayas-Castro, Ph.D. Michael Weng, Ph.D. Kingsley Reeves, Ph.D. Grisselle Centeno, Ph.D. Date of Approval: October 30, 2006 Keywords: healthcare, clinic, waitin g time, eigenvector method, simulation Copyright 2006, Jana Iezzi

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ii Table of Contents List of Tables v List of Figures vii Abstract viii Chapter One Introduction 1 1.1 Patient Priority and Appointment Assignment Models for Outpatient Scheduling Decisions 5 1.2 Research Objective 6 1.3 Organization of Paper 7 Chapter Two Literature Review 8 2.1 System Modeling in Healthcare 8 2.2 Resource Scheduling 9 2.3 Patient Scheduling 10 2.4 Multi-criteria Decision Making 13 2.5 Multi-attribute Deci sion Making 14 2.5.1 Comparison of MADM Methods 15 2.5.2 Comparison of Weighting Methods 17 2.5.3 Saaty’s Method 18 Chapter Three Problem Statement and Approach 21 3.1 Approach 21 3.2 Criteria Generation 22 3.3 Determination of Attribute Weights 23 3.3.1 The Fundamental Scale 24 3.3.2 The Eigenvector Method 25 3.3.3 A Numerical Example 27 3.3.4 Consistency Index and Ratio 28 3.3.5 Synthesizing Judgment Matrices 29 3.4 Relative Performance Values 30 3.5 Score and Rank Alternatives 32 Chapter Four Criteria Genera tion and Weight Results 34 4.1 Criteria Generation 36 4.2 Determination of Relative Weights 38 4.3 Relative Value Calculations 41

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iii 4.3.1 Decision #1 Relative Values and Model 43 4.3.2 Decision #2 Relative Values and Model 44 4.3.3 Decision #3 Relative Values and Model 45 Chapter Five Simulation Logic 47 5.1 Entities 48 5.1.1 Scheduled Patient Entities 48 5.1.2 Walk-in Patient Entities 53 5.1.3 Other Task Entities 54 5.2 Resources 54 5.3 Patient Entity Arrivals and Schedule Creation 55 5.4 Schedule Block Variables Sub-model 57 5.5 Scheduled Patient Arrival to Clinic System 60 5.6 Appointment Assignment a nd Urgent Patients 60 5.7 Processing 62 5.8 Priority 1 Assignment a nd Urgent Patients 63 5.9 Appointment Assignment for Late and Walk-in Patients 66 5.10 Waiting Room Queue and Priority 2 Assignment 69 5.11 Verification and Validation 70 Chapter Six Simulation Results 71 6.1 Analysis of Simulation Variables 72 6.2 Analysis of Variance a nd Setting Selection 73 6.3 Clinic Simulation Output Analysis 78 6.3.1 Clinic Simulation Model Analysis 79 6.3.2 Clinic and Current System Model Comparison 82 Chapter Seven Conclusions and Future Work 89 7.1 H. Lee Moffitt Case Study Conclusions 90 7.2 H. Lee Moffitt Case Study Assumptions and Conditions 91 7.3 Other Applications 92 7.4 Future Work 93 References 95 Appendices 100 Appendix A: Moffitt Clinic Observations 101 Appendix B: Interviews with 3rd floor Clinic Nurses 108 Appendix C: Responses from Clinic Operations Managers Meeting 110 Appendix D: Appointment Assignment Ru les for Late and Walk-in Patients 112 Appendix E: Original Survey 113 Appendix F: Final Survey 118 Appendix G: Simulation Data 123

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iv Appendix H: Simulation Variables 124 Appendix I: Gantt Charts 125

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v List of Tables Table 2.1 Comparisons within Several Weighting Methods 19 Table 3.1 The Fundamental Scale 24 Table 4.1 Criteria Definitions 39 Table 4.2 Weight Results: Original Survey 39 Table 4.3 Survey Sample Size and Distribution 40 Table 4.4 Final Weights 40 Table 4.5 Scaled Values for Criteria 41 Table 4.6 Scaled Values for Distance Traveled Criteria 42 Table 6.1 ANOVA Results 74 Table 6.2 Setting R2 L20 A90 ANOVA Results 75 Table 6.3 Setting R3 L20 A15 ANOVA Results 76 Table 6.4 Setting R2 L20 A90 Average Output Range 77 Table 6.5 Setting R3 L20 A15 Average Output Range 77 Table 6.6 Clinic Model Average Output s: All Settings 80 Table 6.7 Clinic and Current System Model Average Output Comparison 84 Table 6.8 Clinic and Current System Model Variance Comparison 85 Table 6.9 Clinic and Current System Model Comparison with Reduced Patients: Average Output 86 Table E.1 Criteria Table for Factor Comp arisons: Original Survey 113

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vi Table E.2 Factor Definitions: Or iginal Survey 114 Table F.1 Criteria Table for Factor Co mparisons: Final Survey 118 Table F.2 Factor Definitions: Final Survey 119 Table G.1 Add-on Patients, October 2005 123

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vii List of Figures Figure 2.1 A Taxonomy of MADM Methods 15 Figure 4.1 Decision Flow Diagram 37 Figure 5.1 Patient Arrival Data 49 Figure 5.2 Arrival Data Distribution Summary 49 Figure 5.3 Schedule Block Variables Submodel: Block Definition 58 Figure 5.4 Calculation of Schedule Bl ock Variables 58 Figure 5.5 Schedule Block Variables Assignment 59 Figure 5.6 Priority 1 Assignment 64 Figure 5.7 Assign New Appointment Sub-mo del: Block Definition 67 Figure 5.8 New Appointment Assi gnment 68 Figure 5.9 Priority 2 Score Recalculation 70 Figure 6.1 Priority Criteria vs. Clinic Close Time 81 Figure I.1 Setting R2 L0 A15 Gantt Chart 125 Figure I.2 Setting R2 L0 A90 Gantt Chart 126

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viii Multi-Criteria Decision Making in Outpatient Scheduling Jana Iezzi ABSTRACT The healthcare industry ha s found itself in need of improvement, both financially and with respect to patient satisfaction. Hosp ital ambulatory patients are seen in outpatient departments (OPDs) located in the hospital. 83.3 million visits were made to these departments in 2002. A survey of outpati ents listed affordability, waiting time and coordination of care as their measures of quality. Many sources of patient waiting time exist including: poor coordination of inform ation, inefficient scheduling, inaccurate time estimation and others. Well-designed and exec uted patient scheduling has the potential to remedy some of these problems. To properly schedule patients, variability in demand must be addressed. Patients may cancel appointments, arrive late and arri ve without appointments. Therefore, daily decisions must be made to handle these condi tions. We address this problem based on a Multi-attribute Decision Ma king (MADM) approach. Decision models are developed using the Simple Additive Weighting (SAW) method to address scheduling decisions for late-arrival and walk-in patients and the ope rational decision of calling back patients from the waiting room. The models are developed as part of a case study at H. Lee Moffitt Cancer Center. The models are tested in a single-clinic co mputer simulation against the current clinic

PAGE 9

ix system decision process with respect to va rious performance measures: waiting time, number of patients seen, clinic close tim e, and room and practitioner utilization. The proposed decision models (PPM and AAM ) successfully made walk-in and late patient scheduling decisions as well as modified the sequence in which patients were called back. When there was no reduction in number of patients, our models performed the same as the current system. The contributions of this research include identifying, defining and weighting of relevant decision making criteria at H. Lee Moffitt. Our decision models guaranteed all of the defined cr iteria are included every time a walk-in or late patient decision must be made. Based on the findings implementation of the PPM and AAM with no reduction in number of patients would im prove scheduling and operational decisions while not affecting clinic output measures. Using criteria to restrict the number of late and walk-in patients, on average, the clinic closed between 36.20 minutes and 47.95 minutes earlier. Waiting time was also discussed. However, practitioner and r oom utilization suffered. The tradeoff among number of patients seen, resource utilization, waiting time and clinic close time should be considered but cannot be fully assessed solely on the information gathered in this research. As a case study of H. Lee Moffitt Cancer Ce nter, the decision models successfully incorporated all relevant patient criteria w ithout adversely affecti ng the clinic system. Future research is needed to better understand what factors will impact system measures and expand the decision models to ot her outpatient clinic settings.

PAGE 10

1 Chapter One Introduction The United States healthcar e industry, consisting of almost 5,800 hospitals in 2002, is a complex industry utiliz ing a considerable amount of resources. In that same year, the US national healthcare expenditures totaled more than $1.5 trillion. This was a 9.3% increase from 2001. The US allocates a larger portion of its gross domestic product (GDP) to health than any other major i ndustrialized country; 14.9% of the GDP was spent on health in 2002. Of the $1.5 trillion spent that year, 31 % was hospital care expenditures and 22% physician services. Co mmunity hospital expenses increased at an average annual rate of 8% between 2000 and 2002 (Health, United States, 2004). There are a variety of methods for provi ding healthcare servic es in the US, of which ambulatory medical care is domina nt. Ambulatory care is medical services provided as an outpatient. Services can incl ude diagnosis, treatment and rehabilitation. Hospital ambulatory patients are seen in outpa tient departments (OPDs) and represent 9% of all ambulatory care in the US. This is a substantial amount considering 83.3 million visits were made to hospital OPDs in 2002. Clinics are a type of OPD where ambulatory medical care is provided under the supervisi on of a physician. Clinics providing only ancillary services, such as radiology, are not included in the OPD survey (Hing and Middleton, 2004).

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2 OPD visits have multiple characteristics, making them complicated in nature. The provider who sees the patient, the type of visit, continuity of care and the continued treatment of patients over time ar e all traits. The majority of patients will see a physician (i.e., staff physician, resident/i ntern or other physician) at their visit, approximately 80.4%. However, the number of visits to residents/interns decr eased by half between 1992 and 2002. This may be attributed to the 47% increase in OPD visits involving midlevel providers (physician assistants or nurse practitioners ) (Hing and Middleton, 2004). Healthcare services now have a mixt ure of providers, also referred to as practitioners, to coordinate for patient visits. OPD visits may be classified in two ways: episode of care and the type of visit. The episode of care distinguishes whether the patient has an initial or follow-up visit. Injury-related, diagnostic and screening, counse ling/education and medical therapy are all types of visits for which a patient may be seen (Hing and Middleton, 2004). Both the episode of care and the visit type contribute to the va riability in healthca re service time. Another contributing factor to OPD service is continuity of ca re. Continuity of care is defined as follows (Hing and Middleton, 2004). “A goal of healthcare achieved through an interdisciplinary process involving patients, families, healthcare professionals and providers in the management of a coordinated plan of care. Based on the changing needs and available resources, the process optimizes outcomes in the health status of patients. It ma y involve professionals from many different disciplines within multiple systems”.

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3 OPDs must operate within a hospital sy stem, coordinating time and resources to provide quality care to patients. The dynamics of a hospital system add another level of complexity to OPD services. Healthcare providers often treat a patient recurrently. OPDs assess the need for continued care after each visit. The patient ma y be asked to return to the same OPD or be referred to another. In 2002, 63.3 % of all OPD visits were told to return by appointment and 12.7% referred to another physic ian or clinic. It is possibl e for one OPD visit to have multiple follow-up options (Hing and Middleton, 2004). The scheduling of patient visits is another difficulty faced by healthcare services. In addition to tackling the preexisting difficulties faced by healthcare services (variability of services, coordi nation of multiple resources etc. ), the healthcare industry is under pressure for improvement. These pr essures arise from two areas: financial necessity and patient satisfac tion. Hospitals that are unabl e to make their OPDs more cost-effective are finding themselves in a fi nancially undesirable pos ition. Healthcare services need to reduce costs for their patie nts and improve quality (Cayirli and Veral 2003, Rohleder and Klassen 2002). Rising he althcare costs and dissatisfaction with quality has made productivity improvements criti cal to survival in this industry (Ho and Lau, 1992). The issue of quality is important to consider from the patient perspective. Patients are the customers of healthcare servic es and their satisfacti on is also vital to success. Patients listed affordability, waiting time and coordination of care as measures of quality (Sofaer and Firminger, 2005). Waiting time in particular is a common complaint among patients. A lack of coordination exists between the scheduled appointment time and the time a patient is actua lly seen by the provider. Patient waiting

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4 time and waiting room congestion are two el ements of quality, which can assess the appointment time and time called to see th e provider discrepancy (Robinson and Chen 2003, Cayirli and Veral 2003). Many sources of patient waiting time exist. It can be caused by poor coordination of information, inefficient scheduling of resour ces, inaccurate time estimation or others. Well-designed and executed patient sche duling has the potential to remedy these problems. A well-designed patient schedule is a necessary start, but is not enough to effectively see patients and u tilize resources. Sin ce clinic patients cancel appointments, arrive late and arrive without appointments, daily decisions must be made to handle these conditions. Much work has been done in the area of schedule construction, which is explained further in Chapter 2. This research, however, addr esses scheduling operations. Our goal is to accommodate variable patien t demand and conditions, allowing patients to be seen as close to appointment time as possi ble. We suggest two models for operational decisions to improve scheduling, a patient prio rity and a scheduling assignment model. Establishing patient priority ha s been explored to some exte nt in the literature. Three levels of priority are assigned in Risi ng, Baron and Averill (1973) to emergency, previously scheduled and walk-in patients, list ed in decreasing order. Our work is more extensive, considering key f actors that influence patient priority and the relative importance of each. The appointment assignm ent model addresses late-arrival and walkin patient same-day appointment assignments This is different than the patient scheduling literature, which typi cally schedules all patients an d in advance. Both models are dynamic, changing with the conditions of the system. Our models are explained further in the next section.

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5 1.1 Patient Priority and Appointment Assi gnment Models for Outpatient Scheduling Decisions We propose two models, a Patient Prio rity Model (PPM) and an Appointment Assignment Model (AAM), designed to help ou tpatient clinic staff make the best sameday patient scheduling decisions by using a scor e. Same-day scheduling is the scheduling of patients, who do not have a preexisting appointment that day or have missed his/her appointment. Specifically, the following two scenarios are addressed. At a given point in time, there are patients waiting to be seen in a clinic. Changes occur to the existing state of the c linic waiting room under two conditions: 1. A walk-in or late arrival patient arrives at the clinic. A decision must be made as to whether or not the patient can be accepted into the clinic that day. If the patient is accepted, then an approximate time for th e patient to be seen by the practitioner must be assigned. This time is referred to as his / her appointment time. If the patient is not accepted, they are sent home. 2. A practitioner becomes available. A decision must be made as to which waiting patient is seen next. In th is research, practitioner refers to those individuals with whom patients schedule appointments (e.g., medical doctor, surgeon, nurse practitioner etc.). The models consider factors found to influe nce routine patient sc heduling decisions in outpatient clinics. Staff interviews and pa tient shadowing is used to determine the factors. This is a Multi-Attribute Decisi on Making problem, a sub-set of Multi-Criteria Decision Making, which is associated with multiple attributes, also referred to as goals or decision criteria (Trian taphyllou, 2000).

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6 Relative weights are estab lished for each factor th rough the eigenvector method, used in the Analytic Hierar chy Process. Relative values of each factor are also incorporated. The weights and values are us ed to determine a priority score for each patient at a given point in tim e in the PPM, while a similar score is used to select an appointment assignment time in the AAM. In this research, we will assume deterministic data and a single decision maker (DM). Decisions will be made only using the in formation available at that point in time. The factors are representative of an outpatient clinic within a hospital. 1.2 Research Objective Our objective is to provide decision making models that will a ssist daily clinic scheduling decisions with respect to same-day scheduled patients by: 1. Data collection of the process thr ough patient shadowing and time study 2. Identification of key decision making factors 3. Determination of factor levels 4. Administration of survey to clinic staff 5. Computation of relative weight s and values for each factor 6. Validate models through a singleclinic computer simulation The goal of our models is to effectively acco mmodate late-arrival and walk-in patients considering waiting time, resource utilization, overtime and the total number of patients seen each day.

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7 1.3 Organization of Paper The remainder of this thesis is organized in six chapters. Chapter 2 reviews the healthcare modeling and schedul ing literature with an emphasis on outpatient scheduling. Multi-criteria decision making is also discussed. In Chapter 3, the problem statement and research approach is presented. Results of the relative weights a nd development of the models is shown in Chapter 4. Simulation l ogic and results are presented in Chapters 5 and 6 respectively. Conclusion and futu re work are discussed in Chapter 7.

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8 Chapter Two Literature Review Research has been developi ng in all areas of healthcar e including: diagnosis, treatment and operations. This thesis is concer ned with the later. We will review the use of modeling techniques in the healthcare indus try and then more spec ifically, scheduling. Decision-making and its application to health care is also discussed. This review will demonstrate the opportunity for decisionmaking techniques to improve patient scheduling. 2.1 System Modeling in Healthcare An overview of healthcare modeling is presented in Vissers (1998a). The applications within healthcare for modeling include, but are not limited to: disease prevention, capacity planning, estimating future resource needs, appointment systems and staff scheduling. Vissers reviews healthcare on the national, regional and local level as well as from different perspectiv es (e.g. process-oriented). Two popular modeling techniques in hea lthcare are queuing a nd simulation. The following examples use simulation to model a h ealthcare system. First, Sepulveda et al. model a cancer treatment cente r using ARENA (1999). The purpose of the model is to analyze and improve patient flow in an existi ng outpatient system and then to convert the model to a new building. In Baesler and Sepulveda (2001), the cancer treatment center

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9 work presented in Sepulveda et al. (1999) is continued. Baesler and Sepulveda (2001) explains in more depth the development of a multi-objective optimization heuristic integrated with their simulation. The methodol ogy is presented and integrates simulation, goal programming and genetic algorithms. Simulation has also been used to model a family practice hea lthcare clinic found in Swisher et al. (2001). The authors build a simulation, which included a theoretical centralized information center and a single clinic. De Angelis, Felici and Impelluso (2003) applied simulation to model another heal thcare system, a transfusion center. This thesis addresses management decision-making a nd provides an analysis of alternatives to produce best solutions. Further review of computer simulation modeling in the healthcare industry can be found in Fone et al. (2003). Our wo rk is based in healthcare scheduling. A review of resource and patient scheduling follows. 2.2 Resource Scheduling The healthcare scheduling literature en compasses several areas. Resource scheduling is one area that has been pur sued over the years, nurse scheduling in particular. Several authors have studied operations resear ch, work analysis and other mathematical tools to further nurse sche duling: (Soliman 1997, Millar and Kiragu 1999, Abernathy et al. 1973, Warner and Pr awda 1972, Jaumard, Semet and Vovor 1998, Ferland 2001, Miller, Pierskalla and Rath 1976 and Warner 1976) Although nurse scheduling is a highly reviewed topic, th e scheduling of other resources such as emergency room physicians is also studied (Carter and Lapierre, 2001). Resource scheduling in healthcare extends beyond staff scheduling. The scheduling of beds, staff

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10 and rooms is addressed in Vissers (1998b) a nd Harper (2002). Vari ous bed-reservation schemes are evaluated in Kim et al. (2000), whic h look at beds in an intensive care unit. Another area of healthcare scheduling is patient scheduli ng. The scheduling decisions addressed this research are with respect to th e patients, therefore we review some of the patient scheduling literature. 2.3 Patient Scheduling Patient scheduling still contains a rang e of applications. Denton and Gupta (2003) and Everett (2002), for ex ample, address the scheduling of elective surgeries. The scheduling of patient tests is al so found in the literature. Th e scheduling of tests involves the coordination of resources, medical condi tions and the patient (Kokkotos, Ioannidis and Spyropoulos 1997). Since our case study is a cancer center clin ic, our work is concentrated in outpatient clinic appointm ents. Outpatient appointment scheduling literature follows. Some common themes have been found in the outpatient sche duling literature. Simulation and queuing models are frequently used. The outpatient scheduling literature reviewed in this thesis use simulation, queui ng models or both in their work. Similarly, cost, throughput, resource utiliz ation and particularly wait time are common performance criteria. The balance of physic ian idle time and patient wa it time is repeated throughout the literature and service time and arrival pa tterns are often considered as sources of variation. Different approaches can be taken to an appointment-scheduling problem. A simulation was built to model a two-room clin ic (Lehaney, Clarke and Paul 1999). The

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11 authors take a soft systems approach to reduce wait time and the number of no-show patients. A more quantitative approach is used in Robeinson and Chen (2003). Their objective is to minimize the weighted sum of patient waiting time and physician idle time. A heuristic is developed that perfor ms within 2% of the optimal policy. Random service time is considered, how ever the authors assume the patient schedule is known. Brahimi and Worthington (1991) and Wo rthington and Brahimi (1993) evaluated the appointment system of seven “plaster check ” clinics. These clin ics see patients who have previously attended the Emergency R oom. Time study data is gathered and a queuing model approach is used. The objec tive is to balance patient wait time and physician idle time. This work takes no-show patients into account and improves patient wait time by varying the patient queue at the st art of the day. An additional point is made in this work, the concept of physician beha vior. Due to the nature of healthcare organizations, environmental factors such as no-show patients and the number of patients per session are often addressed in outpatient scheduling research. Ho and Lau (1992) consider 27 combinat ions of three environmental factors; probability of a no-show, coefficient of variation of service time and number of customers per service session. Nine sc heduling rules are evaluated under these conditions. The authors tackle the cost in scheduling outpatient appointments. Their model minimizes the weighted sum of staff and patient idle time. Efficient frontiers are used to help distinguish the be st rule for a given environment. The authors continued this work in Ho and Lau (1999) where they evaluated the same environments. Service quality, facility utilization and variability of service tim es, in addition to cost are considered. Rohleder and Klassen (2002) also use cost of idle and wait times to evaluate

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12 an appointment system. This appointment system is done as a “rolling horizon” to capture the nature of scheduling, which is typically done over a period of time. Six different demand patterns, three static and three dynamic, are generated to simulate different loads of patient demand. These de mand patterns are tested with six different overloading rules, which use double booking and overtime approaches. Variability in demand have caused double booking and overtime has become a reality in many healthcare organizations, which the authors address to help clinics make the best scheduling decisions under varying conditions. Another environmental factor of outpatie nt scheduling is walk-in patients. Whether critical or not, walk-i n patients arrive to a clinic with no previously scheduled appointment. Rising, Baron and Averill (1973) discusses the impact of walk-in patients on scheduling. Patients are classified as cont rolled if they have an appointment and uncontrolled for walk-in or emergency. The auth ors analyze the daily arrival patterns and create a schedule to smooth demand over the days of the week and the hours of each day. This system is conceptualized as a comp lex queuing system and computer simulation modeling was used. The idea of a priority syst em is also incorporat ed. Three levels of priority are assigned. The highest level is assigned to emergency patients and those returning from an ancillary service. The ne xt level is previously scheduled patients and the lowest priority is assigned to walk-in patie nts. Increased patient throughput resulted. Su and Shih (2003) also deals with walk-in pati ents at outpatient cl inics. Similarly, the scheduling system is designed to lower wa it times and improve patient throughput. The authors address the case of a high level of wa lk-in patients, more than half. Scheduling policies are evaluated to impr ove already scheduled inter-arrival times with a mixed

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13 registration type appointment system. Furthe r outpatient scheduli ng literature can be found in Cayirili and Ve ral’s (2003) review. While we have found environmental factors considered in the literature, we have not found outpatient-scheduling research that addresses factors that account for the environment, patient and the external syst em. We have also not found dynamic patient priority and appointment assignment models to help make same-day patient scheduling decisions. Clearly, there is a research oppor tunity for such models. These scheduling decisions can be represented as a multi-cr iteria decision making problem. An introduction to multi-criteria decision making is presented in the following section. 2.4 Multi-criteria Decision Making The consideration of multiple factors to schedule late-arrival and walk-in patients creates a cognitive and time burden for clinic staff. Therefore, a method is needed to address these factors. The problem presented in this work can be formulated as a type of Multi-criteria decision making (MCDM) problem. MCDM is a well-establishe d branch of decision maki ng that may be used to analyze the way people make decisions or the way people should make decisions. Two classifications of MCDM exists, Multiobjective decision making (MODM) and Multiattribute decision making (MADM). MODM studies problems with a continuous decision space. An example of MODM is a mathematical programming problem with multiple objective functions. MADM addresse s discrete decision spaces where decision alternatives are predetermined. MCDM methods may be further classified by data type

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14 (deterministic, stochastic or fuzzy) and nu mber of decision makers (single or group) (Triantaphyllou 2000). MADM met hods are explored further. 2.5 Multi-attribute Decision Making Although diverse, MADM problems shar e the following ch aracteristics (Yoon and Hwang 1995): 1. Alternatives – a finite number of alternat ives are screened, prioritized and selected and/or ranked. This term is interchang eable with “option”, “policy”, “action”, “candidate” or others. 2. Multiple attributes – multiple relevant attributes for each problem. The number of attributes is problem dependant. This te rm may be interchang ed with “goals”, “criteria” or “factors” 3. Incommensurable units – different units of measurement among the attributes. 4. Attribute weights – most MADM methods require information about the relative importance of each attribute, usually in the form of an ordinal or cardinal scale. Weights may be assigned by the decisi on maker (DM) or by other methods. 5. Decision matrix – MADM problems may be expressed in a matrix format, where columns indicate attributes and rows indicate alternatives. Yoon and Hwang (1995) have also created a taxonomy of MADM methods shown in Figure 2.1. A comparison of these me thods follow in the next section.

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15 2.5.1 Comparison of MADM Methods The taxonomy illustrates a number of methods that address MADM problems with cardinal attribute information. These me thods may, however, yi eld different results when applied to the same problem. Inconsis tencies may be attributed to the following: use of weights, approach to selecting th e ‘best’ solution, scaling of objectives and introduction of additional parameters. The vari ety of methods creates the need to select the most appropriate, for which validity is stressed as the most important criterion. Validity implies that the values of the DM ar e accurately reflected in the choices. Due to the variation in how preference can be expresse d, there is no absolute objective standard of validity (Zanakis et al.1998). These methods have been compared in the literature with respect to various criteria. MADM N o information Information on Environment Information on Attribute Dominance Maximin Maximax Conjunctive Method Disjunctive Method Pessimistic O p timistic Standard Level Ordinal Cardinal Salient Feature of Information Type of Information from Decision Makers Major Class of Method Lexicographic Method Elimination by Aspect Simple Additive Weighting Weighted Product TOPSIS ELECTRE Median Ranking Method AHP Figure 2.1 A Taxonomy of MADM Methods SOURCE: Yoon and Hwang 1995, pg 6

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16 Yeh (2002) reviews the Simple Additiv e Weighting (SAW), Weighted Product (WP) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) methods. These methods were chosen because they are applicable to large-scale decision problems where the rankings produced would likely be different. They are also simple in concept and computation. The decision probl em considered is a single-level case, although the three methods are applicable to mu lti-level hierarchies. When an attribute hierarchy has more than three levels, the Analytic Hierarchy Process (AHP) should be applied. A procedure is used to determine the degree of sens itivity of each attribute to the ranking outcome of each method. TOPSIS wa s determined to be the most sensitive, matching the decision information from the d ecision matrix best. WP was found to be the least sensitive. The author also notes that no one best method can be assumed in general and a validation method is provided to identify an approach based on a specific data set. A simulation comparison of methods is pr esented in Zanakis et al. (1998). The authors review; Elimination and Choice Translating Reality (ELECTRE), TOPSIS, Multiplicative Exponential Weighting (MEW), SA W and four versions of the AHP. The decision problem considered has N criteria weights and L alternatives. Simulation parameters included number of alternatives, criteria and criteria distributions. Two performance measures are used, comparison of final weights or ra nks to the SAW method and rank reversal measures. The four AHP methods produced indistinguishable results and were always the closest method to SAW. In general as the num ber of alternatives increased, the methods produced overall weight s closer to SAW, but large discrepancies in rank. On the contrary, as the number of cr iteria decreased, differe nces in final weights

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17 were greater. With respect to rank re versal, SAW and MEW did not produce any. TOPSIS performed the next best followed by AHP. It is noted that the SAW method should be used as a standard for comparisons, giving the most acceptable results for most single-dimensional problems. Additional dimensions for method comparison are listed: simplicity, trustworthiness, robustn ess and quality. The authors also discuss the efficiency of a method as not only a result of the supporting theory or rigorousness of the math. Efficiency is also related to ease of use, user understandi ng and faith in results. These dimensions may also be applicable to revi ew weighting methods. Most MADM methods require a relative weight for each criteria and therefore, a weighting method must also be selected. 2.5.2 Comparison of Weighting Methods As in MADM methods, the weighting met hod used to assign attribute weights can also vary. Chang (2005) compares the AHP weighting method (Saaty’s method) to utility theory and the Delphi technique (see Ta ble 2.1). Hobbs (1980) compares weighting methods in power plant siting with respect to the weighting summation or linear model multi-attribute decision rule. This rule a ssumes the weights are proportional to the relative value of unit change in each attr ibute value function. This means is W1 = 2 and W2 = 4, the unit change in V1(X1) must be half as valuab le as a unit change in V2(X2). This is a condition assumed by other decisi on rules, including the SAW method. Hobbs reviews many weighting methods: Ranki ng and Categorization, Rating, Ratio Questioning, Saaty’s method and Metfessel Allocation, Indifference Trade-off method,

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18 the Churchman-Ackoff met hod, Decision Analysis Weight Selection and Observerderived techniques. Only the Indifferen ce Trade-off and Decision Analysis Weight Selection methods adhere to the propor tionality assumption. However, these theoretically valid methods are difficult to use and therefore often give inconsistent results. The ability to test consistency of judgments is a strength of Saaty’s method and is explored further in the following section. 2.5.3 Saaty’s Method The AHP is a MADM method developed by Thomas L. Saaty. It follows the descriptive theory and can accommodate either relative or absolute measurement. The AHP is used to develop ratio scales from pair wise comparisons in a multilevel hierarchy. Comparisons among these elements may be from actual measurements or the fundamental scale. The eigenve ctor formulation is used to determine relative weights of the criteria (Saaty and Vargas 2001). The literature has addressed the advantag es and disadvantages of Saaty’s method. One key advantage is that inconsistency in j udgments is allowed and able to be measured (Kamenetzky 1982). If consistency does not hold, which it often does not, the eigenvector still produces a set of priorities that ar e all acceptable approximation, allowing 10% error (Forman and Gass 2001). Kamenetzky also mentions the easy elicitation of pairwise judg ments as an advantage. Pairwise comparisons are straightforward, understandable and made effici ently. The relative judgments also tend to be more accurate than absolute ju dgments and individual comparisons.

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19 Table 2.1 Comparisons within Several Weighting Methods SOURCE: Chang 2005, pg 62 They produce ratio-scale measures, which c onvey more information than interval or ordinal scales, and dimensionless ratio-scale pr iorities when no scale exists (Forman and Gass 2001). Additionally, the synthesized inform ation contained in all possible pairwise comparisons (information redundancy) adds to the robustness of estimates (Kamenetzky 1982). The fundamental scale, also devel oped by Saaty, represen ts intensities of judgments and has also been discussed in the literature. The fundamental scale has been theoreti cally justified for the comparison of homogeneous elements. The scale provides measurement for comparisons where one wants to know what fraction X is larger than Y, not how many more times is X larger Methods Descriptions Strengths Weaknesses Utility theory Empirical modeling procedure Also use experts’ opinion for a qualitative problem structure Can present a preference function called utility function An utility function can be used as an objective function in MODM environment When a problem size becomes big, this method gives more cognitive burden than AHP method For that reason, right decision is more challenge than AHP method Delphi technique Use experts opinion with several times of interviewing or surveying Gives DM a chance to see what other DMs opinions are and how his/her opinion is different from them Relatively convenient than utility theory because an analyst dose not need any conditional types of question used in utility theory Good quality of results Asking several times for the same problem by showing other DMs opinions can forces DMs to move into median or mean values which does not need to be best solution AHP method Pairwise comparison is used Eigenvector and eigenvalue approach are used By using pairwise comparison, this method has less cognitive burdens than other two methods By using consistence index, any irrational response can be filtered to determine weights Still subjective as other two methods because this method is also dependents of experts opinion

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20 than Y. These situations occur when elemen ts are near equal (Saaty and Vargas 2001). This theory of near-equal elements came from Weber in 1846 who formulated a law regarding a stimulus of magnitude s Weber’s law states that “a change in sensation is noticed when the stimulus is increased by a c onstant percentage of the stimulus itself.” Therefore, s can be increased by s to reach the point wher e human senses can just distinguish the difference between s and s + s Then the ratio r = s / s does not depend on s itself (Saaty 1980). The scale itself has been a subject of inquir y, as has the question asked to the decision maker. The question “what fraction is X more im portant than Y?” has been considered ambiguous and in need of a reference point for the comparisons (Forman and Gass 2001, Dryer 1990). Harker and Vargas (1990) confir m that a reference point is required for pairwise comparisons. Sim ilarly, vagueness of definition is a concern for Saaty’s fundamental (verbal) scale (Donegan, D ood and McMaster 1992, Bard 1992). Donegan, Dodd and McMaster also ques tion the rounding of values to Saaty’s numbers and the assumption of least detectable differences in the numeric scale. Harker and Vargas (1990) explain the scale used only need to be bounded and compare criteria that are homogeneous with respect to it. They continue to justify the fundame ntal scale as robust, able to handle cases when errors are made. Bard (1992) notes that this method is better for individuals not familiar with decision making methods and when the majority of attributes are measured subjectively. Our research uses the SAW and Saaty’s method to build decision making models for outpatient clinic scheduling decisions. Th e model and approach follow in the next chapter.

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21 Chapter Three Problem Statement and Approach Scheduling decisions must be made when a patient arrives to a clinic late or without an appointment. Clinic staff woul d like to consider all relevant patient information when making these decisions. An effective and efficient method is needed to integrate the information and support the decision maker. At any point in time there are a given numb er of patients waiting to be seen in a clinic, where n is the total number of patient s waiting. This state can change under two conditions requiring a scheduling decision to be made: (1) patie nt i (i = 1,2,…, n) arrives without an appointment (walk-in ) or arrives after his/her a ppointment time (late arrival) and wants to be added to the existing schedul e and (2) of the n patie nts waiting, one must be selected to be seen when a practitioner becomes available. These decisions should be based on a set of factors (j = 1,2,… m) that de termine patient and appointment priority. Due to time and cognitive burden, it is not realis tic for clinical staff to consider all factors when making these decisions. Therefore, a decision model is needed for better scheduling decisions. 3.1 Approach Clinic decisions to handle late arrival and walk-in patients have been identified as a MADM problem. The approach taken follo ws problem identification, the three basic

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22 steps for utilization of a decision making tech nique and simulation. The three basic steps are as follows (Triantaphyllou 2000): 1. Determine the relevant criteria (attributes) and alternatives 2. Attach numerical measures to the relative importance of the criteria and to the impacts of the alternatives on these criteria 3. Process the numerical values to de termine a ranking of each alternative Several alternatives exist to accomplish each st ep. Criteria can be generated via various methods just as many weighting methods exist to attach measures of relative importance to each criteria. Similarly, the taxonomy of MADM methods from Chapter 2 list options to determine the ranking of alternatives. Ou r approach used interviews and observation of the clinic system to gene rate criteria. The eigenvector method was used to determine relative weights of importance and indexa tion and normalization were used to find relative performance values of each alternative with respec t to each criteria. The SAW method was chosen to score and rank each alternative. A single-clinic computer simulation tests the impact of our models on the clinic system. Steps 1, 2 and 3 are explained further in the following sections. 3.2 Criteria Generation Relevant criteria are established based on the problem definition. Criteria are generated via several methods. Literature su rvey, panel of expert s and construction of goal hierarchy are all plausible. It is recommended that a desirable list of attributes should be complete and exhaustive, contain mutu ally exclusive items a nd be restricted to performance attributes of the highest degree of importance. Once the attributes have

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23 been established, the relative importance of each must be assigned (Yoon and Hwang 1995). Although this is a vital step, formulation of criteria does not have a standard procedure. More art then science may be involved (Triantaphyllou 2000). Our approach used observation to create an in itial list of criteria followed by interviews of experts to confirm and amend the list. 3.3 Determination of Attribute Weights Weights play an important role in th e MADM process and provide valuable information. They quantitatively express with which items the DM is most concerned. Two types of attribute weighting are from ranks and ratio weighting. The simplest method is the use of ranks. Weighting from ra nks requires that the at tributes be listed in order of importance, most to least important 1 is assigned to the most important and m (the total number of attributes ) assigned to the least. Th e cardinal ranks can then be calculated from this rank. Although more di rect, the rank method can place a cognitive burden on the DM. The preferred approach is the use of pairwise judgments, which provides a complete ranking. Th is method compares two attribut es at a time and asks for the ration (importance) between them. The question asked, for example, may be “How much more important is attribute X than at tribute Y?” (n-1) pairwise comparisons are needed to assign weights for m attributes (Yoon and Hwang 1995). The study presented in Zanakis et al. ( 1998) comments on dominating and domin ated criteria (attributes). That is, once the weights have been determine d, any criteria that dominates all others or is dominated by all others is remove d. Weights are then reassessed.

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24 3.3.1 The Fundamental Scale One challenge of pairwise comparisons is how to quantify the qualitative answers provided by the DM. This can be accomplished by using a scale. A scale is simply a one-to-one mapping of a set of discrete qualitative answers for the DM to choose from and a discrete set of numerical values representing the im portance of the choice. Two scales are based on numbers derived from ps ychological theories, linear and exponential. No scale can be determined as the best for all cases of decision making problems (Triantaphyllou 2000). The linear s cale is preferred for cases w ith less then 10 entities. The fundamental scale, developed by Saaty, is a linear scale and us ed as part of our approach to determine relative weig hts of importance (see Table 3.1). The eigenvector method uses these quan tified judgments to calculate relative weights and is explaine d in the next section. Table 3.1 The Fundamental Scale Intensity of importance Definition Explanation 1 Equal Importance Two activities contribute equally to the objective 2 Weak 3 Moderate importance Experience and judgment slightly favor one activity over another 4 Moderate plus 5 Strong importance Experience and judgment strongly favor one activity over another 6 Strong plus 7 Very strong or demonstrated importance An activity is favored very strongly over another; its dominance demonstrated in practice 8 Very, very strong 9 Extreme importance The evidence favo ring one activity over another is of the highest possible order of affirmation SOURCE: Saaty and Vargas 2000, pg 6

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25 3.3.2 The Eigenvector Method To calculate the vector of weights us ing the eigenvector method, a pairwise comparison matrix A must be determined. A is an m m matrix, where m is the number of factors (attributes) being considered. Let C1, C2, …, Cn be the set of factors. A pairwise comparison of factors Ci and Cj will result in a quantified judgment aij (i, j = 1, 2, …, n), where aii for all i and aij = 1/ aji, for all i > j That is, matrix A takes the following form. 1 / 1 / 1 1 / 1 12 1 2 12 1 12 n n n na a a a a a A This matrix represents the following rule s that govern the pairwise judgments. Rule 1. If aij = then aji = 1/ 0 Rule. If factor Ci is judged to be k times as important relative to factor Cj, then aij = k and aji = 1/ k (i.e., factor Cj is judged to be 1/ k times as important relative to factor Ci). In particular, aii = 1 for all i, since factor Ci has to be exactly as important as itself. One judgment matrix will result from each DM. Multiple DMs may be surveyed and result in a synthesized judgment matrix (Saaty 1980). Ideally, aij = j iw w (for i, j = 1, 2, …, n). This w ould only occur in the case that exact measurement with wi representing the weight of i = 1, 2, …, n is available. Since

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26 quantified judgments are used, al lowances must be integrated. Deviations in the ratio aij and the number n, now denoted by max, lead to Equation 3.1. n 1 j j ij max iw a 1 w, i = 1, 2, …, n. (3.1) Deviations in aij can lead to large deviations in max and wi normally, but is not the case for the reciprocal matrix A satisfying the rule presented earlier. Associated with matrix A, there exists a stab le solution. In matrix notation, the original problem is stated in Equation 3.2 as follows. Aw = nw, (3.2) where matrix A is consistent. When considering the reciprocal matrix A', which is a variation of A created from the pairwise comparisons, the wei ght vector is a solution to Equation 3.3, where max is the largest eigenva lue of A' (Saaty 1980). A'w' = max w' (3.3) Several approximation methods exist to com pute the vector of weights. Only one gives a very good approximation according to Saaty (1980). We be gin with the single m x m matrix created from the synthesized j udgments. The values in each row are multiplied creating an m x1 column vector. Each value is now raised to the power 1/m.

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27 Next, the column vector must be normalized; linear normalization is us ed. Therefore, the sum of the m values is calculated and then each value is divided by that sum. The resulting m x1 column vector is the vector of re lative weights. A numerical example follows in the next section. 3.3.3 A Numerical Example A', created from pairwise comparison judgments, is given as 14/16/17/1 414/16/1 6415/1 7651 A' The multiplication of each row results are (210, 24/5, 1/6, and 1/168) respectively. Each value is raised to the power 1/n. In this ex ample n = 4. This results in the following. )4/1( )4/1( )4/1( )4/1(168/1 6/1 5/24 210 m = 278.0 639.0 480.1 807.3 These values now need to be normalized. The sum of the four values of m is calculated, each value is then divided by that sum. In this example, the sum is found to be approximately 6.204. After normalization, th e vector of weights is given by w

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28 6.2040.278 6.2040.639 6.2041.480 6.2043.807 w = 045.0 103.0 239.0 614.0 3.3.4 Consistency Index and Ratio One strength of the eigenvector method is the ability to calcul ate the consistency of pairwise judgments. The consistency of each matrix should be tested and deemed acceptable prior to the use of attribute weights. In a consistent matrix, the ratio of values for each pair of attributes is the same. max, the principle eigenvalue, is used to help estimate consistency. The closer max is to n (the number of activities in the matrix), the more consistent is the result. The prin ciple eigenvalue is f ound through a series of matrix multiplication. Matrix A' is multiplied on the right by the vector of weights, w. Let us call the resulting column vector z. Each value of z is divided by the corresponding value of w, creating a new vector y. Summing the values of y and taking the average gives max, shown in Equation 3.4. ii 2 1 2 12 1 12zw 1 /1/1 1/1 1n n n naa a a aa z iiiywzy

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29 n y n 1 i i max (3.4) Deviation from consistency is represented by the Consistency Inde x (CI) (see Equation 3.5). A Consistency Ratio (CR) of 0.10 or le ss is considered accepta ble. The CR is the ratio of CI to the average (Random Index) RI, the consistency index of a randomly generated reciprocal ma trix (Saaty 1980). 1 n n CImax (3.5) 3.3.5 Synthesizing Judgment Matrices The matrices of acceptable consistency n eed to be combined into one matrix before final weights can be calcula ted. For each pair of factors (Ci and Cj), the judgments will be combined using the geometric mean method. The consistency of a synthesized judgment matrix using geometric mean will be acceptable under the condition that each individual judgment matrix is acceptable (Xu 2000). Geometric mean is computed by taking the nth root of the produc t of n terms. The n terms represent the ratio judgments made a bout a specific pairwise comparison in each of the accepted matrices. For example, five experts were surveyed and each of their judgment matrices found to be consiste nt. When comparing the factors Pending information and Estimated treatment time the judgment ratios from the five experts were (5, 7, 5, 6, and 4). If all judgments are c onsidered equal, the ge ometric mean is then calculated as follows.

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30305 5 4200 4200 4 6 5 7 55 / 1 Otherwise, the judgments are combined first by staff type, weighted and then combined to a single value. Once the geometric mean has been calculated for each pairwise judgment, a single matrix will result and will be used to determine the relative weight values as explained in section 3.3. 2. (Saaty 1986, Aczel and Saaty 1983). 3.4 Relative Performance Values Criteria are not uniform. They may be described by either quantitative or qualitative information and have different uni ts of measurement. An example of these differences is the evaluation of a car based on miles/gallon and aesthe tics. If the number of qualitative attributes is much larger than quantitative, methods can be applied to convert quantitative into qualitative. Otherwise, numeri cal values can be assigned to qualitative attributes. Scaling is the preferre d approach for quantification. A Likert-type scale is often appropriate. Once all attributes are described by either data type, the values of each attribute must be normalized. This el iminates the comparison of attributes with different measurement units. To use the car example again, one would not be able to compare the cost of a car in dollars and the mileage in miles/gallon. Normalized values are dimensionless, allowing interattribute and intra-attribute comparisons (Yoon and Hwang 1995).

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31 Attributes can be classified into thre e groups, for which each has a normalization technique. The three attribute cl assifications are (Yoon and Hwang 1995): 1. Benefit attributes – the greater the attribute value, the more its preference 2. Cost attributes – the greater the at tribute value, the less its preference 3. Nonmonotonic attributes – the preferred va lue is located somewhere in the middle of the attribute range Benefit attributes can be normalized by either linear or vector normalization. Linear normalization divides the rating of an attribute by its maximu m value. The normalization of xij is given by x x rj ij ij, i = 1, …, n; j = 1, …, m (3.6) where x* j is the maximum value of the jth attribute and rij represents the normalized value. Vector normalization divides the rating of each attribute by its norm. Cost attributes can be transformed to benef it attributes by taking th e inverse of the rating (i.e., 1/ xij). Then the transformed attribute (fro m cost to benefit) follows the same normalization process (see equation 3.7). ij j ijx x r, i = 1, …, n; j = 1, …, m (3.7) The relative value, rij, is the ratio of the minimum value of the jth attribute (xj -) and the attribute value (xij).

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32 Nonmonotonic attributes are transformed to monotonic through the z score. A relative value is then obtained through one of the pr eviously mentioned nor malization processes (Yoon and Hwang 1995). 3.5 Score and Rank Alternatives The Simple Additive Weighting (SAW) method is the most commonly used MADM. A SAW score is calculated by adding th e contributions of each attribute. This is done through the multiplication of comparable ratings (relative values) and the weight of importance (weights) of each attribute, wh ich is then summed over all attributes. The SAW method is generally expressed as m 1 j ij j ir w V, i = 1,…, n (3.8) where rij is the relative attribute value obtained from the normalization process. Each alternative then given a score, Vi, which is used to rank the alternatives. The underlying assumption of the SAW met hod is the independence of attributes. This implies that the contribution of an individual attribute to the total score is independent of any other attribute values. The SAW method still produces very close results to the “true” value even when i ndependence does not completely hold. This method also has a required characteristic for weights.

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33 It is assumed that weights are proportional to the relative value of unit change: if the relationship of w2 to w1 is 2, then the DM must be indi fferent to the difference between 2 units of v2 and 1 unit of v1 (Yoon and Hwang 1995).

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34 Chapter Four Criteria Generation and Weight Results The clinics of H. Lee Moffitt Cancer Center were the source of information used to establish relevant criteria and weights of importance for scheduling late arrival and walk-in patients. H. Lee Moffitt Cancer Center is located on the campus of the University of South Florida in Tampa and has over a dozen disease-specific outpatient clinics. The Comprehensive Breast, Cutaneous Genitourinary, Senior Adult, Sarcoma, Thoacic and Gastrointestinal clinics were st udied. Although located in a hospital setting, Moffitt’s outpatient clinics function similar to a typical doctor’s office. Patients have specific practitioners (oncologist s, surgeons or others) who pr ovide treatment at the clinic visit. A clinic visit may be scheduled for a follow-up or to establish a new patient and can range in length from 15 minut es to an hour and a half. Although patients may go to the clinic fo r various reasons, all patients follow the same general process within a clinic. Patients arrive to the clinic and check-in at the front desk. The majority of patients have a schedu led appointment to see their practitioner. Those individuals without an appointment inqui re at the front desk about an appointment time. After check-in, patients will wait in the waiting room until a medical assistant calls their name. The medical assistant calls th e patient from the waiting room, performs a screening of the patient (height, weight, bl ood pressure and temper ature) and places the patient in an exam room. The nurse will see the patient next followed by the practitioner.

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35 After the visit is complete, the patient exits the exam room, checks out at the front desk and leaves the clinic. This process is consistent for the clinics at Moffitt although individual clinics differ in specialty and size. The clinic setting used in this research is modeled after the outpatient clinics of H. Lee Moffitt. Each practitioner at Moff itt has his/her own schedule of patients and personal scheduling style (e.g., new patient appointments may be 60 minutes for one practitioner and 90 minutes for another). A sing le practitioner is used in our simulation of a Moffitt clinic. Two types of patient schedules are tested, one representative of a surgeon schedule the other of an oncologist schedule. The majority of surgeon appointments are follow-ups and tend to be shorter in length than oncologist appointments. The number of exam rooms each practitioner has avai lable can range from one to many depending on the number of practi tioners in a clinic on a given day. We tested two exam rooms and three exam ro oms in our simulation model. The other resources are a single medical assistant and a single nurse. No front desk resources were included due to negligible process times. Th e process data used to create our simulation of a Moffitt clinic was collected through patient shadowing, time studies and staff interviews at the Moffitt clinics mentioned above. Further information was needed from Moffitt clinics to develop our patient priority and appointment assignment models. Clinic Operations Managers, practitioners, nurses, medical assistants and service representatives from the clinics also participated in the criteria generation and survey phases of our research. The criteria weights and values generated from the survey are used in th e following general SAW model (see equation 4.1).

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36 (4.1) (t) irepresents the priority of patient i (the score of time slot i) i = 1, 2,…, n, n is the number of patients waiting to be seen at a given point in time (n is the number of time slots remaining in the day) j = 1, 2, …, m, where m is the number of factors wj, the weight of each factor vij(t) the value of each factor The criteria, weights and values generated from the Moffitt survey for the patient priority and appointment assignment models in this re search are explained in the remainder of this chapter. 4.1 Criteria Generation Several methods were used to generate the criteria used by th e clinic staff to schedule late arrival and walk -in patients, which includes: 1. Staff interviews 2. Patient and staff shadowing 3. Expert opinion 4. Decision flow diagrams The decision flow diagram (see Figure 4.1) i llustrates the decision process and identifies three decisions made by the clinic staff. m 1 j ij j i(t) v w (t)

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37 1. Take the patient today? 2. When can the patient be seen? 3. Call back patient? The first question is a yes or no question. E ither the patient can or cannot be seen that day in the clinic. If the patie nt is able to be seen, the s econd decision is to determine the best time to schedule to patient. The first 2 decisions only pertain to late arrival and walk-in patients. The third decision determines which patient waiting in the waiting room should be called back next to an exam room. This decision considers all patients in the waiting room. Notes from interviews and staff shadowing (see Appendices A, B and C) are used to validate the decision process and list of criteria. A total of nine criteria were found for the three decisions. Figure 4.1 Decision Flow Diagram

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38 1. Distance Traveled 2. Urgency 3. Schedule disruption 4. Other appointment 5. Time to appointment time 6. Cause of delay 7. Estimated treatment time 8. Demand per practitioner 9. Pending information The definitions of each criterion are given in Table 4.1. A survey was administered to the clinic staff at H. Lee Moffitt Cancer Center. The survey results and relative criteria wei ghts are explained in the next section. 4.2 Determination of Relative Weights Two versions of our survey were administered to the clinic staff at H. Lee Moffitt Cancer Center. The original version of the survey can be found in Appendix E. The surveys were individually tested for consistenc y. Of the original surveys, six had a CR 0.24 and all six surveys were completed by nur ses. The final weight results from the original survey are shown in Table 4.2.

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39 Table 4.1 Criteria Definitions Criteria Definition Distance Traveled the time traveled by the patie nt from home to Moffitt (1 hour, 2 hours, etc.) Urgency a medical state dete rmined by clinical staff Schedule Disruption the number of patients scheduled in that same hour Other Appointment a scheduled appointment for the same day within Moffitt Time to Appointment Time the difference between the current time and the appointment time. Cause of Delay the reason the patient was late Estimated Treatment Time the appointment length predetermined by the type of visit and the physician being seen Demand per Practitioner the ratio of minutes scheduled for a given practitioner per hour Pending Information any information, such as lab results or X-rays, needed for treatment in the clinic that day Table 4.2 Weight Results: Original Survey Criteria Weights Distance traveled 0.05 Urgency 0.35 Schedule disruption 0.05 Other appointment 0.08 Time to appointment time 0.05 Cause of delay 0.07 Estimated treatment time 0.11 Demand per practitioner 0.14 Pending Information 0.10 Clearly, Urgency is a dominant factor and is therefore removed from the list or criteria. Additionally, using a CR of 0.24 was not accepta ble by literature standards (Saaty 1980, Apostolou and Hassell 2002, Chu and Liu 2002) and th e sample contained only nurses. A second survey (see Appendix F) was rest ructured to reduce consistency errors and administered. Urgency was eliminated a nd weights were calculated for the criteria of each decision. A CR of 0.10, recommended by the literature, is used. The second survey increased the sample size and the variety of staff included. The results are as follows:

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40 Table 4.3 Survey Sample Size and Distribution CR 0.10 n = 5 Decision #1 Take the patient today? 4 Pract., 1 Nurse n = 12 Decision #2 When can the patient be seen? 4 Pract., 7 Nurses, 1 MA n = 4 Decision #3 Call back patient? 4 Nurses Table 4.4 Final Weights Decision #1 Take the patient today? Decision #2 When can the patient be seen? Decision #3 Call back patient? Criteria CR 0.10 CR 0.10 CR 0.10 Distance traveled 0.28 Schedule disruption 0.46 Other appointment 0.07 0.22 Time to appointment time 0.26 Cause of delay 0.06 0.19 Estimated treatment time 0.12 0.15 Demand per practitioner 0.17 0.54 Pending information 0.30 0.18 The weight results differ for decisions #1 and #3. This could be attrib uted to the different samples. As shown in Table 4.3, the weight s for Decision #1 criteria are almost entirely based on the practitioner option. Where as th e opposite is true for Decision #3 weights, based only the nurse opinion. Since consiste ncy (CR) was tested for each question for each survey, the staff mix used for Decision 1, 2 and 3 weights are all different. All surveys were able to be used for Decision #2 we ights. When only two criteria exist, there is no test for consistency. The amount of importance placed on the factors changes with respect to the surveyed popul ation. A large difference is observed when weighting pending information, 0.30 for Decision #1 and 0.18 for Decision #3. Pending

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41 information was weighted much more heavil y when practitioners were the majority. Differences are also observed for ot her appointment and cause of delay. The nurses placed a higher importance on both of these criteria. The opinions of each staff type were also weighted based on expert opinion. P hysician opinion is weighted twice that of nurses and nurses twice that of Medical Assist ants. No service representative data was included. The score calculations require both relative weights and relative values for each criterion. Relative value computati on is explained in the next section. 4.3 Relative Value Calculations Relative values must be calculated for each of the eight criteria (the original nine criteria listed in 4.1 minus Urgency). Scali ng is used to convert qualitative criteria to quantitative, and then all eight criteria are no rmalized. Scaling is used for the following qualitative information: Table 4.5 Scaled Values for Criteria Criteria Criteria Value Scale Value No 0 Other appointment Yes 1 Not Moffitt 0 Cause of delay Moffitt 1 Yes 0 Pending information No 1 A scale value of 1 indicates high er priority for that criteria va lue. For example, a patient who has another appointment that day, given all other criteria are the same, has a higher priority then the patient that does not. Pa tients who have been delayed by the hospital system (Moffitt) and who do not have any missing information (e.g. diagnostic reports),

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42 are given a higher priority. One other criteri a is scaled, Distance traveled. Although not qualitative, a scale is used for ranges of distance traveled since that is how judgments are made currently at Moffitt. Table 4.5-B shows the Distance traveled scale. Table 4.6 Scaled Values for Distance Traveled Criteria Criteria Criteria Value Scale Value 0 – 1 hour 1 1 – 2 hours 2 Distance traveled 2+ hours 3 The patients who traveled the farthest are gi ven the highest priority. Values of the remaining criteria are as follows: Schedule disruption = (0, 8) number of pa tient’s with appointments beginning in a specified block of time. The maximum va lue of this criterion is determined by the minimum estimated treatment time and the ability to doubl e or triple book. Here it is assumed that double booking is allowed. The minimum estimated treatment time is 15 minutes. Time to appointment time = (0, ) MAX (current time – appointment time, 0) (negative values represent patien ts who have arrived early). Estimated treatment time = 15, 30, 60 or 90 minutes Demand per practitioner = (0, 2) scheduled time / specified block of time. The maximum value of 2 represents a completely double booked block of time.

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43 The eight criteria are now able to be normali zed as described in section 3.3. Linear normalization is used. The criteria represent both benefit and cost attributes. Benefit attributes are more preferred as the attribut e value increases. 1. Distance traveled 2. Other appointment 3. Time to appointment time 4. Cause of delay Cost attributes are less preferred as the attribute value increases. 1. Schedule disruption 2. Estimated treatment time 3. Demand per practitioner 4. Pending information Relative value calculations are not needed for binary attribute values (Other appointment, Cause of delay and Pending information). Th e maximum attribute value is always 1, otherwise the value is zero. The next sections describe the specific relative value calculations for each decision. 4.3.1 Decision #1 Relative Values and Model The relative attribute values for D ecision #1 are calculated as follows: Relative Distance traveled = Distance traveled / 3 Relative Demand per practitioner me) current ti (5pm / time scheduled minutes 30 / time scheduled MIN

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44 Relative Estimated treatment time = 15 / Estimated treatment time Other appointment, Cause of delay a nd Pending information are all binary The Decision #1 model compares a single late-a rrival or walk-in patient to the system. Multiple patients are not compared. The valu es specific to that patient are used to calculate the relative values. Patient priority increases with the score. Decision #1 SAW model is shown in equation 4.2. Score = 0.28(Relative Distance Traveled) + 0.07(Other appointment) + (4.2) 0.06(Cause of Delay) + 0.12(Relati ve Estimated treatment time) + 0.17(Relative Demand per practitio ner) + 0.30(Pending information) 4.3.2 Decision #2 Relative Values and Model The relative attribute values for D ecision #2 are calculated as follows: Relative Schedule disruption = Schedule disruption / MAX (Schedule disruption) Relative Demand per practitioner = Dema nd per practitioner / MAX (Demand per practitioner) The relative values for Decisi on #2 correspond to a specific bloc k of time in the schedule. The maximum value is the highest schedule di sruption or demand per practitioner of the remaining time blocks in that day’s schedule. Both of these criteria are cost attributes calculated as benefit attributes, therefore the lowest score will be selected. Decision #2 SAW model is shown in equation 4.3.

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45 Score = 0.46(Relative Schedule disruption) + (4.3) 0.54(Relative Demand per practitioner) 4.3.3 Decision #3 Relative Values and Model The relative attribute values for D ecision #3 are calculated as follows: Relative Time to appointment time = Ti me to appointment / MAX( Time to appointment) Relative Estimated treatment time = MIN (Estimated treatment time) / Estimated treatment time Other appointment, Cause of delay a nd Pending information are all binary Decision #3 relative values compare patient s in waiting room. The maximum and minimum values of Time to appointment ti me and Estimated treatment time respectively are the extreme values of the waiting room pa tients at a given point in time. Similar to Decision #1, the patient prior ity increases with the score. The SAW model for Decision #3 is as follows: Score = 0.22(Other appointment) + (4.4) 0.26(Relative Time to appointment time) + 0.19(Cause of Delay) + 0.15(Relative Estimated treatment time) + 0.18(Pending information) Relative weights resulting from consistent surveys (CR 0.10) are used SAW model equations of sections 4.3.1 – 4.3.3.

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46 The three SAW models are suggested as a better approach to current scheduling practices at Moffitt clinics. The decision pr ocess incorporating the three SAW models is tested using a discrete-event computer simula tion. Both the current decision practices and the new approach are modeled. The simu lation logic used is discussed in the next chapter.

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47 Chapter Five Simulation Logic The simulation model represents a single outpatient clinic system. The system includes patient arrival, waiting room and treat ment. It is a terminating system, each run representing one day. The day begins 8 am and ends when the last patient exits the system. A one-hour lunch break is assumed from noon to 1pm. All times are represented in minutes, starting at 8am. While hospital conditions such as other appointments are incorporated, none are specifically modeled. Each random distribu tion is individually seeded and thirty replications are run. All patient entities entering the system re present patients seeking treatment in the clinic that same day. Patients can arrive to the clinic as either a scheduled or walk-in patient. Punctual scheduled patients, those who arrive wi thin 30 minutes of their appointment time, are directed to the waiting ro om, represented by a queue, to be treated. The remaining patients, late scheduled patien ts or walk-ins, are sent through a set of decisions the clinic staff must make to incor porate them into the clinic that day. After which, the late and walk-in patients may join the waiting room queue. Patients are called back from the waiting room to begin the treatment process. The treatment process includes a Medical Assistant (MA) screening process, nurse and practitioner processes. The treatm ent process begins with the MA when one exam room becomes available. Patients are delayed for a few minutes after the

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48 practitioner process, then exit the system. The next section describes all the entities modeled and thei r attributes. 5.1 Entities There are four entity types (scheduled pa tients, late patients, walk-in patients and other tasks). All patient enti ties represent patients seeking treatment in the clinic that day. Patients enter the system as either a scheduled or walk-in patient. These two patient types are generated separately and with diffe rent arrival patterns. Scheduled patient entities are described further in the next section. 5.1.1 Scheduled Patient Entities All scheduled patients set their appointmen ts in advance. Therefore, scheduled patient entities are generated with one ar rival and 32 entities per arrival at 0.00001 minutes. This is done to construct a patient sc hedule prior to the beginning of the clinic that day. Scheduled patient entities take one of two paths in the simulation. They will either remain a scheduled patient entity or may become a late patient entity. Scheduled patients are redefined as “lat e” patients, based on the arri val and appointment time. Those who arrive more than 30 minutes after their appointment are considered “late”. Redefining the entities is necessary because late patients have to be reassigned appointment times. Once a patient is classified as “late”, they follow the same path as walk-in patients. Patient ar rival distribution is based on real data, expert opinion or system observation at H. Lee Moffitt Ca ncer Center in Tampa, Florida.

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49 Times studies, patient shadowing and sta ff interviews were conducted in multiple clinic of H. Lee Moffitt Cancer Center. Time study records of 83 patient visits were used to find the scheduled patient arrival distri bution (see Figures 5.1 and 5.2). Figure 5.1 shows approximately 20% of the patients arri ve after their appointment time. The data from Figure 5.1 was input into Arena’s Input Analyzer to determine the most suitable distribution. Figure 5.1 Patient Arrival Data Figure 5.2 Arrival Data Distribution Summary -150 -100 -50 0 50 100 150 83 samplesMinutes Late 20.48%

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50 The Beta distribution -87 + 108 BETA(2.38, 1.39) is used to represent scheduled patient arrival. Arrival tim e is one of many attributes assigned to each patient entity, which are us ed in the scheduling and operations of the clinic. Every patient entity is assi gned a set of attributes as it enters the system. The following attributes are assigned to the sche duled patients immediately after they are created. 1. Length the length of the assi gned appointment in minutes DISC(0.4, 15, 0.95, 30, 0.98, 60, 1, 90) The type of appointment and the practitione r determines the appointment length. For example, a follow-up appointment is typica lly 15 minutes long while a new patient appointment may be 60 minutes long. The a bove distribution is re presentative of a surgeon, who typically has more follow-up appointments. The distribution used to represent an oncologist appoint ment schedule is as follows DISC(0.05, 15, 0.3, 30, 0.8, 60, 1, 90) 2. Appointment end time = Appointment end time of the previous patient + length The Appointment end time is assigned as an attribute to create the schedule of patients. The end time of the previous patien t is used as the appointment time of the next patient. The schedule creation is explained further in section 5.3.

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51 3. Appointment time = Appointment end time-length An appointment time is assigned to each pati ent. This attribute is used to make scheduling and operational decisions. It is also used to calculate waiting time. Waiting time of a patient is the difference between the appointment time and the time a patient enters an exam room. 4. Arrival time represen ts the time the patient physi cally arrives at the clinic The patient arrival time is used to assign the late patient entity type. It is also used to assign appointment times for a specific set of patients, urgent patie nts as well as those who arrive after 4 pm. Tw o distributions are used. Appointment time + (-87 + 108 BETA(2.38, 1.39)) includes all patient arrivals (on-time and late). Appointment time EXPO(26.3485) only represents on-time patient arrivals. 5. Distance traveled the time a patient travels from home to the clinic (1 = less than 1 hour, 2 = 1-2 hours and 3 = more than 2 hours) DISC(0.65, 1, .76, 2, 1,3) The distance a patient travels to the clinic is taken into consideration when making scheduling and operational decisions. This distribution is specific to H. Lee Moffitt Cancer Center and was collected from th e Human Resources department at Moffitt. 6. Urgency the medical state of the pa tient (0 = not urgent, 1 = urgent) DISC(0.95, 0, 1.0, 1) Only a clinical staff member can determine the medical urgency of a patient. Urgent patients are given the highest priority and se nt to the front of the waiting room queue.

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52 7. Another appointment – a appointment after the clinic appointment also at Moffitt (0 = no other appointment, 1 = another appointment) DISC(0.78, 0, 1.0, 1) Patients at H. Lee Moffitt often have multiple appointments in a single day. These appointments could be at multiple clinics or a clinic and diagnostic testing, treatment or consultations. Only a single clinic is mode led in this simulation, but it is taken into consideration if the patient has another a ppointment later that same day at Moffitt. 8. Time to appointment time = TNOW – Appointment time This attribute is used to track the patient relative to their appointment time. This attribute is time dependant and ch anges as the day progresses. 9. Cause of delay – the reason the patient arrived after the appointment time (0 = external cause, 1 = caused by Moffitt) DISC(0.25, 0, 1.0, 1) The staff interviews and patient shadowing revealed that there are many reasons why a patient may arrive late to an appointme nt. Generally, the clinical staff only considers whether or not Moffitt delayed the patient. If a previous appointment or transaction that day at Moffitt caused the patient to be late to their clinic visit, that is included in scheduling and ope rational decisions. This distribution is based on the expert opinion of Clinic Operations Managers. 10. Pending information – Missing diagnostic info rmation needed for clinic treatment (0 = pending information, 1 = no pending information) DISC(0.1, 0, 1.0, 1)

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53 Often lab results or other dia gnostic test results are needed for the practiti oner to treat the patient. Pending information represen ts any information needed to treat the patient in the clinic that day. If any pi ece of information is missing, the patient has pending information. A 30 minute loop is used to change the pending information attribute status after the patient arrives to th e clinic. This distri bution is also based on expert opinion of Clinic Operations Manage rs. Walk-in patients are also assigned a similar set of attributes. Their attributes as well as their generation are explained in the next section. 5.1.2 Walk-in Patient Entities Walk-in patient entities are generated separate ly from the scheduled patients. The first walk-in patient is generated with a distribution of UNIF(1, 480) minutes UNIF(1, 480) minutes between arrivals and a maximum of 4 arrivals. 10% walk-in pati ents, about two patients, are typical of the clinic modeled. Therefore, four walk-in patients were used as an upper bound. See Appendix G for walk-in arrival data. Walk-in patients are also assigned a set of attributes after they are created. Walkin patient attributes are the same as for scheduled patients (Length, Appointment end time, Distance traveled, Urgency, Other appoi ntment, Time to appoi ntment time, Cause

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54 of delay and Pending information). The arriva l time is assigned differently. Walk-in patient arrival time is set at the current clock time (TNOW) of the day. 5.1.3 Other Task Entities The last entity type, other tasks, repres ents other work for which the practitioner is responsible. The other tasks may be phone calls, reviewing patient records, dictation or others. Time between arrivals is UNIF(37,60) with the first arrival at 5 minutes. Other tasks entities are assigned an attribute, Practitioner Process Time, equal to 15 minut es. The practitioner resource will only perform other tasks between patients. An ot her tasks entity will not interrupt a patient being processed and a maximum of 11 entities are generated. 5.2 Resources Four resources are defined (MA, nurse, practitioner and exam room). There is one MA, nurse and practitioner and two or thr ee exam rooms. Both the MA and nurse are assumed to be available to see a patient once an exam room is available and have no other tasks. Processing time s for the MA and nurse are: MA = UNIF (1,4) Nurse = UNIF(5,10)

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55 The practitioner processing time is based on the length of appointment assigned to each entity. Practitioner = length*NORM(0.675,0.10833) If a patient has a one-hour appointment, th e practitioner spends between 56.667% and 78.333% of that time in the exam room with the patient. The remaining time represents other obligations for the pract itioner such as phone calls, dictating notes and reviewing patient records, which will account for the remaining working time. These obligations are generated by the other tasks entities. There is no processing time for the exam room When an exam room is available, the next patient in the waiting room queue will seize it. After the practitioner process, the patient is delayed (uniformly distributed be tween 2 and 10 minutes) then the exam room resource is released. All resource processing times are based on patient shadowing and expert opinion. 5.3 Patient Entity Arrivals and Schedule Creation There are two creation modules for patient entities, one generating scheduled and one generating walk-in patients. Scheduled pa tients are all created at one time. The max number of arrivals is one and there are 32 entities per arrival. 32 entities are generated to ensure that enough patients are in the system to fill the schedule. Th e bulk entity creation is needed to assign each patie nt the set of attributes liste d in section 5.2 prior to the arrival to clinic.

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56 One of these attributes is the appointment time. The appointment time is assigned using a system variable, End time. This vari able keeps track of th e last appointment end time assigned an entity (see equation 5.1). End Time = End Time + le ngth of appointment (5.1) The end time for the second entity will be the end time of the first entity plus the appointment length of the second. The attribut e, Appointment end time, is then equal to the system variable, End time. Then th e appointment time is assigned as the Appointment end time minus the appointm ent length (see equations 5.2 and 5.3) Appointment end time = End Time (5.2) Appointment time = Appointment end time – Appointment length (5.3) After the entity is created and assigned a set of attributes, it goes through four decision models. The first decision checks th e arrival time of the entity. The arrival distribution generates mostly early patients. If the arrival time is less than zero, the entity arriving before 8am, the arrival time is rea ssigned to zero. The second decision module checks the appointment time attribute. If the appointment time is less than or equal to 4pm (480 minutes), the patient continues to the third decision. Entities with appointments after 4pm are disposed, guarant ying the last scheduled appointment each day is no later than 4pm. The third decision checks if the appointment time is between

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57 11:30am and 1:00pm. If true, the entity is se nt through an assign module to reassign the appointment time. The appointment time is r eassigned to 1:00pm. Th is ensures that the last appointment before lunc h is not later than 11:30am and no patients are scheduled during the lunch hour. To reassign the appointme nt time, the system variable End time is redefined as follows: End time = 300 + Appointment length (5.4) where 300 represents 1:00pm. Once all appoint ments times are assigned, the entities are sent through the Scheduled Bl ock Variables sub-model. 5.4 Schedule Block Variables sub-model As the entity enters the sub-model, it first goes through an N-way by condition decision module. The attributes position the entity based on the current system time (see Figure 5.3). The entity will be gin at the earliest time block and go through the remaining blocks for that day. These sub-models ar e used to update thre e systems variables: scheduled time, number of appoi ntments and demand. Scheduled time is the total time in minutes during the hour block for which a patient is scheduled. This value could be less than, equal to or greater than 60 minutes. Appointments variable record the number of appointment that begin during the one-hour bl ock. Demand variable is the scheduled time divided by 60 minutes. The system vari ables are recorded in a Schedule Block Variables sub-model using decide and assign modules.

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58 Figure 5.3 Schedule Block Variab les Sub-model: Block Definition The entity enters a second sub-model where it goes through another decision module (see Figure 5.4). Figure 5.4 Calculation of Schedule Block Variables Depending on the appointment time and end time, an assign module (a, b, c, or d) will add the correct number of minutes and number of appointments to the scheduled time and appointments variables respectively. 60 appointment time 120 && appointment end time 120 60 appointment time 120 && appointment end time 120 appointment time 60 && 60 appointment end time 120 9-10 a m appointment time 60 && 120 appointment end time a b c d 9-10 a m 0 TNOW 60 60 TNOW 120 120 TNOW 180 480 TNOW 540 8-9am 9-10am 10-11am 4-5 pm Define Schedule Blocks

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59 The demand variable will also be updated. Continuing with the 9-10 am block example from Figure 5.5, the four assign modules ar e as follows where 9-10 SchedTime is the scheduled time system variable, 9-10 Appt s is the appointments system variable and 910 Demand is the demand variable for the 9-10 am time block. Figure 5.5 Schedule Block Variables Assignment One Schedule Block Variables sub-model is us ed, located just before the hold block representing the arrival of scheduled patient entities into the clinic system. 9_10SchedTime + (120-appointmenttime) a b 9_10SchedTime + length 9_10Appts + 1 9_10Appts + 1 9_10SchedTime + (appointmentendtime-60) 9_10SchedTime + 60 c d 9_10SchedTime / 60 9_10SchedTime / 60 9_10SchedTime / 60 9_10SchedTime / 60

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60 5.5 Scheduled Patient Arrival to Clinic System The 32 scheduled patient entities are sent to a hold block. The hold block queue represents the clinic arrival for scheduled patients. Patients are released from this queue when the arrival time attribute equals the cu rrent simulation time (TNOW). In physical terms, this models the patient walking into the clinic and checking in at the front desk. The actual check-in process is not modeled due to the minimal processing time. As patients are released from the queue for sche duled patient arrivals, they are sent through the fourth decision module. If the scheduled patient entity is punctu al, it is sent to the waiting room queue. If the schedu led patient entity is late, it is reassigned the entity type “late” and joins walk-in patient entities to go through a new appointment time decision process. 5.6 Appointment Assignment and Urgent Patients Once the late and walk-in entities have been assigned the set of attributes a few decisions are made prior to new appointment assignment. 1. If the entity is urgent and it is befo re 5pm (540 minutes), it is assigned an appointment time of TNOW and sent straig ht to the waiting room queue. Urgent patients are assigned TNOW as an appointment time to ensure the practitioner sees them as soon as possible. 2. The non-urgent entities go through anothe r decide module that checks the current system time. If TNOW is less than 480 minutes, the entities are sent to a submodule to be assigned a new appointment time. If TNOW is between 480 and 540 minutes, the entity is assign an appoi ntment time of TNOW and sent to the

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61 waiting room queue. Patients who arrive before 4pm are assigned an appointment time. Patients who arrive after 4pm, but before 5pm use their arrival time as an appointment time since the clin ic only schedules through 5pm. 3. If the entity arrives after 540 minutes, it is disposed. This represents a patient arriving after 5pm. Late and walk-in patie nts are only taken the same day if they arrive before 5pm. Entities are assigned new appointment times in a sub-model. Entities are first separated by time as shown in Figure 5.3. After which, they are sent through an assign module assigning an attribute of the demand of each hour block remaining in that day’s schedule. After the attribute assignment, the entities go through another decision module. If the demand of an hour block is less than 1, the en tity is assign a new appointment time at the beginning of that hour. If multiple blocks ha ve a demand less than 1, the earliest hour is selected. The following blocks are checked in this decision module: 9-10am 10-11am 11am-12pm 1-2pm 2-3pm 3-4pm If all of these blocks have a demand greater than or equal to 1, the entity is sent through another set of decisions.

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62 The next hour block checked is the l unch hour, 12-1pm. If the demand of that hour is less than 1, the entity is assigned to 12pm. If the lunch hour demand is greater than or equal to 1, the last hour of the clinic is checked, 45pm. If that hour has a demand less than 1, the entity is assi gned 4pm as an appointment time. Otherwise, the entity will be double booked. An entity is double booke d by beginning assigned to the earliest available time that is already booked with one 15-minute appointment. Only 15 minute appointments are double booked. Once the late or walk-in entity has a new appointment time, it is sent to a hold block before the waiting room queue. This is to prevent an entity entering the waiting room queue significantly before the new appoi ntment time. The following distribution is used to delay the entity. UNIF(appointmenttime-TNOW-10, appointmenttime-TNOW-1) It is assumed that all late and walk-in patients with new appointment times will be punctual. After the patient is released from the hold module, it enters the waiting room queue, which is ordered by appointment time. The earliest appointment time is released first. Finally, the entity seizes an exam room and is processed. 5.7 Processing After an entity is called back, it will sei ze one room resource. This represents the patient occupying the exam room. Following the seize module, the entity is sent through a decide block that checks the pending information status of the entity.

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63 If the entity still has pending information when it is seizes a room, it will be sent to a delay block and be held for th e following number of minutes: 30-(tnow-arrivaltime) (5.5) The delay represents the time required for the nurse to obtain the pending information needed to treat the patient. Patient inform ation is typically received 30 minutes after the patient arrives. Once all information is availabl e, the patient begins to be processed. The MA sees the patient first. The entity is processed by the MA first and then sent to a hold block. The release condition for the hold is the practitioner resour ce is not busy. Once the entity is released from the hold, it is processed by the nurse fo llowed by the practitioner. After the entity releases the practitioner resour ce it is sent through one more module. The patient is delayed for a few minutes after the practitioner is done to re present the time needed to wrap up the visit. Finally, the patient entity exits the clinic. Our model modifies the late and walk-in entity decision process, new appointment assignment and waiting room queue. The logic of our suggested system is explained in the remainder of this chapter. 5.8 Priority 1 Assignment and Urgent Patients Late and walk-in patient entities merge in to the same path. This occurs at the assign module, Assign Priority 1 (see Figure 5.6). The purpose of this module is to assign a priority 1 score to each late and walk -in entity. Priority 1 is the product sum of a

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64 relative weight and relative va lue of six predetermined fact ors discussed in Chapters 3 and 4: 1. Distance traveled 2. Estimated treatment time 3. Another appointment 4. Practitioner demand 5. Cause of delay 6. Pending information This module assigns a tota l of four attributes: 1. Relative distance traveled 2. Relative estimated time 3. Relative demand 4. Priority 1 Figure 5.6 Priority 1 Assignment After entities (late and walk-in) have been assigned a priority 1 attribute, they go to a decision module. The question, “Is the pa tient urgent?” is asked. If the entity is urgent, urgency attribute is one, the entity is sent to another assign module. Urgent entities are reassigned an appointment time equal to the current time (TNOW) and a Walkin Patient Generator Assign Late Assign Walkin Patient Conditions Assign Priority 1

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65 corresponding appointment end time (Appointme nt time + length). These reassignments are done to send urgent entities to the front of the waiting room queue, which is explained further in section 5.10. If the entity is not urge nt, it is sent to another decide module asking “Will the patient be seen today?”. This decision model determines if the late or walk-in patient will be seen in the clinic that day. The decisi on is two-way by condition. If the priority 1 attribute is greater than the specified valu e, the patient will be accepted and assigned an appointment time. If not, the patient is dis posed and assumed to return another day. Before the accepted entities are assigned an appointment time, they go through one more decision module that checks the arrival time a ttribute. This decision module is three-way by condition: 1. If the arrival time is between 4pm ( 480 minutes) and 5pm (540 minutes), the entity is assigned an appointment time equal to TNOW and sent to the waiting room queue. Physically, this represents a patient coming very close to the clinic closing time. In which case, the patient is added directly to the waiting room to be seen as soon as possible. 2. If the arrival time is before 4pm, the entity is sent to a sub-model for an appointment assignment. 3. Any entities that arrive after 5pm are disposed. The clinic does not accept patients after 5pm.

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66 5.9 Appointment Assignment for Late and Walk-in Patients The accepted late and walk-in entities ar riving prior to 4pm (condition 2 listed above) must have an appointment time attribut e assigned to them. Fo r late entities, the appointment time attribute will be reassigne d. Appointment time assignment is based on half-hour blocks of time. Half-hour blocks are defined beginning with 8-8:30am (0-30 minutes) and ending with 4:30-5pm (510-540 minutes). The block for which the appointment time will be assigned is selected based on two criteria: 1. Practitioner demand 2. Schedule disruption The Appointment Selection scor e is an attribute and is ca lculated by adding the product of the relative weights and values for each crite ria. The block with the lowest score is selected. To find the relatives values of each block, the current block value must be known. This is captured using system variables b ecause the values are dynamic. Three system variables are used for each time block: sche duled time, appointments and demand and are updated in the Schedule Block Vari ables sub-model, section 5.5. As the entities enter this sub-model, they will first go through a decision model like Figure 5.3. They are positioned according to the current system time, but instead of going to a second sub-model, the entities are sent to an assi gn module (see Figure 5.7). Three types of attributes are assigned: relative demand, relative number of appointments and a score.

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67 Figure 5.7 Assign New Appointment Sub-model: Block Definition These three attributes will be assigned for all time blocks remaining that day. In other words, if the current time is 3:15pm, the entity will be assigned attributes for 330pm, 3:30-4pm, 4-4:30pm and 4: 30-5pm. It is assumed that no late or walk-in entity will be added to the block in which it arrives. This means, if an entity arrives at 9:15am, the 9:30-10am block will be the first considered and the 8-8:30am block will never have a late or walk-in patient added. To guarantee this, the score of all other blocks (earlier and current) are assigned a high score since the time block with the lowest Appointment Selection score will be selected. Following the assign modules, all entit ies are sent through a second decision module. This decide module determines which time block has the lowest score (see Figure 5.8). 30 TNOW 60 60 TNOW 90 90 TNOW 120… 510 TNOW 540 8:30-9a m Define Schedule Blocks 9:30-10am 4:30-5pm 9-9:30am

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68 Figure 5.8 New Appoi ntment Assignment Depending on which condition is found to be tr ue, the entity will go to an assign module and an appointment time will be asigned. 4pm is the last appointment time that will be assigned for this appointment assignment process. After a new appointment time has been assi gned, the entities are sent through the Schedule Block Variables sub-model to update the system variables. Since an entity could be assigned an appointment time severa l hours later, a hold modul e is used after the schedule block variables sub-model. Only non-ur gent late or walk-in entities before 4pm are sent to the hold module. The release c ondition form the hold is the current time equal to 1 minute before the appointment time. Once an entity is released from the hold module, it will merge with the scheduled entiti y path to join the waiting room queue. The waiting queue and resrouce process logic follows in the next section. 9_930Score == MIN(9_930Score, 930_10Score, 10_1030Score,… 430_5Score) 930_10Score == MIN(9_930Score, 930_10Score, 10_1030Score,… 430_5Score) 10_1030Score == MIN(9_930Score, 930_10Score, 10_1030Score,… 430_5Score) Minimum score 3_30Score == MIN(9_930Score, 930_10Score, 10_1030Score,… 430_5Score) 9:00 9:30 10:00 3:00 4:00

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69 5.10 Waiting Room Queue and Priority 2 Assignment Selection of the next entity from th e waiting room queue is based on a second priority score. Priority 2 score, like the fi rst, is the product sum of a relative weight and relative value of five predetermined factors. 1. Relative Time to appointment time 2. Relative Estimated treatment time 3. Relative Other appointment 4. Relative Pending information 5. Relative Cause of delay 6. Priority An entity is to be released from the wa iting room queue when a room resource is available. It then goes through decide modules, which check the urgent and pending information conditions of each entity. If the en tity is urgent, a priority 2 score of 2 is assigned. This ensures that urgent patients will be released to the exam rooms first. If a patient has been in the system for at leas t 30 minutes, the pending information condition is changed to no pending information. The pr iority 2 score is assigned after the decide modules. The entities enter a hold block af ter the assign module where they are ordered by priority 2 score. The entity to be released is the one with the highest Priority 2 score. A last decide module is used to send the fi rst entity in the Ordered queue to an exam room and redirect all other back to the waiting room queue (see Figure 5.9). To guarantee the highest Priority 2 score is select ed, the scores of each entity in the queue are recalculated each time a room is available. A series of hold and signal blocks are used to release the queues.

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70 Figure 5.9 Priority 2 Score Recalculation 5.11 Verification and Validation The simulations were verified using seve ral techniques. Many variable displays were used to ensure correct appointment assignment, variable calculation, resource utilization, and time. The time the last entity left the system was continuously used to ensure no unexpected delays existed. The current system time was also used extensively to verify the timing of simulation events. Entities were sent through the system at a significantly decreased speed to verify the si mulation decisions at each step. The number of patients generated and percentage of late patients for each run were also used for verification. Validation was done by using information from the real clinic system and its staff. Clinic closing time, practitioner ut ilization, number of pa tients seen, and waiting time were used to validate the simulation model. The two computer simulations described in this chapter are used to determine the effect the patient priority a nd appointment assignment models have on the clinic system. Results from the simulations are given in the next chapter. Waiting Room Ordered Assign Decide

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71 Chapter Six Simulation Results The purpose of our clinic simulation is two-fold, to replicate the current system and decision making process at H. Lee Moffitt and test the effect of our decision models in the Moffitt clinic. Two computer simulati ons were built to be identical except for the decision making processes. A number of variab les can be tested using these simulations. Preliminary analysis was done to determine which variables would be tested for this research. Eight settings and f our variations of our clinic si mulation were defined. A total of 40 different model and setting combinations were run (four vari ations of our model and the current system model each run under eight settings). Analysis was based on six outputs: 1. Number of patients 2. Practitioner utilization 3. Clinic close time 4. Waiting room wait time 5. Total wait time 6. Room utilization The average output of 30 runs was used. Out put definitions are given in the following section. The remainder of this chapter di scusses preliminary an alysis, selection and definition of the eight settings a nd results of the simulation models.

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72 6.1 Analysis of Simulation Variables A number of variables (s etting conditions and inputs) can be modified in the clinic simulations. An initial list of setti ng conditions and inputs is found in Appendix H. The outputs used in this research to test all variables are cons istent throughout the document and are defined as follows: 1. Number of patients – the total number of patients (scheduled, late and walk-in) seen by the MA, nurse and practitioner. Patients turned away and expected to return to the clinic another day are not included. 2. Practitioner utilization – the ratio of the total value-added time of the practitioner (seeing patients and doing other task s) to the clinic close time. 3. Clinic close time – the time the last patient exits the system. 4. Waiting room wait time – time spent by a patient in the waiting room after their appointment time. 5. Total waiting time – time spent by a patie nt in the waiting room after their appointment time plus the idle time (patie nt not being seen by an MA, nurse or practitioner) in the exam room. 6. Room utilization – the ratio of the total time spent by patients in an exam room (the time the patient entered the exam ro om to the time he/she exits the exam room) to the clinic close time and number of rooms. Four variables were selected and an anal ysis of variance (ANOVA) was performed for each of the six outputs. Preliminary analysis and the selection of settings are explained in section 6.2.

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73 6.2 Analysis of Variance and Setting Selection To maintain a manageable number of comb inations, four variables were selected to test for statistical significance. Two of the variables were specific to our decision model: 1. Block length – the amount of time for which the clinic schedule is divided into and evaluated. In other words, when l ooking to assign an appointment time to a patient, how much of the schedule is eval uated at a time. The block length was tested at 30 minutes and 60 minutes. 2. Priority criteria – the patient priority criteria value set for Question #1 (Take the patient today?). If a patient’s priority score is less than this criterion, the patient will be sent home. The priority criterion was tested at 0.00, 0.25, 0.50 and 0.75. The other variables tested were setting variables: 3. Number of rooms – the number of exam room s was tested at two and three rooms. 4. Percentage of late patients – the patient arrival distribution ca lculates the patient arrival time to the clinic with respect to their appointment time. Two arrival distributions were tested, one calculated from all the Moffitt patient arrival data and the other calculated from only the pa tient arrival data where the patient arrived prior to the appointment time. An analysis of variance was performed to test the impact of the four variables on system outputs. The ANOVA results are shown in Table 6.1.

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74 Table 6.1 ANOVA Results Number of Patients Practitioner Utilization Clinic Close Time Waiting Room Wait Time Total Wait Time Room Utilization p-value p-value p-value p-value p-value p-value Source Prob > F Prob > F Prob > F Prob > F Prob > F Prob > F Model < 0.0001 < 0.0001 < 0.0001 0.0003 0.3440 < 0.0001 A-Block 0.9363 0.3608 0.7278 0.9835 0.3210 0.6435 B-Rooms 09928 0.0218 0.2017 0.0005 0.3488 < 0.0001 C-Late Percent 0.0396 < 0.0001 0.9863 0.7599 0.2905 < 0.0001 D-Priority < 0.0001 < 0.0001 < 0.0001 0.0001 0.2122 < 0.0001 None of the four variables had a significan t effect on all six outputs. The number of rooms, percentage of late patients and prior ity criteria did impact some of the outputs. The block length did not have a ny statistically significant aff ect and none of the variables affected the total waiting time. Total waiting time is much larger in magnitude than the waiting room wait time. A statistically signif icant variation in time only appears in the waiting room wait time output. Variable interact ions were excluded from analysis. From these results two settings were defined to run a second ANOVA. The settings were defi ned by three variables: 1. Number of rooms two and three ex am rooms were tested (R2, R3) 2. Percentage of late patients two distributions were tested all patient arrivals with approximately 20% late patients (L20) and only on-time patient arrivals (L0) An additional variable was added to the previous four, patient appointments. As mentioned in Chapter 4, the type of scheduled appointments can vary with respect to the practitioner. 3. Appointments two appointment schemes are tested, one representative of a surgeon schedule (A15) and the other repr esentative of an oncologist schedule (A90).

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75 Surgeon schedules are typically shorter appoint ments. The results are shown in Tables 6.2 and 6.3. Table 6.2 Setting R2 L20 A90 ANOVA Results Number of Patients Practitioner Utilization Clinic Close WR Wait Time Room Utilization p-value p-value p-value p-value p-value Source Prob > F Prob > F Prob > F Prob > F Prob > F Model < 0.0001 0.0022 0.0006 0.0047 < 0.0001 A-Block 0.9992 0.7578 0.7476 0.7141 0.7899 B-Priority < 0.0001 0.0006 0.0001 0.0010 < 0.0001 C-Late definition 0.1161 0.0129 0.8338 0.8941 0.0163 The first setting (R2 L20 A90) shown in Table 6.2 is a clinic with two exam rooms, approximately 20% late patient arriva ls and an oncologist appointment scheme. Total wait time was removed from this analys is since none of the previous variables had a significant affect on total wait time. All other outputs remain the same. Three variables were tested in the R2 L 20 A90 setting. All fo ur variables shown in Table 6.1 were incorporated. The number of rooms and percentage of late patients became part of the setting definition. Th e remaining two variables; block length and priority criteria are tested again. A third va riable, late patient definition, is added. Late patient definition – the amount of time a patient arrives after his/her appointment time used as a criteria to clas sify the patient as a late patient. Two definitions are tested. Any patient arriving more than 15 minutes after his/her appointment and any patient ar riving more than 30 minutes after his/her appointment. Table 6.2 shows block length to again ha ve no statistically significant affect on the outputs in the R2 L20 A90 setting. Priori ty criteria were found to impact all of the

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76 outputs while the late patient definition only affected practitioner and room utilization. The same outputs and variables were used in a third ANOVA for the setting R3 L20 A15. The setting R3 L20 A15 has th ree exam rooms, approximately 20% late patient arrivals and a surgeon appointment scheme. The ANOVA results for setting R3 L20 A15 are shown in Table 6.3. Setting R3 L20 A15 results are similar to setting R2 L20 A90. Block length has no affect on the system outputs. Priority cr iteria again have a st atistically significant affect on all five outputs while late patient definition impacts waiting room wait time in setting R3 L20 A15. Table 6.3 Setting R3 L20 A15 ANOVA Results Number of Patients Practitioner Utilization Clinic Close WR Wait Time Room Utilization p-value p-value p-value p-value p-value Source Prob > F Prob > F Prob > F Prob > F Prob > F Model 0.0030 0.0064 0.0090 0.0142 0.0012 A-Block 0.9997 0.7605 0.9302 0.5679 0.8874 C-Priority 0.0006 0.0015 0.0020 0.0052 0.0003 D-Late definition 0.2965 0.1431 0. 3729 0.0326 0.0528 In addition to the ANOVAs shown in Tables 6.2 and 6.3, the simulation output results from settings R2 L20 A90 and R3 L20 A15 are also analyzed. The average output range for each of the three va riables (block length, prior ity criteria and late patient definition) is shown in Tables 6.4 and 6.5. Tables 6.4 and 6.5 show the physical impact each variable had on the five outputs when a ll other variables are held constant. The following units are used to report the outputs 1. Number of patients = number of patients 2. Practitioner utilization = percent utilization 3. Clinic close time = number of minutes

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77 4. Waiting room wait time = number of minutes 5. Room utilization = percent utilization Table 6.4 Setting R2 L20 A90 Average Output Range Number of Patients Practitioner Utilization Clinic Close WR Wait Time Room Utilization Block 0.01 0.08% 1.61 0.31 0.17% Priority 0.92 0.76% 19.90 1.88 4.79% Late definition 0.08 0.54% 4.57 0.69 1.20% Table 6.5 Setting R3 L20 A15 Average Output Range Number of Patients Practitioner Utilization Clinic Close WR Wait Time Room Utilization Block 0.00 0.13% 0.77 0.28 0.26% Priority 1.01 1.10% 17.78 0.88 3.17% Late definition 0.27 0.36% 10.51 0.87 1.16% As expected, the actual impact block le ngth had on each of the output measures was negligible. Minimal effects were observed in five of the Clinic close time was the only output with notable changes in value. Although late de finition was statistically significant in waiting room wa it time, practitioner and room utilization, the physical impacts on those three outputs were minor. Si nce priority criteria had the largest range values, it will be tested in the final simula tions. The other two variables were held constant at the following levels: 1. Block length = 30 minutes 2. Late patient definition = 30 minutes The block length of 30 minutes was select ed because it can schedule in smaller increments than hour blocks. Moffitt clin ics did not have a st andard late patient definition. The staff used a va riety of times to determine if a patient was late. 30 minutes was selected as the late patient definition a nd used in both our clinic simulation model as

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78 well and the current system simulation model. As a result of the preliminary analysis, eight final settings were de fined and one variable used. An explanation of output analysis for the eight settings follows in the next section. 6.3 Clinic Simulation Output Analysis Following the preliminary analysis discusse d in section 6.2, eight clinic settings were defined to run simulations of our clinic model and the current system model. The eight settings are combinations of three variab les, two levels of each. Number of rooms, percentage of late patients and appointment s are the three setting variables defined in section 6.2. The eight setti ngs are defined as follows 1. R2 L0 A15 – two exam rooms, no late pa tient arrivals and surgeon appointments 2. R2 L0 A90 two exam rooms, no la te patient arrivals and oncologist appointments 3. R2 L20 A15 two exam rooms, all patie nt arrivals and surgeon appointments 4. R2 L20 A90 two exam rooms, all patient arrivals and oncologist appointments 5. R3 L0 A15 – three exam rooms, no late patient arrivals and surgeon appointments 6. R3 L0 A90 three exam rooms, no la te patient arrivals and oncologist appointments 7. R3 L20 A15 three exam rooms, all pa tient arrivals and surgeon appointments 8. R3 L20 A90 three exam rooms, all patie nt arrivals and onc ologist appointments Each model was run under all eight settings and information on six outputs was collected (number of patients, practitioner utilization, clinic close time, waiting room wait time, total wait time and room utilization).

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79 Total wait time was collected to provide a co mplete analysis of the clinic simulations. An analysis of our clinic model outputs is discussed in 6.3.1. 6.3.1 Clinic Simulation Model Analysis The Patient Priority Model and Appoint ment Assignment Models developed in this research were tested through a simulation of a Moffitt clinic. Four versions of our model were run in each of th e eight settings. Changing the priority criteria variable generated the four versions. Priority criterion was tested at 0.00, 0.25, 0.50 and 0.75. Altering the priority criteria changed the stri ctness of the system by allowing more or less walk-in and late patients to be added to that day’s schedule. The higher the criteria, the fewer patients permitted into the schedule. Table 6.6 shows the simulation results for our model. Each setting was replicated 30 times and the average output is reported. The outputs in Table 6.6 show the prior ity criteria variable has minimal to no impact when changed from 0.00 to 0.25. A small change in output values is observed when the priority criterion is set at 0.50. Th e greatest change in values is observed when the priority criterion is 0.75. At this le vel, all of the output values are decreased. Therefore, an improvement is seen for clinic close, waiting room wait time and total wait time outputs. A decrease in the number of patie nts, practitioner and room utilizations are not considered an improvement. The cause of the lowered output values is the decrease in the number of patients. Patients wait less, the clinic closes earlier and the practitioner and rooms are used less when fewer patients are seen.

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80 Table 6.6 Clinic Model Average Outputs: All settings Number of Patients Practitioner Utilization Clinic Close Time Waiting Room Wait Time Total Wait Time Room Utilization R2 L0 A15 Priority = 0.00 19.3 84.76% 598.06 24.312 55.034 93.87% Priority = 0.25 19.3 84.79% 596.2 24.062 54.765 93.91% Priority = 0.50 19.1 84.79% 591.23 23.742 54.497 93.82% Priority = 0.75 17.7 84.33% 557.87 16.01 46.599 91.36% R2 L0 A90 Priority = 0.00 10.7 89.12% 589.03 11.366 56.396 80.50% Priority = 0.25 10.7 89.12% 589.03 11.366 56.396 80.50% Priority = 0.50 10.5 89.14% 583.86 9.4605 54.298 79.60% Priority = 0.75 9.1 88.27% 550.5 3.7861 46.422 73.24% R2 L20 A15 Priority = 0.00 18.8 83.82% 596.22 27.987 59.466 93.04% Priority = 0.25 18.8 83.82% 596.22 27.987 59.466 93.04% Priority = 0.50 18.5 83.81% 590.8 26.81 58.455 92.86% Priority = 0.75 17.1 83.74% 556.91 18.831 50.086 90.32% R2 L20 A90 Priority = 0.00 10.7 88.09% 597.61 13.078 56.211 77.97% Priority = 0.25 10.7 88.09% 597.61 13.078 56.211 77.97% Priority = 0.50 10.4 88.25% 590.54 10.11 53.164 77.03% Priority = 0.75 9.1 87.45% 557.59 5.6628 45.215 69.93% R3 L0 A15 Priority = 0.00 18.7 86.88% 573.67 5.8344 52.838 81.43% Priority = 0.25 18.7 86.88% 573.67 5.8344 52.838 81.43% Priority = 0.50 18.4 86.82% 567.26 5.0728 51.933 80.89% Priority = 0.75 17.2 86.22% 536.71 2.8316 47.324 76.96% R3 L0 A90 Priority = 0.00 10.7 89.79% 583.46 2.5838 57.294 60.22% Priority = 0.25 10.7 89.79% 583.46 2.5838 57.294 60.22% Priority = 0.50 10.5 89.79% 578.87 1.9084 55.227 58.73% Priority = 0.75 9.1 88.82% 546.47 0.35074 48.017 51.99% R3 L20 A15 Priority = 0.00 18.7 86.14% 579.16 8.1425 53.801 79.02% Priority = 0.25 18.7 86.14% 579.16 8.1425 53.801 79.02% Priority = 0.50 18.5 86.20% 573.99 7.4896 53.008 78.62% Priority = 0.75 17.2 85.53% 543.51 5.5822 48.443 74.19% R3 L20 A90 Priority = 0.00 10.7 88.68% 593.58 4.4041 56.671 57.99% Priority = 0.25 10.7 88.68% 593.58 4.4041 56.671 57.99% Priority = 0.50 10.4 88.56% 588.45 3.4147 54.3 56.30% Priority = 0.75 9.1 87.48% 556.79 2.8671 46.784 49.19%

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81 To better understand the behavior of th e outputs with respect to the priority criteria variable, outputs for three settings (R2 L0 A15, R2 L20 A15 and R2 L20 A90) Figure 6.1. Priority Criteria vs. Clinic Close Time were plotted. Minimal variation was obser ved for practitioner and room utilization. Similar behavior was observed for clinic close time, waiting room wait time and total wait time outputs. Clinic close time behavior w ith respect to priority criteria is shown in Figure 6.1. Priority criterion of 0.75 appears to be the lowest criteria value to achieve the lowest clinic close time. When the priority criterion is set at 0.00, all patients (walk-in or late) who arrive before the clinic closes will be added to th e days’ schedule. No patients will be sent 530 540 550 560 570 580 590 600 610 0.000.250.500.550.600.650.700.750.800.850.90 Priority CriteriaMinutes R2 L0 A15 R2 L20 A15 R2 L20 A90

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82 home. This is the current practice at Moff itt. Using the 0.00 version of our model will directly compare the decision model developed in this research to the current decision processes at Moffitt. Therefore, the remain ing analysis will compare the current system model to only two versions of our clinic model, priority criteria of 0.00 and 0.75. Output analysis of our clinic model and the current system model are discussed in the next section. 6.3.2 Clinic and Current System Model Comparison All eight settings are used to compare the impact of our decision models on a Moffitt clinic. Table 6.7 shows the average ou tputs for each setting for both the clinic model with a priority criteri on of 0.00 and the current system model. A third line is included in the table to show any improve ment. A negative improvement, the current system performed superior to our clinic m odel, is shown in parentheses. No clear difference is observed and for that reason, our decision model appears to perform similar to the current practice. One possible reas on our model performed so closely to the current system model is because of the numbe r of scheduled patients in the system. The number of scheduled patients generated in the settings is a direct result of the appointment schemes, the distributions of a ppointment lengths. Th ese distributions are based on surgeon and oncologist appointments at Moffitt. Surgeon appointment scheme generated between 18 and 20 sc heduled patients each day. Oncologist appointment scheme generated 10 or fewer scheduled pa tients per day. The small number of scheduled patients minimized the number of op portunities for our mode l to be utilized. The fewer scheduled patients entering the system, the fewer late patients and smaller

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83 waiting room queue. Under the surgeon appoi ntment scheme, waiting room queues were observed, but generally in the later part of the day. Multiple patients in the waiting room under the oncologist appointments was infrequent. To test the system response under different conditions, the R2 L 20 A15 setting was used to overload the system with scheduled patients. Reducing the appointment lengths to 10-minute and 15-minute visits generated over 30 patients per day. The late patient definition was also adjusted to allow for more late patients in the system. A 21. 61 minute improvement was observed in clinic close time. 13.23-minute and 14.67-minute improvements were also observed for waiting room wait time and total waiting time resp ectively. Practically no difference was found in practitioner or room utilization. Therefore, given more opportunities to be utilized, our model may improve clin ic close time and waiting times. To illustrate the scheduling and operational differences of the clinic and current system models under Moffitt clinic conditions, two gantt charts (setting R2 L0 A15 and R2 L0 A90) can be found in Appendix I. Table 6.8 shows the out put variance for each setting.

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84 Table 6.7 Clinic and Current System Model Average Output Comparison Number of Patients Practitioner Utilization Clinic Close Time Waiting Room Wait Time Total Wait Time Room Utilization R2 L0 A15 Clinic Model, priority = 0.00 19.3 84.76% 598.06 24.31 55.03 93.87% Current System 19.3 83.70% 605.82 23.78 55.35 94.03% Improvement 1.06% 7.76 (0.54) 0.31 0.16% R2 L0 A90 Clinic Model, priority = 0.00 10.7 89.12% 589.03 11.37 56.40 80.50% Current System 10.7 89.04% 591.31 9.81 55.14 80.68% Improvement 0.08% 2.28 (1.55) (1.25) 0.18% R2 L20 A15 Clinic Model, priority = 0.00 18.8 83.82% 596.22 27.99 59.47 93.04% Current System 18.8 83.23% 601.38 25.14 57.02 92.88% Improvement 0.59% 5.16 (2.84) (2.45) -0.16% R2 L20 A90 Clinic Model, priority = 0.00 10.7 88.09% 597.61 13.08 56.21 77.97% Current System 10.7 88.06% 597.32 12.92 56.61 78.53% Improvement 0.04% (0.29) (0.15) 0.40 0.57% R3 L0 A15 Clinic Model, priority = 0.00 18.7 86.88% 573.67 5.83 52.84 81.43% Current System 18.8 86.55% 577.65 5.45 52.75 81.26% Improvement 0.33% 3.98 (0.39) (0.09) -0.18% R3 L0 A90 Clinic Model, priority = 0.00 10.7 89.79% 583.46 2.58 57.29 60.22% Current System 10.7 89.84% 584.80 2.39 57.56 60.54% Improvement -0.05% 1.34 (0.19) 0.26 0.32% R3 L20 A15 Clinic Model, priority = 0.00 18.7 86.14% 579.16 8.14 53.80 79.02% Current System 18.8 85.95% 581.68 8.08 53.84 78.89% Improvement 0.19% 2.52 (0.06) 0.04 -0.13% R3 L20 A90 Clinic Model, priority = 0.00 10.7 88.68% 593.58 4.40 56.67 57.99% Current System 10.7 88.69% 592.99 3.95 57.08 58.57% Improvement -0.01% (0.59) (0.46) 0.41 0.59%

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85 Table 6.8 Clinic and Current System Model Variance Comparison Number of Patients Practitioner Utilization Clinic Close Time Waiting Room Wait Time Total Wait Time Room Utilization R2 L0 A15 Clinic Model, priority = 0.00 19.3 0.03% 1313.49 205.35 221.73 0.16% Current System 19.3 0.04% 1576.87 206.69 249.14 0.18% R2 L0 A90 Clinic Model, priority = 0.00 10.7 0.10% 1420.02 199.22 381.61 0.78% Current System 10.7 0.11% 1245.71 179.35 354.98 0.82% R2 L20 A15 Clinic Model, priority = 0.00 18.8 0.06% 1573.26 243.95 274.76 0.19% Current System 18.8 0.07% 1951.21 230.24 266.74 0.18% R2 L20 A90 Clinic Model, priority = 0.00 10.7 0.10% 1192.70 140.73 338.51 0.98% Current System 10.7 0.10% 1268.93 137.69 323.94 0.98% R3 L0 A15 Clinic Model, priority = 0.00 18.7 0.07% 1193.82 35.58 124.39 0.80% Current System 18.8 0.07% 1015.62 41.26 122.92 0.66% R3 L0 A90 Clinic Model, priority = 0.00 10.7 0.09% 1312.48 18.07 343.54 1.23% Current System 10.7 0.10% 1086.03 33.27 377.98 1.28% R3 L20 A15 Clinic Model, priority = 0.00 18.7 0.07% 1183.24 30.90 128.74 0.72% Current System 18.8 0.07% 1028.07 31.82 140.23 0.77% R3 L20 A90 Clinic Model, priority = 0.00 10.7 0.11% 1038.48 14.87 294.79 1.23% Current System 10.7 0.11% 1117.17 15.75 296.84 1.29%

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86 Table 6.9 Clinic and Current System Model Comparison with Reduced Patients: Average Output Number of Patients Practitioner Utilization Clinic Close Time Waiting Room Wait Time Total Wait Time Room Utilization R2 L0 A15 Clinic Model, priority = 0.75 17.7 84.33% 557.87 16.01 46.60 91.36% Current System 19.333 83.70% 605.82 23.78 55.35 94.03% Improvement / Patient Loss 1.63 0.63% 47.95 7.77 8.75 -2.68% % gain 8.45% 0.75% 7.91% 32.66% 15.81% -2.85% R2 L0 A90 Clinic Model, priority = 0.75 9.0666 88.27% 550.50 3.79 46.42 73.24% Current System 10.733 89.04% 591.31 9.81 55.14 80.68% Improvement / Patient Loss 1.67 -0.77% 40.81 6.03 8.72 -7.44% % gain 15.53% -0.87% 6.90% 61.41% 15.81% -9.22% R2 L20 A15 Clinic Model, priority = 0.75 17.1 83.74% 556.91 18.83 50.09 90.32% Current System 18.766 83.23% 601.38 25.14 57.02 92.88% Improvement / Patient Loss 1.67 0.51% 44.47 6.31 6.93 -2.55% % gain 8.88% 0.61% 7.39% 25.10% 12.15% -2.75% R2 L20 A90 Clinic Model, priority = 0.75 9.0666 87.45% 557.59 5.66 45.22 69.93% Current System 10.733 88.06% 597.32 12.92 56.61 78.53% Improvement / Patient Loss 1.67 -0.61% 39.73 7.26 11.40 -8.61% % gain 15.53% -0.69% 6.65% 56.18% 20.13% -10.96%

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87 Table 6.9 (Continued) Number of Patients Practitioner Utilization Clinic Close Time Waiting Room Wait Time Total Wait Time Room Utilization R3 L0 A15 Clinic Model, priority = 0.75 17.166 86.22% 536.71 2.83 47.32 76.96% Current System 18.766 86.55% 577.65 5.45 52.75 81.26% Improvement / Patient Loss 1.60 -0.33% 40.94 2.62 5.43 -4.29% % gain 8.53% -0.38% 7.09% 48.03% 10.28% -5.28% R3 L0 A90 Clinic Model, priority = 0.75 9.0666 88.82% 546.47 0.35 48.02 51.99% Current System 10.733 89.84% 584.80 2.39 57.56 60.54% Improvement / Patient Loss 1.67 -1.02% 38.33 2.04 9.54 -8.55% % gain 15.53% -1.14% 6.55% 85.34% 16.58% -14.12% R3 L20 A15 Clinic Model, priority = 0.75 17.166 85.53% 543.51 5.58 48.44 74.19% Current System 18.766 85.95% 581.68 8.08 53.84 78.89% Improvement / Patient Loss 1.60 -0.43% 38.17 2.50 5.40 -4.70% % gain 8.53% -0.50% 6.56% 30.93% 10.02% -5.96% R3 L20 A90 Clinic Model, priority = 0.75 9.0666 87.48% 556.79 2.87 46.78 49.19% Current System 10.733 88.69% 592.99 3.95 57.08 58.57% Improvement / Patient Loss 1.67 -1.21% 36.20 1.08 10.30 -9.38% % gain 15.53% -1.36% 6.10% 27.35% 18.04% -16.02% Similarly, all eight settings are used to evaluate the output improvements that result from our clinic model with priority crit eria 0.75. As previously mentioned, clinic close time, waiting room wait time and total wait time show an improvement as compared to the current system. However, poorer performance in practitioner and room utilization also occurs. The output changes can be attributed to the change in number of patients. By using the stricter acceptance prio rity criteria, fewer late and walk-in patients are added to the day’s schedule. The actual improvement / patient loss is shown in Table 6.9. The percent gain, the ratio of the act ual output improvement to the current system value, is also shown in Table 6.9. The percen tage of patients lost can be compared to the

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88 percent gain for each output to evaluate tota l system impact. Unfortunately, information outside the scope of this work (e.g., cost, patient satisfaction a nd hospital reputation) would be needed to determine if a loss in number of patients is justified by an improvement in clinic close time and waiting times. An analysis of results from the clinic and current system simulation models was presented in this chapter. The decision models developed in this resear ch were tested as a case study of an H. Lee Moffitt outpatient clinic. Conclusions from this case study, additional applications of the decision mode ls and future research extensions are discussed in the Chapter 7.

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89 Chapter Seven Conclusions and Future Work We were motivated to provide a decisi on making model for outpatient clinics to improve patient waiting time. The obvious disconnect between a scheduled appointment time and the actual time a patient sees his/ her practitioner initiat ed our research. Eventually, our work focused on the daily sc heduling decisions clinics make to handle variable patient demand. The purpose of our models is to handle the scheduling and rescheduling of walk-in and late patients respectively as well as determine in what order the practitioner should see patients. Due to the complicated nature of hea lthcare and patient conditions, scheduling and operational decisions in an outpatient clinic are complex. Many factors can influence these decisions, many of which are dynamic. C linics may not have the resources (time or staff) to thoroughly evaluate all relevant f actors and make a well-in formed decision every time. This work attempts to improve system performance (including patient waiting time) by developing decision models that inco rporate all relevant factors and generate information to make the decision. The inclus ion of all relevant f actors was expected to improve scheduling and operational decisions. A computer simulation modeled after a Moffitt clinic tested our models. Conclusi ons from this case study are discussed in the next section.

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90 7.1 H. Lee Moffitt Case Study Conclusions The proposed decision models (PPM a nd AAM) successfully made walk-in and late patient scheduling decisions as well as modified the sequence in which patients were called back. When there was no reduction in number of patients, our models performed the same as the current system. Differences were within one percentage for practitioner and room utilization and within three minutes for waiting time. The greatest improvement in any of the eight settings was an average clin ic close time improvement of 7.76 minutes. Although our decisions models did not generate a clear improvement to the system outputs measures, the models did incorporate all the rele vant criteria defined by Moffitt without any adverse effect. The contributions of this re search include identifying, defining and weighting of relevant decision making criteria at H. L ee Moffitt. The criteria and weights were successfully modeled in our Patient Priority and Appoint ment Assignment Models and tested using a single-clinic computer simulati on. Our decision models guaranteed all of the defined criteria are included every time a walk-in or late patie nt decision must be made. Therefore, making more informed d ecisions that are centered on the patient and clinic conditions. Based on these findings implementation of the PPM and AAM with no reduction in number of patients would im prove scheduling and operational decisions while not affecting clinic output measures. C onsidering a reduction in number of patients through the use of our PPM should also be discussed. One aspect of our PPM is the priority criteria. This criterion determines if a late or walk-in patient will be a dded to the day’s schedule. Th is is not current practice at Moffitt. Using our PPM to create a score for each walk-in and late patient and setting the

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91 criteria at 0.75 reduced the average number of patients seen and showed some system improvement. On average the clinic clos ed between 36.20 minutes and 47.95 minutes earlier. Waiting time was also lowered, although not as significantly as clinic close time. Average total waiting time was reduced betw een 5.43 minutes and 11.40 minutes. While reducing patients made improvements in clin ic close time and waiting time, practitioner and room utilization suffered. Generally, the current system (with all patients) reported better practitioner and room utilizations. The tradeoff among number of patients seen, resource utilization, waiting time and clinic close time cannot be fully assessed solely on the information gathered in this research. A dditional information such as costs, patient satisfaction and clinic/hospital reputation w ould also need to be considered. These recommendations are based only on the decisi on model performance in the Moffitt clinic setting. Using H. Lee Moffitt as a case st udy imposed certain assumptions and conditions on this research. The implications of usi ng Moffitt clinics as a case study are discussed in the following section. 7.2 H. Lee Moffitt Case Study Assumptions and Conditions H. Lee Moffitt is a hospital providing comprehensive treatment to a specific segment of the population, cancer patients. Moffitt patients are e ither in need of diagnosis, receiving treatment or monitoring previous condition s. Patients are generally assigned to a practitioner and have scheduled appointments. As a result of the highly specialized nature of Moffitt and its reputati on, people travel distances and wait months to become a Moffitt patient. Clearly, this patient population is different than the population of a community hospital, for example.

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92 The patient attributes (fac tors defined in Chapter 4) used to in the clinic simulation models were all based on Moffitt patients. The list of attributes and distributions of each attribute were generate d by Moffitt clinic staff. Urgency, distance traveled and a second same-day appointment are a few examples of patient attributes where the distribution would most likely change in an alternate hos pital setting. In addition to the list of patient attributes and corresponding distributions, Moffitt staff was also used to generate the relative weights a nd values used in our decision models. The Moffitt clinic staff was surveyed and respons es were used to calculate the relative weights and values reported in Chapter 4. Th e results reported in this work are specific to Moffitt. However, the decision models are tr ansferable to other outpatient facilities. 7.3 Other Applications The decision model concept described in this work can be transferred to other outpatient settings. Although the specific factor s, weights and values defined in Chapter 4 may not be applicable, they can be replaced. Any outpatient facility is able to generate a list of factors that influence scheduling a nd operational decisions. Relative weights and values are able to be produced in a fashion si milar to that described in Chapters 3 and 4. To create a global set of factors, weights and values that are ab le to effectively be used in any outpatient setting would involve the coll aboration of a multi-d iscipline healthcare team. However, creating a set of factors, we ights and values specific to a facility is plausible. The outpatient clinics at Moffitt are just that, outpatient clinics within a hospital setting. Our decision models are just as a ppropriate for independent outpatient facilities,

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93 such as a primary care doctor’s office, dentist or eye doctor. Any f acility that is subject to patient demand that includes walk-in and/ or late patients could apply our decision models. The decision models could also be appl ied to a strictly walk-in patient facility or a system that does not assign a patient to a practitioner. Some modification might be needed. For example, late patients w ould not exist if there were no scheduled appointments. Although the original motiva tion for the decision models stemmed from the adherence to a scheduled appointment time a schedule is not necessary to apply our decision models. The PPM and AAM do address same-day decisions, therefore are less likely to apply in an inpatient setting. Extension outside the healthcare industry is also possible. The decision models are applicable where there exists a server, a ppointment system and variable demand. If everyone always arrived on time and with an appointment, there would be minimal need for these decision models. Plans for further work are discussed in the last section. 7.4 Future Work The first step in this research was to test our decision models against the current system at Moffitt. The decision models we re expected to improve clinic system performance. However, our findings do not s upport that suspicion. Therefore, future work is needed to understand why the perf ormance was the same despite the changes made to scheduling and operational decisions. Future work is also needed to determine what changes will affect clinic system performance or if there was in impact at the hospital level of performance. Alterations to patient distributions factors or weights

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94 could potentially change system outputs. This can be accomplished my modifying the information gathered from Moffitt or by studying a different outpatient clinic setting.

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95 References Abernathy, W. J., Baloff, N., Hershey, J. C., Wandel, S., 1973, “A three-stage manpower planning and scheduling model – a service sector example,” Operations Research, 21 (3), 693-711. Aczel, J. and Saaty, T. L.,1983, “Procedures for Synthesizing Ratio Judgment,” Journal of Mathematical Psychology, 27, 93-102. Baesler, F.F., Sepulveda, J.A., 2001, “Multi -objective simulation optimization for a cancer treatment center,” Proceedings of the Winter Simulation Conference, 1405-1411. Bard, J. F., 1992, “A comparison of the anal ytic hierarchy proce ss with multiattribute utility theory: a cas e study,” IIE Transactions, 24 (5), 111-121. Brahimi, M., Worthington, D.J., 1991, “Queuei ng models for out-patient appointment systems-A case study,” The Journal of the Operational Research Society, 42(9), 733-746. Carter, M. W., and Lapierre, S. D., 2001, “S cheduling emergency room physicians,” Health Care Management Science, 4 (4), 347-360. Cayiril, T., and Veral, E., 2003, “Outpatient scheduling in health care: a review of literature,” Production and Operations Management, 12 (4), 519-549. Chang, J., 2005, “A generalized decision model for naval weapon procurement: Multiattribute decision making,” Unpublished disse rtation, University of South Florida. De Angellis, V., Felici, G., and Impelluso, P., 2003, “Integrating simulation and optimization in health care centre mana gement,” Eruopean Journal of Operational Research, 150, 101-114. Denton, B., and Gupta, D., 2003, “A se quential bounding approach for optimal appointment scheduling,” IIE Tr ansactions, 35 (11), 1003-1016. Donegan, H. A., Dodd, F. J. and McMaster, T. B. M., 1992, “A new approach to AHP decision-making,” The Statistician, 41 (3), 295-302.

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96 Dryer, J. S., 1990, “Remarks on the analytic hierarchy process,” Mana gement Science, 36 (3), 249-258. Everett, J. E., 2002, “A decision support si mulation model for the management of an elective surgery waiting system,” Health Care Management Science, 5 (2), 89-95. Fbregas, A. et al., 2004, Simulacin de sistemas productivos con Arena EdicionesUninorte. Barranquilla. Ferland, J. A., 2001, “Generalized assi gnment type goal programming problem: application to nurse scheduling, ” Journal of Heuristics, 7, 391-413. Fone, D., Hollinghurst, S., Temple, M., Round, A ., Lester, N., Weightma n, A., Roberts, K., Coyle, E., Bevan, G., and Palmer, S., 2003, “Systematic review of the use and value of computer simulation modelli ng in population health and health care delivery,” Journal of Public Health Medicine, 25(4), 325-335. Forman, E. H. and Gass, S. I., 2001, “The an alytic hierarchy proce ss” An exposition,” Operations Research, 49 (4), 469-486. Harker, P. T. and Vargas, L. G., 1990, “Reply to “Remarks on the analytic hierarchy process” by J. S. Dryer*,” Management Science, 36 (3), 269-273. Harper, P. R., 2002, “A framework for opera tional modeling of hospital resources,” Health Care Management Science, 5 (3), 165-173. Hing, E., and Middleton, K. (2004). National hospital ambulatory medical care survey: 2002 outpatient department summary (345). Advance Data fr om Vital and Health Statistics, US Department of Health and Human Services. Ho, C., Lau, H., 1992, “Minimizing total cost in scheduling outpat ient appointments,” Management Science, 38(12), 1750-1764. Ho, C., Lau, H., 1999, “Evaluating the impact of operating conditions on the performance of appointment scheduling rules in se rvice systems,” European Journal of Operational Research, 112, 542-553. Hobbs, B. H., 1980, “A comparison of wei ghting methods in power plant siting,” Decision Sciences, 11, 725-737. Jaumard, B., Semet, F., and Vovor, T., 1998, “A generalized linear programming model for nurse scheduling,” European Jour nal of Operational Research, 107, 1-18. Kamenetzky, R. D., 1982, “The relationship be tween the analytic hierarchy process and the additive value function, ” Decision Sciences, 13, 702-713.

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97 Kim, S., Horowitz, I., Young, K. K., Buckley, T. A., 2000, “Flexible bed allocation and performance in the intensive care unit, ” Journal of Operational Research, 18, 427443. Klassen, K. J., and Rohleder, T. R., 2004, “Outpatient appointment scheduling with urgent clients in a dynamic, multi-period environment,” International Journal of Service Industry Management, 15 (2), 167-186. Kokkotos, S., Ioannidis, E. V ., and Spyropoulos, C. D., 1997, “A system for efficient scheduling of patient tests in hospita ls,” Medical Informatics, 22 (2), 179-190. Lehaney, B., Clarke, S. A., and Paul, R. J ., 1999, “A case of an intervention in an outpatients department,” Journal of Operational Res earch Society, 50, 877-891. Miller, H. E., Pierskalla, W. P., and Ra th, G. J., 1976, “Nurse scheduling using mathematical programming,” Operations Research, 24 (5), 857-870. Millar, H. H., Kiragu, M., 1998, “Cyclic and non-cyclic scheduling of 12 h shift nurses by network programming,” European J ournal of Operational Research, 104, 582592. National Center for Health Statistics, Centers for Disease Control and Prevention. (2004). Heath, United States, 2004 with Chartbook on Trends in the Health of Americans (28).Hyattsville, Maryla nd: US Department of Health and Human Services. Rising, E., Baron, R. and Averill, B., 1973, “A systems analysis of a university health service outpatient clinic,” Operat ions Research, 21(5), 1030-1047. Robinson, L. W., Chen, R. R., 2003, “Sche duling doctor’s appointments: optimal and empirically-based heuristic polic ies,” IIE Transactions, 35(3), 295-307. Rohleder, T. R., Klassen, K. J., 2002, “R olling horizon appointment scheduling: A simulation study,” Health Care Management Science, 5(3), 201-209. Saaty, T. L. (1980). The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation. McGraw-Hill. New York. Saaty, T. L.,1986, “Axiomatic Foundation of the Analytic Hierarchy Process,” Management Science, 32 (7), 841-855. Saaty, T. L. and Vargas, L. G. (2001). Models, Methods, Concepts and Applications of the Anal ytic Hierarchy Process. Kluwer Academic Publishers. Boston.

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98 Sepulveda, J.A., Thompson, W.J., Baesler, F. F., Alvarez, M.I. and Cahoon, L.E., 1999, “The use of simulation for process impr ovement in a cancer treatment center,” Proceedings of the Winter Simulation Conference, 1541-1548. Sofaer, S., and Firminger, K., 2005, “Patient perceptions of the quality of Health services,” Annual Review of Public Health, 26, 513-559. Soliman, E., 1997, “Improving resource utiliza tion through patient dependency systems,” Journal of Medical Systems, 21 (5), 291-302. Swisher, J.R., Jacobson, S.H., Jun, J.B., a nd Balci, O., 2001, “Modeling and analyzing a physician clinic environment using discre te-event (visual) simulation,” Computers and Operations Research, 28, 105-125. Su, Syi, Shih, Chung-Liang, 2003, “Managing a mixed-registration-type appointment system in outpatient clinics,” Internationa l Journal of Medical Informatics, 70(1), 31-40. Triantaphyllou, Evangelos (2000). Multi-criteria Decision Making Methods: A Comparative Study. Kluwer Academic Publishers. Boston. Vaidya, O. S., and Kumar, S., 2006, “Analy tic hierarchy process: an overview of applications” European Journal of Operational Research, 169, 1-29. Vissers, J.M.H., 1998a, “Health care manageme nt modeling: a process perspective,” Health Care Management Science, 1, 77-85. Vissers, J. M. H., 1998b, “Patient flow-based allocation of inpatient resources: a case study,” European Journal of Oper ational Resources, 105 (2), 356-370. Warner, D. M., 1976, “Scheduling nursing pers onnel according to nursing preference: a mathematical programming approach,” Operations Research, 24 (5), 842-856. Warner, D. M., Prawda, J., 1972, “A mathem atical programming model for scheduling nursing personnel in a hospital,” Management Science, 19 (4), 411-422. Worthington, D., Brahimi, M., 1993, “Improvi ng out-patient appointment systems,” International Journal of Health Quality Assurance, 6(1), 18-23. Xu, Z., 2000, “On consistency of the weighted geometric mean complex judgment matrix in AHP,” European Journal of Op erational Research, 126, 683-687. Yeh, C., 2002, “A problem-based selection of multi-attribute decision making methods,” International Transactions in Op erational Research, 9, 169-181.

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99 Yoon, P. K. and Hwang, C., (1995). Multiple Attribute Decision Making: An Introduction. Sage Publications. California. Zanakis et al., 1998, “Multi-att ribute decision making: A simula tion comparison of select methods,” European Journal of Op erational Research, 107, 507-529.

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100 Appendices

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101 Appendix A: Moffitt Clinic Observations PSRs GU Tuesday, December 20 2005 If patient arrives within 15 mi nutes of appointment time o checked in as usual If patient arrives more than 15 minutes late o Patient asked why they are late o PSR does not change anything in the sy stem when a patient arrives late o PSR consults with Nurse before the patient can be checked in o According to PSR, Nurse typically asks PSR why the patient arrived late o PSR may use their own discre tion if Nurse is unavailable o Nurse may also consult with the Physician If a patient needs to be added on o PSRs (Check-in and Scheduler) consult with Nurse before a patient without an appointment can be added into the schedule o Needs to be a clinical reason for the patient to be an add-on o If the patient is physically in the clinic, a NOW appointment (for that current time) is made – otherwise, the Nurse determines what time to add the patient o Some patients who arrive without an appointment may only need to speak to the Nurse, an appointment is not made Physician preference or common practice is used as a guideline for decision making Type of visit (ex. New Patient) is taken into consideration when a patient arrives late GI Tuesday, December 27 2005 If the patient arrives late o PSR consults with Nurse and asks how it should be handled o Nurse either tells the PSR to register the patient or consults with the Physician and then instructs the PSR If the patient needs to be added on o PSR consults with Nurse ( avg of 12 add-ons / day ) o Nurse either tells the PSR to register the patient or consults with the Physician and then instructs the PSR – some Physicians are always consulted o When Nurse instructs PSR to add the patient, the PSR “pre-registers” the

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102 Appendix A: (Continued) o patient – the patient is then sent to another PSR (scheduler) to be added into the schedule. o Scheduler consults with the Nurse ag ain about what time to add in the patient o If a Nurse specifies a time, the scheduler adds the patient in at that time regardless of availability. The Nurse may also leave the appointment time up to the scheduler’s discretion (next tim e slot – regardless of availability) Cutaneous Tuesday, January 3 2006 If a patient arrives late o PSR handles differently depending on P hysician, some Physicians always have to be consulted o Patients always fit into the schedule – Physicians are only in clinic certain days each week. o Patient appointments adjusted at Physician’s request o PSR will check with the MA and Nurse – they make the decision about when to call back the patient – Patient appointment not changed in the schedule If a patient needs to be added on o Nurse is consulted o Patients always fit into the schedule o Happens frequently Breast Thursday, January 5 2006 If the patient arrives late o The check-in PSR contacts the registrati on PSR that the patient is late and asks if / when the patient will be seen o Registration PSR decides if the patient will be registered – they usually take into account the condition of the patient o Visit type is considered (ex. Proce dures) may be rescheduled due to the length of the visit If the patient needs to be added on o PSR contacts the scheduler or sends th e patient directly to the scheduler o 3 add-ons / day is high for this clinic PSRs have very little contact with the Nurses

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103 Appendix A: (Continued) MA GU Thursday, December 22 2005 Call back o Generally, in appointment order MA If patients arrive early MA o Patients may be taken early, Physician dependant o MA asks and Physician d ecides if the patient is brought back to a room early o May depend on type of visit (N ew vs. Established patients) o May depend also on Physician “speed” and preference If the patient arrives late (more than 15 minutes) MA o Moffitt will always see the patient, becomes a matter of priority o Patient may be put at the end of clinic for that day (after the last scheduled patient) if a low priority o May consider past behavior (i s the patient always late?) o May also consider the cause of delay (patient coming from IC) o The MA screen shows who is checked in Cutaneous Tuesday, January 3 2006 Call back MA o Normally, by appointment o If no show – go to next appointment o If double booked – call back whomever arrived first If the patient is early o May take early if the Physician is available If the patient is late o MA will consult Nurse o Emergencies are a priority o Will consider if the patient had another Moffitt appointment (ex. IC) Breast Thursday, January 5 2006 Call back MA1 o As Arrive, not necessarily by appointment (as long as it is close to the appointment time)

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104 Appendix A: (Continued) o Wont call back 2 or 3 hours early o If the patient is ill, they will bring them back to rest in a bed until their appointment time (may call back to a room if one is available) o Call back when you don’t have anyone who is scheduled If the patient is early MA1 o Will only take a patient a few minutes early (10 minutes) If the patient arrives late MA1 o (30 min – 1 hour) MA will call back at their discretion o Patient wont have to wait all da y, just until there is a space o If (5-10 min) late MA will still call back as usual as long as no other patient was called back or if the patient’s name was not called yet If the patient needs to be added on MA1 o MA will consult Nurse Call back MA2 o Ill patients are a priority o Physicians preference is considered – want situations handled differently o If the patients are waiting for labs or reports – will delay call back – MA will call next patient instead If the patient is early MA2 o Check if patient had labs done o Wont call a patient back ju st because they are early If the patient is late MA2 o Consult Nurse If the patient needs to be added on MA2 o Decision made by Physician and Nurse

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105 Appendix A: (Continued) Nurses GU Thursday, December 22 2005 If the patient is late (more than 15 minutes) Nurse o Nurse decides how to schedule the patient o If the patient is really late, they ma y be turned away (more than 2 hours) if: Physician is already backed up It is a follow-up appointment Habitual lateness o Nurse does not want to back up other patients o Nurse may consider: Appointment type Illness Distance (Patient’s who travel) Overbooked anyway Physician is backed up and thei r ability to see the patient If the patient needs to be added on Nurse o Use the same criteria if at the clinic or on phone (medical need) o Nurse may decide or may consult the physician o Nurse cannot consider all factors o Use experience and judgment Senior Adult Thursday, December 22 2005 If the patient is late Nurse o Will see even if late o Find a time in the schedule If the patient needs to be added on Nurse o Finds a place in the schedule o Try not to make on-time patients wait Cutaneous Tuesday, January 3 2006 Call back Nurse o Generally, in appointment order o Nurse makes most calls, may even te ll MA when to call back the next patient

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106 Appendix A: (Continued) If the patient is late Nurse o If the patient is “very late” (not specifically defined) treated the same as an add-on o If the patient is not “very late” (15-30minutes) they are treated as usual – the clinic is usually running late – late patients end up being “on time” If the patient needs to be added on Nurse o Added in as able o Patients brought in at the end of clinic if needed o Already scheduled patients have priority General priority to patients who Nurse o Very sick o VIP o Causing an issue in the waiting room Breast Thursday, January 5 2006 If the patient is late Nurse o Try to see – have other resources (Fellows, residents… anyone on the same Physician team) can see the patient o Generally consider the symptoms If the patient needs to be added on Nurse o If it is an emergency – patient will be seen in the first available space o If the patient just walked in, they wi ll wait – the registered patients have priority o Some patients will be turned away – very rarely Call back Nurse2 (plastic surgery) o Critical patients have priority o Physicians want rooms filled o Will call back patients who are in the waiting room – even if early – wont take a patient in front of anot her (as far as appointment time) o If the patient is late Nurse2 (plastic surgery) o Less than 20 – 30 min – treated as usual o More than 20 – 30 min – treated like an add on

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107 Appendix A: (Continued) If a patient needs to be added in Nurse2 (plastic surgery) o Will overbook and double book o Typically added on at the end of the day Patients can be sent to Triage Summary What patient to call back next: 1. Appointment time (in order) 2. Arrival time a. If double booked b. As long as close to appointment time c. Wont take back 2-3 hours early, on ly take a few minutes early 3. Physician preference 4. Physician ability to see patients (speed) 5. Medical condition / urgency 6. Pending labs / reports (will delay patient call back) 7. VIP patients When to schedule / see a late or add-on patient: 1. How late is the patient a. 15 min criteria b. 30min – 1hr criteria c. 15-30 min criteria d. More than 2 hours – may be turned away 2. Current Physician schedule a. If already backed up b. Don’t want to cause delay for scheduled patients c. Scheduled patients have priority 3. Cause of delay a. Coming from another Moffitt appointment 4. Medical condition / urgency 5. Physician Preference 6. Type of visit / expected length of visit 7. Past behavior (habitually late) 8. Physician ability to see patients (speed) Standard – next appointment End of clinic mentioned more than once

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108 Appendix B: Interviews with 3rd floor Clinic Nurses May 19, 2006 Decision: to see a walk-in patient the same day Based on medical condition (urgency) If the patient is unable to be treated in th e clinic (very urgent) they will be sent to the Direct Referral Center (DRC) Patient may be sent home if condition doe s not warrant being seen the same day – although one nurse said they will always see them Decision: choose an approxima te time to see the walk-in 1. an open space (possibly from a no-show or cancellation) 2. use some of the lunch hour 3. end of the day 4. If nothing is available at the end of the day… may double book 1 nurse does NOT ever double book No triple booking Will only double book so many patients in a day (2 or 3) Double book shorter appointment lengt hs (follow-ups 10 or 15 mins) Do NOT double book new patient appt s (longer appointment lengths) If 2 patients are double boo ked – take in arrival order or shortest appt length first. The best place to put a patient is wher e there is the least delay for patients They do consider medical state – an urgent patient will be seen ASAP. Less urgent walk-ins will wait for the next opening after the sc heduled patients have been seen. If the walk-in is urgent, they may be seen before a scheduled patient. One nurse said the scheduled patient is ALWAYS the priority over the walk-in. They would have the walk-in wait as long as needed. Decision: to see a late patient Will only NOT see if very late (hours) or the clinic is already closed (5pm) Will see late patients since they had a scheduled appointment Decision: choose an approximate time to see the late patient 5. if less than ~ 30 min late – will see as us ual (will take the next patient on the schedule first and then the late pati ent right after) – appointment order 6. if more than ~ 30 min late next open space 7. lunch hour 8. end of day 9. If nothing is available at the end of the day… may double book 1 nurse does NOT ever double book No triple booking Will only double book so many patients in a day (2 or 3)

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109 Appendix B: (Continued) Double book shorter appointment lengt hs (follow-ups 10 or 15 mins) Do NOT double book new patient appt s (longer appointment lengths) If 2 patients are double boo ked – take in arrival order or shortest appt length first. General clinic information: Last patient usually scheduled around 3:30 / 4pm. Number of patients able to be a dded to the end of the schedule 1-2 (said by 2 nurses) Up to 5 (said by 1 nurse) Clinic closes at 5pm – means that the PSRs leave – nurses and practitioners may still be there. They don’t bring anyone back after 5pm. The nurses / practitioners stay until the last patient is seen. Of working time in the clinic – practiti oners spend between 60% and 75% of their time in the exam rooms with patients Maximum number of patient s seen in a day 13-17 Assigned appointment lengths are pretty a ccurate for the total amount of time a patient spends in the exam ro om (time after called back) After the practitioner leaves the patient sp ends ~ 5 min extra in the exam room – may be more if there is education/teachi ng involved – they will try to move the patient to a consult room in this case.

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110 Appendix C: Responses from Clinic Operations Managers Meeting May 25, 2006 Clinic hours Normal clinic hours are 8am-5pm The first patient typica lly scheduled at 8am It is possible to see patients befo re 8am since staff arrives early Lunch Some practitioner take a l unch break, some schedu le patients straight through(particularly if they are not working a full day) Those who schedule a lunch break, schedule it from noon-1pm If there is a lunch from 12-1, the la st patient is sche duled at 11:30am Taking late/ walk-in patients May continue to take late or walk-in patients even after 5pm if there are other patients still in exam rooms and the practitioner is still there If there is an available slot, staff does NOT consider the length of the slot. The patient will be given that time to be seen If the patient is URGENT, they will be seen at the next available time – even if they need to double book If the patient is NOT URGENT, the staff will schedule them in the following order: o Open slot o Lunch o End of schedule o Double book Clinic performance measures A patient satisfaction score is used for a number of measures – each clinic is surveyed twice a year The performance of the schedule is discu ssed with individual practitioners when needed COMs typically consider patients being seen close to appointment time as evaluation criteria for schedul e or practitioner performance Scheduled Appointments 5%-10% new patients Established patient(EP), Post Operation(PO ), Pre-Chemo(PC) visits are either 15 or 30 minutes New patient (NP) or New established patie nt(NEP) visits are either 30, 60 or 90 minutes Surgeons see more patients/day than Medi cal Oncologists because of the types of visits typically scheduled for each. Patient demographics(from Jenny Mikos) 65% from surrounding 7 counties 11% from Hernando, Manatee and Sarasota 21% from other areas in Florida 3% from outside of Florida

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111 Appendix C: (Continued) Distribution estimates 5% urgent patients (or less) 75% (or more) of patient delays caused by Moffitt 10% of patients have pending information wh en they arrive to the clinic that is needed for their visit Pending information causes delays from 30-60minutes Walk-in arrival patterns are random (m ajority before noon, but can continue throughout the rest of the day) Practitioners spend 50% of their time in the rooms with patients Practitioners work for ~ 15mins (at a time) when doing other work(calls, reviewing patient information, etc.) Average number of rooms per practitioner: 2-3 rooms, 4 is high. May have up to 6 if no other practitioner is working that day.

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112 Appendix D: Appointment Assignment Ru les for Late and Walk-in Patients Moffitt clinic rules (based on nurse and staff interviews) Walk-in patients Decision to accept patients: Assume all patients will be seen unless expected beginning appointment time is after 5pm Assume all walk-in patients that arrive will be seen in the clinic (not sent to Direct Referral Center) Decision to assign an appr oximate appointment time: 1. Consider patient medical state (urgency) urgent patients moves to the front of the queue to be seen by the practitioner 2. an open space (possibly from a no-show, can cellation or a patient visit that ended early) 3. lunch hour 4. end of day (up to 5pm for the start of the appointment) 5. double book Time that disturbs the least numbe r of patients (schedule disruption) o Will only double book so many patients in a day (2 or 3) o Double book shorter appointment lengt hs (follow-ups 10 or 15 mins) o Do NOT double book new patient a ppointments (longer appointment lengths) Late patients Decision to accept patients: Assume all patients will be seen unless expected beginning appointment time is after 5pm Assume all late patients that arrive will be seen in the clinic (n ot sent to Direct Referral Center) Decision to assign approx imate appointment time: 1. if less than 30 min late – add to queue and take in appointment order 2. if more than 30 min late next open space 3. lunch hour 4. end of day 5. double book o Will only double book so many patients in a day (2 or 3) o Double book shorter appointment lengt hs (follow-ups 10 or 15 mins) o If multiple follow-up slots – choose first o Do NOT double book new patient a ppointments (longer appointment lengths)

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113 Appendix E: Original Survey Pair-wise Comparison Survey for Patient Priority Factors This survey form is designed to determine the amount of importance placed on different factors that affect decisions made with respec t to the priority of a patient. We hope to capture how decisions are made by clinic st aff by asking you to rate the importance you place on each factor when making decisions such as: 1. Can you add a late or walk-in pati ent to the existing schedule today? 2. Among all the waiting patients, whic h one should be called back next? Your sincere answers are very important to develop a successful decision model, which is expected to help clinical sta ff make the best scheduling deci sions with respect to multiple influencing factors. Please read each question carefully and give your answers. General Questions 1. What is your current job title? a. Clerical b. Medical Assistant c. Nurse d. Practitioner e. Management 2. How many years have you worked at Moffitt? a. Less than 1 b. 1-5 c. 5-10 d. more than 10 3. How many years have you been in the healthcare field? __________ years 4. What role do you play in the daily decisions made about patient scheduling? a. Supervisor b. Decision maker c. Carry out the decision d. None Factor Comparisons The criteria below show how to compare tw o factors at a time. If you think Factor A (Urgency) is very strongly more important than Factor B (Schedule Disruption), you should mark on the number 7 placed on the A-side as follows. Table E.1Criteria Table for Factor Comparisons: Original Survey Intensity of Importance Definition Explanation 1 Equal Importance Two activities contribute equally to the objective 3 Moderate Importance Experience and judgment slightly favor one activity over another 5 Strong Importance Experience and judgment strongly favor one activity over another 7 Very Strong Importance An activity is very strongly favored over another; its dominance demonstrated in practice 9 Extreme Importance The evidence fa voring one activity over another is of the highest possible order of affirmation Intermediate values such as 2, 4, 6 and 8 ar e possible to use by se lecting the dash ( ) between values.

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114 Appendix E: (Continued) Factor (A) Relative Im portance Factor (B) Urgency 9 7 5 3 1 3 5 7 9 Schedule Disruption A is more important B is more important Nine factors have been identified and defi ned for you. Please read them carefully. Answer the factor comparisons as you would when determining the priority of a patient with respect to scheduling walk-in or late arrival patients or which patient to call back next. Table E.2 Factor Definitions: Original Survey Factor Definition Distance Traveled the time traveled by the patient from home to Moffitt Urgency a medical state dete rmined by clinical staff Schedule Disruption the number of patient with previous appointment times Other Appointment a scheduled appointment for the same day within Moffitt that will be delayed if the patient is not seen at the current time Time to Appointment Time the difference between the current time and the appointment time. (Current time Appointment time) Cause of Delay the reason the patient was late Estimated Treatment Time the appointment length predetermined by the type of visit and the physician being seen Demand per Practitioner the daily ratio of patient hours scheduled for a given practitioner compared to the patient hours available in the schedule Pending Information any information, such as lab results or X-rays, needed for treatment in the clinic that day

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115 Appendix E: (Continued) Factor (A) Relative Im portance Factor (B) Distance Traveled 9 7 5 3 1 3 5 7 9 Urgency Distance Traveled 9 7 5 3 1 3 5 7 9 Schedule Disruption Distance Traveled 9 7 5 3 1 3 5 7 9 Other Appointment Distance Traveled 9 7 5 3 1 3 5 7 9 Time to Appointment Distance Traveled 9 7 5 3 1 3 5 7 9 Cause of Delay Distance Traveled 9 7 5 3 1 3 5 7 9 Estimated Treatment Time Distance Traveled 9 7 5 3 1 3 5 7 9 Demand per Resource Distance Traveled 9 7 5 3 1 3 5 7 9 Pending Information A is more important B is more important Urgency 9 7 5 3 1 3 5 7 9 Schedule Disruption Urgency 9 7 5 3 1 3 5 7 9 Other Appointment Urgency 9 7 5 3 1 3 5 7 9 Time to Appointment Urgency 9 7 5 3 1 3 5 7 9 Cause of Delay Urgency 9 7 5 3 1 3 5 7 9 Estimated Treatment Time Urgency 9 7 5 3 1 3 5 7 9 Demand per Resource Urgency 9 7 5 3 1 3 5 7 9 Pending Information A is more important B is more important

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116 Appendix E: (Continued) Schedule Disruption 9 7 5 3 1 3 5 7 9 Other Appointment Schedule Disruption 9 7 5 3 1 3 5 7 9 Time to Appointment Schedule Disruption 9 7 5 3 1 3 5 7 9 Cause of Delay Schedule Disruption 9 7 5 3 1 3 5 7 9 Estimated Treatment Time Schedule Disruption 9 7 5 3 1 3 5 7 9 Demand per Resource Schedule Disruption 9 7 5 3 1 3 5 7 9 Pending Information A is more important B is more important Other Appointment 9 – 7 – 5 – 3 – 1 – 3 – 5 – 7 – 9 Time to Appointment Other Appointment 9 – 7 – 5 – 3 – 1 – 3 – 5 – 7 – 9 Cause of Delay Other Appointment 9 – 7 – 5 – 3 – 1 – 3 – 5 – 7 – 9 Estimated Treatment Time Other Appointment 9 – 7 – 5 – 3 – 1 – 3 – 5 – 7 – 9 Demand per Resource Other Appointment 9 – 7 – 5 – 3 – 1 – 3 – 5 – 7 – 9 Pending Information A is more important B is more important Time to Appointment 9 – 7 – 5 – 3 – 1 – 3 – 5 – 7 – 9 Cause of Delay Time to Appointment 9 – 7 – 5 – 3 – 1 – 3 – 5 – 7 – 9 Estimated Treatment Time Time to Appointment 9 – 7 – 5 – 3 – 1 – 3 – 5 – 7 – 9 Demand per Resource Time to Appointment 9 – 7 – 5 – 3 – 1 – 3 – 5 – 7 – 9 Pending Information A is more important B is more important

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117 Appendix E: (Continued) Cause of Delay 9 – 7 – 5 – 3 – 1 – 3 – 5 – 7 – 9 Estimated Treatment Time Cause of Delay 9 – 7 – 5 – 3 – 1 – 3 – 5 – 7 – 9 Demand per Resource Cause of Delay 9 – 7 – 5 – 3 – 1 – 3 – 5 – 7 – 9 Pending Information A is more important B is more important Estimated Treatment Time 9 – 7 – 5 – 3 – 1 – 3 – 5 – 7 – 9 Demand per Resource Estimated Treatment Time 9 – 7 – 5 – 3 – 1 – 3 – 5 – 7 – 9 Pending Information A is more important B is more important Demand per Resource 9 – 7 – 5 – 3 – 1 – 3 – 5 – 7 – 9 Pending Information A is more important B is more important Open-ended Questions 1. If you think there is room for improvement in the current patient scheduling practices of the clinics, what area do you thin k could use the grea test improvement? 2. Are there any other factors affecting the priority of a patient, with respect to scheduling, that you think should be included in this survey?

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118 Appendix F: Final Survey Pair-wise Comparison Survey for Patient Priority Factors This survey form is designed to determine the amount of importance placed on different factors that affect decisions made with respec t to the priority of a patient. We hope to capture how decisions are made by clinic st aff by asking you to rate the importance you place on each factor when making decisions such as: Question #1. Can you add in a late or wa lk-in patient to the schedule today? Question #2. Which patient s hould be called back next? Your sincere answers are very important to develop a successful decision model, which is expected to help clinical sta ff make the best scheduling deci sions with respect to multiple influencing factors. Please read each question carefully and give your answers. General Questions 1. What is your current job title? a. Clerical b. Medical Assistant c. Nurse d. Practitioner e. Management 2. How many years have you worked at Moffitt? a. Less than 1 b. 1-5 c. 5-10 d. more than 10 3. How many years have you been in the healthcare field? __________ years 4. What role do you play in the daily decisions made about patient scheduling? a. Supervisor b. Decision maker c. Carry out the decision d. None Factor Comparisons The criteria below show how to compare tw o factors at a time. If you think Factor A (Other Appointment) is very strongly more important than Factor B (Pending Information) with respect to the given ques tion, you should mark on the number 7 placed on the A-side as follows. Table F.1 Criteria Table for Fact or Comparisons: Final Survey Intensity of Importance Definition Explanation 1 Equal Importance Two activities contribute equally to the objective 3 Moderate Importance Experience and judgment slightly favor one activity over another 5 Strong Importance Experience and judgment strongly favor one activity over another 7 Very Strong Importance An activity is very strongly favored over another; its dominance demonstrated in practice 9 Extreme Importance The evidence fa voring one activity over another is of the highest possible order of affirmation Intermediate values such as 2, 4, 6 and 8 ar e possible to use by se lecting the dash ( ) between values.

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119 Appendix F: (Continued) Factor (A) Relative Im portance Factor (B) Other Appointment 9 7 5 3 1 3 5 7 9 Pending Information A is more important B is more important PART A Factors related to Question #1 have been id entified and defined for you. Please read them carefully. Answer the factor comp arisons as you would when determining the priority of a walk-in or late arrival patient with respect to: Question #1: Can you add in a late or wa lk-in patient to the schedule today? Table F.2 Factor Definitions: Final Survey Factor Definition Distance Traveled the time traveled by the patie nt from home to Moffitt (1 hour, 2 hours, etc.) Other Appointment a scheduled appointment for the same day within Moffitt Cause of Delay the reason the patient was late Estimated Treatment Time the appointment length predetermi ned by the type of visit and the physician being seen Demand per Practitioner the daily ratio of patient hours scheduled for a given practitioner compared to the patient hours available in the schedule (e.g., double booked) Pending Information any information, such as lab results or X-rays, needed for treatment in the clinic that day Factor (A) Relative Im portance Factor (B) Distance Traveled 9 7 5 3 1 3 5 7 9 Other Appointment Distance Traveled 9 7 5 3 1 3 5 7 9 Cause of Delay Distance Traveled 9 7 5 3 1 3 5 7 9 Estimated Treatment Time Distance Traveled 9 7 5 3 1 3 5 7 9 Demand per Resource Distance Traveled 9 7 5 3 1 3 5 7 9 Pending Information A is more important B is more important

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120 Appendix F: (Continued) Other Appointment 9 – 7 – 5 – 3 – 1 – 3 – 5 – 7 – 9 Cause of Delay Other Appointment 9 – 7 – 5 – 3 – 1 – 3 – 5 – 7 – 9 Estimated Treatment Time Other Appointment 9 – 7 – 5 – 3 – 1 – 3 – 5 – 7 – 9 Demand per Resource Other Appointment 9 – 7 – 5 – 3 – 1 – 3 – 5 – 7 – 9 Pending Information A is more important B is more important Cause of Delay 9 – 7 – 5 – 3 – 1 – 3 – 5 – 7 – 9 Estimated Treatment Time Cause of Delay 9 – 7 – 5 – 3 – 1 – 3 – 5 – 7 – 9 Demand per Resource Cause of Delay 9 – 7 – 5 – 3 – 1 – 3 – 5 – 7 – 9 Pending Information A is more important B is more important Estimated Treatment Time 9 – 7 – 5 – 3 – 1 – 3 – 5 – 7 – 9 Demand per Resource Estimated Treatment Time 9 – 7 – 5 – 3 – 1 – 3 – 5 – 7 – 9 Pending Information A is more important B is more important Demand per Resource 9 – 7 – 5 – 3 – 1 – 3 – 5 – 7 – 9 Pending Information A is more important B is more important

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121 Appendix F: (Continued) PART B Factors related to Question #2 have been id entified and defined for you. Please read them carefully. Answer the factor comp arisons as you would when determining the priority of a patient with respect to: Question #2: Which patient should be called back next? Factor Definition Other Appointment a scheduled appointment for the same day within Moffitt Time to Appointment Time the difference between the current time and the appointment time. (Current time – Appointment time) Cause of Delay the reason the patient was late Estimated Treatment Time the appointment length predetermi ned by the type of visit and the physician being seen Pending Information any information, such as lab results or X-rays, needed for treatment in the clinic that day Time to Appointment 9 – 7 – 5 – 3 – 1 – 3 – 5 – 7 – 9 Cause of Delay Time to Appointment 9 – 7 – 5 – 3 – 1 – 3 – 5 – 7 – 9 Estimated Treatment Time Time to Appointment 9 – 7 – 5 – 3 – 1 – 3 – 5 – 7 – 9 Other Appointment Time to Appointment 9 – 7 – 5 – 3 – 1 – 3 – 5 – 7 – 9 Pending Information A is more important B is more important Cause of Delay 9 – 7 – 5 – 3 – 1 – 3 – 5 – 7 – 9 Estimated Treatment Time Cause of Delay 9 – 7 – 5 – 3 – 1 – 3 – 5 – 7 – 9 Other Appointment Cause of Delay 9 – 7 – 5 – 3 – 1 – 3 – 5 – 7 – 9 Pending Information A is more important B is more important

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122 Appendix F: (Continued) Estimated Treatment Time 9 – 7 – 5 – 3 – 1 – 3 – 5 – 7 – 9 Other Appointment Estimated Treatment Time 9 – 7 – 5 – 3 – 1 – 3 – 5 – 7 – 9 Pending Information A is more important B is more important Other Appointment 9 – 7 – 5 – 3 – 1 – 3 – 5 – 7 – 9 Pending Information A is more important B is more important Open-ended Questions 1. If you think there is room for improvement in the current patient scheduling practices of the clinics, what area do you thin k could use the grea test improvement? 2. Are there any other factors affecting the priority of a patient, with respect to scheduling, that you think should be included in this survey?

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123 Appendix G: Simulation Data Table G.1 Add on patients, October 2005 Clinic # visits # addons % Direct Referral Center 136 130 95.6 Amb Internal Medicine Clinic 72 1 1.4 Integrative Medicine Clinic 27 3 11.1 GI Clinic 892 20 2.2 Neuro Clinic 489 51 10.4 Infusion Center 3847 863 22.4 GU clinic 770 35 4.5 Breast Clinic 488 19 3.9 Senior Adult Clinic 288 11 3.8 Heme Clinic 729 51 7.0 BMT clinic 430 35 8.1 BMT Infusion Area 1325 400 30.2 Women's Clinic 401 20 5.0 Sarcoma Clinic 294 23 7.8 Head & Neck Clinic 514 29 5.6 Thoracic Clinic 699 27 3.9 Breast Clinic 720 38 5.3 Cutaneous Clinic 833 40 4.8 Anesthesia Pain Clinic 46 2 4.3

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124 Appendix H: Simulation Variables System Settings 1. # rooms 2. # practitioners 3. # nurses 4. # MAs 5. Clinic hours 6. Lunch hour 7. Last appointment 8. Last appointment before lunch 9. Time last add-in patients accepted 10. Double booking 11. Patient assignment to Practitioner Input Data 1. Arrival distribution (% late patients) 2. Walk-in arrival distribution 3. Max # of walk-in patients 4. Appointment distribution 5. Practitioner extra task distribution 6. Max # of Practitioner extra tasks 7. Nurse extra task distribution 8. Max # of Nurse extra tasks 9. MA extra task distribution 10. Max # of MA extra tasks 11. Practitioner process distribution 12. Nurse Process distribution 13. MA process distribution Outputs 1. Number of patients 2. Practitioner Utilization 3. Clinic close time 4. Waiting room wait time 5. Room utilization

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125 Appendix I: Gantt Charts Figure I.1 Setting R2 L0 A15 Gantt Chart

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126 Appendix I: (Continued) Figure I.2 Setting R2 L0 A90 Gantt Chart