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PAGE 1 Modeling Alternate Strategies for Airline Revenue Management b y Kapil Joshi A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Industrial Engineering Department of Industrial and Management Systems Engineering College of Engineering University of South Florida Major Professor: Suresh Khator, Ph.D. Qiang Huang, Ph.D. Kaushal Chari, Ph D. Date of Approval: November 10 2004 Keywords: network, simulation, yield, ticket, pricing Co pyright 2004, Kapil Joshi PAGE 2 i TABLE OF CONTENTS LIST OF TABLES iv LIST OF FIGURES v ABSTRACT v i CHAPTER 1. INTRODUCTION 1 1.1 Revenue Management in Airline Industry 2 1.1.1 Seat or Discount Allocation 2 1.1.2 Overbooking 3 1.1.3 Ticket P ricing 4 1.2 Characteristics of Revenue Management 5 1.3 Revenue Management in Other Industries 6 1.4 T hesis Organization 6 CHAPTER 2. L ITERATURE REVIEW 7 2.1 Seat Inventory Control 7 2.1.1 Single Leg Inventory Control 7 2.1.1.1 Static Solution Methods 8 2.1.1.2 Dynamic Solution Methods 8 2.1.2 Network Inventory Control 9 2.2 Ticket Pricing Models 10 2.2.1 Dynamic Prici ng Models 10 CHAPTER 3. RESEARCH STATEMENT 13 3.1 Problem Statement 13 3.2 Research Assumptions 1 4 3.3 Factors and Str ategies Considered 14 3.3.1 Pricing Str ategy 15 3.3.2 Acceptance Probability 15 3.3.3 Customer Arrival Rate 1 5 3.4 Research Objectives 15 CHAPTER 4. MODELING AND SOLUTION METHODOLOGY 16 4.1 Pricing Str ategy 16 4.1.1 Time Remaining Approach 16 PAGE 3 ii 4.1.2 Seats Remaining Approach 17 4.1.3 Hybrid App roach 18 4.2 Acceptance Probability 18 4.2.1 Probability with R esp ect to Price Offered 18 4.2.2 Probability with R espe ct to Time Remaining 19 4.2.3 Com posite Probability 19 4.3 Customer Arrival Rate 20 4.4 Simulation as A Tool 20 4.5 Model Development 21 CHAPTER 5. EXPERIMENT DESIGN AND ANALYSIS OF RESULTS 2 3 5.1 Single L eg Models 2 3 5.1.1 Normalizing Constants 2 3 5.1.1.1 Time Remaining Approach 2 3 5.1.1.2 Seats Remaining Approach 2 4 5.1.1.3 Hybrid Approach 2 4 5.1.1.4 Probability of Acceptance with R espect to Price Offered 2 5 5.1.1.5 Probability of Acceptance with R espect to Time Remaining 25 5.1.1.6 Co mposite Probability 25 5.1.2 Arrival Rate 2 7 5.2 Results and Analysis 3 1 5.2.1 Sensitivity Analysis 32 5.2. 2 Analysis of Variance 3 4 CHAPTER 6. NETWORK MODELS 37 6.1 Flight Network 37 6.2 Pricing Strategy 37 6.2.1 Pricing Strateg y for Tampa New York (1 3) Direct Flight 38 6.2.2 Pricing Strategy for Tampa New York ( 1 2 3) Indirect Flight 38 6.3 Acceptance Probability Strategy 39 6.3.1 Probability of Not Buying 41 6.3.2 Price Differential 41 6.4 Arri val Distribution 42 6.5 Model Development 42 6.5.1 Blocking of Seats in 1 2 3 43 6.6 Results and Analysis 4 3 CHAPTER 7. CONCLUSIONS 50 7.1 Summary and Conclusions 50 7.2 Scope for Further Research 51 REFERENCES 53 PAGE 4 iii APPENDI CES 5 5 Appendix A Analysis of Variance 56 A.1 The analysis of variance for the medium rate of arrival 56 A.2 The analysis of variance for the high rate of arrival 56 Appendix B Method for Calculating the N umber of Replications 57 PAGE 5 iv L IST OF TABLES Table 1 Model Combinations 2 2 Table 2 Table of Normalizing Constants and t heir V alues 26 Table 3 Arrival Rates 27 Table 4 Comparison of Single Le g Models for L ow A rrival R ate 28 Table 5 Comparison of Single Leg Models fo r Medium A rrival R ate 29 Table 6 Comparison of Single Leg Models for H igh A rrival R ate 30 Table 7 Best Pricing Strategy 32 Table 8 Revenues for Low and Adjusted Low Rate of Arrival 33 Table 9 Revenues for Medium and Adjusted Medium Rate of Arrival 33 Table 10 Controls and Their Levels 34 Table 11 Flight Capacities and Pr ice Ranges 3 7 Table 12 Normalizing Constants for Pricing Strategy 40 Table 1 3 Normalizing Constants for Acceptance Probability 40 Table 14 Arrival Rate s and Pattern 44 Table 1 5 Results for Arrival Pattern 1 4 5 Table 16 Results for Arrival Pattern 2 4 6 Table 17 R esults for Arrival Pattern 3 47 Table 1 8 Best Pricing Strategy for Network Model 49 PAGE 6 v LIST OF FIGURES Figure 1 The Demand Curve 5 Figure 2 Graph of Price Offe red and Remaining Time 1 7 Figure 3 Graph of Price Offered and Remaining Seats 17 Figure 4 Graph of Probability of Acceptance and Price Offered 19 Figure 5 Graph of Probability of Acceptance and Time Remaining 19 Figu re 6 Flight Network 37 Figure 7 Arrival Patterns 4 4 PAGE 7 vi MODELING ALTERNATE S TRATEGIES FOR AIRLINE REVENUE MANA GEMENT Kapil Joshi ABSTRACT Ever since the deregulation of the airline industry in 1978, fierce competition has made every airline to try and gain a competitive edge in the market. In order to accomplish this, airlines are turning to advance d optimization techniques such as revenue manag ement. Revenue management is a way for airlines to maximize capacity and profitability by managing supply and demand through price management. Over the last few years research in the field of revenue management has steadily progressed from seat inventory control techniques such as single leg seat inventory and network inventory control to ticket pricing techniques. T icket pricing technique s involve setting ticket prices according to the time remaining to depart and inventory level conditions at that point in time These models can be solved either by dynamic or mathematical programming. However, these models in addition to having increased complexity are based on several assumptions which may not be valid in real life situations thereby limiting there appli cability In this research, we have developed computer simulation model s using Arena software as a tool to solve airline revenue management problem Different models based on factors such as customer behavior, which would involve the probability of a custo mer accepting a ticket and relevant pricing methods such as seats remaining and time PAGE 8 vii remaining have been developed with the objective to reach an optimal revenue management policy. Initially, the strategies have been developed and tested for a single fligh t leg for different types of destinations such as tourist, business and mixed tourist and business It was found that models where pricing was based on seats remaining generated the most revenue for the tourist destinations time remaining for the business destinations and pricing based on time and seats remaining for the mixed type. T wo different strategies one where the ticket price f or the indirect (stop over) flight increases as more seats for direct flight are sold and the second where the ticket pric e for the indirect flight decreases have been developed for a network of three cities with direct and stop over flights It was found that the first strategy works well for the business destination There was no significant difference between the two strat egies for the other two destinations. Also the model was run w here a set percentage of seats on the direct flight are sold prior to the opening of indirect flight bookings (blocking) It was found that blocking of seats d id not increase the total revenue g enerated. PAGE 9 1 CHAPTER 1 INTRODUCTION The airline industry has become extremely competitive in recent years. The number of airlines operating within the United States has increased tremendously. Since the deregulation of the airline industry in 197 8, airlines have been allowed to choose their own market segments, decide their own routes and set their own fares as long as they comply with the regulations laid down by the Federal Aviation Authority (FAA) [Yu, 1998]. Th is fierce competition has made mo st airlines turn to advanced optimization techniques to develop decision support systems for management and control of airline operations. An important aspect considered in any airline industry is the maximization of revenue from the sale of seats in the a ircraft. This is called revenue management. Originally known as yield management, revenue management has been successfully adapted to numerous industries in recent years including utilities, cruise lines, trucking, amusement parks, hotels, rental cars and others. Revenue management is a business practice that enables companies to increase revenue by accurately matching product availability and pricing to the market demand. Basic principle of revenue management is to maximize the revenue by controlling inve ntory levels and pricing of perishable products. Airline revenue management other than the maximization of revenue allows an airline a chance to operate a large variety of fares so as to enhance the attractiveness of that airline to the consumers. PAGE 10 2 1.1 R evenue Management in the Airline Industry Over the years airline revenue management systems have progressed from simple leg control through segment control and finally to the origin destination or network control. The problem of r evenue management is divid ed in to Seat or Discount Allocation and Ticket Pricing. 1.1.1 Seat or Discount Allocation Also known as seat inventory control, it is the determination of optimal booking limits for the seats in each fare class such that total revenue is maximized. Two ap proaches namely single leg control and network control have been explored till now. In single leg control the flights legs are optimized separately or one at a time where as in network inventory control all the flight legs including connecting and direct f lights between a pair of cities are optimized simultaneously. Hence, n etwork revenue management is to manage the sales of ticket to local passengers as well as connecting passengers in order to maximize revenue for the entire airline network. Typically in case of all major airlines 25 50% of passengers will have at least one connection. Thus when connecting traffic is a significant portion of total traffic, leg based revenue management can result in allocation that are clearly sub optimal. Seats on an air craft are categorized as Executive class with high fares and Economy class with low fares. However if you consider the economy section of the aircraft, although all seats are physically identical they are never priced identically. This gives rise to differ ent fare classes. So the question is how to and how many tickets to sell within the coach class to different customers. In the seat inventory control approach it is assumed that prices for different fare classes are given according to some predetermined cr iteria and only seat allocation needs to be determined so as to maximize the total revenue. A system called nested reservation system [Belobaba, 1989] for determining booking limits for the fare classes is the most common system used by airlines today. A nested reservation system is one in which fare class inventories are structured such that a high fare request will not be refused as long as any seats remain available in PAGE 11 3 lower fare classes. A nested reservation system is thus binding in its limits on lowe r fare classes but its limits are transparent from above (for higher fare classes). Booking limit for a fare class is maximum number of seats that can be sold f o r that fare class. For example, if a three fare class nested reservation system is considered t hen the booking limit for the highest fare class will be the total capacity of the cabin and the next fare class will have the booking limit equal to the total cabin capacity less the seats protected for the higher fare class from the lower classes. By hav ing a nested reservation system the airline ensures that higher fare class demands are always accepted as long as there are seats available in the cabin. In a nested reservation system the difference between the binding limit of a higher fare class and bin ding limit of the immediate lower class is called the protection level for the higher fare class. These are the seats that are reserved or protected from sale in the lower classes. It is desirable for the airline to sell as many tickets in the highest fare class as possible. But just increasing number of seats that are allocated for the highest fare class would not be beneficial because some of the seats in the highest fare class may remain vacant when the flight takes off thus generating no revenue. On the other hand had these seats been allocated to a lower fare class for which there may possibly be more demand than a higher fare class, more revenue would have been generated Hence objective of the airline is to allocate seats for each fare class such that the mix of seats sold on the aircraft generates max revenue. 1.1.2 Overbooking If an airline accepts reservations only for the number of seats available then there is always a risk of flight departing with vacant seats because of cancellations or no sho ws. However if the airline sells seats more than its capacity, then there is a possibility that the airline may have to bump some ticket holding passengers. Such passengers are usually rebooked on a later flight and given some compensation. However there is a loss of good will and a bumping cost is incurred. Usually a fixed percentage is used as an overbooking factor. PAGE 12 4 1.1.3 Ticket Pricing Differential pricing is the determination of prices for each class of tickets such that the total revenue is maximize d. The profit maximization price of a ticket depends on market reactions and marginal cost, i.e., both the market and the companys internal structures are determinants of a ticket price. There are two key elements to a price: the market side or the demand and supplier side or supply [Yeoman and Ingold, 1997]. Market side is the relative perceived value of a product and the consumers willingness and the ability to buy the product. Sales volume represents the amount consumed at various price levels and when combined with the value (price) indicates the turnover generated. This relationship reflects the principles of the demand curve D1 shown in Figure 1 [Yeoman and Ingold, 1997] Here P1 and P2 on the Y axis represent the two price levels, P2 being a greater price than P1 and Q1, Q2 and Q3 on the X axis represent the sales volume wherein Q3 is the most number of seats sold, Q2 least and Q1 in between them. The total turnover is calculated by multiplying Q1 and P1 or Q2 and P2. The revenue can be increased in two ways, either lower prices and raise volumes or raise prices and accept lower volumes. These are called movements along the demand curve. As demand is an independent variable, these movements can only result in an increase or decrease in price. This fi gure basically represents the price elasticity and explains the relationship between a change in price and change in quantity demanded. The main thing to be considered here is that the price volume relationship can vary considerably between and even with in markets, making the pricing decision difficult, yet critical. In addition to such movements along the demand curve, the curve can also shift to the right or left. When the demand curve shifts to the right (D2), it represents an increase in demand, where as a shift to the left (D1) represents reduced demand. The cases of such shifts arise due to changing business environments such as good marketing, offering promotional fares, lower rates offered by competing airlines etc. PAGE 13 5 Price D1 D2 P2 P1 Q2 Q1 Q3 Quantity Figure 1 The Demand Curve Hence, a shift in the demand curve to the right can result in a greater revenue generation without a reduction in price (D2) or a potential to raise price an d maintain volume, perhaps raising profitability. 1.2 Characteristics of Revenue Management The characteristics of revenue management are 1. Relatively fixed capacity Only a fixed amount of capacity is available and cannot be easily added or reduced, e. g. an aircraft has fixed number of seats due to cabin restrictions and a hotel has fixed number of rooms when it is built. 2. Perishable inventory This means there is a deadline up to which the inventory can be sold. After that the inventory is worthless jus t like food items and cannot be reused. The seats on an aircraft after it takes off cannot be sold and will not generate any revenue. 3. Fluctuating demand In most service industries demand is seasonal. Revenue management can be used to generate more demand than usual during off peak periods and can help to increase revenue during peak demand period. 4. Product differentiation This important characteristic is the main reason for a price differential. In the coach class of an aircraft even though the seats are physically the same the y cost different as the two individuals occupying the seats have purchased them at a different point in time. PAGE 14 6 1.3 Revenue Management in Other Industries Since American Airlines pioneered revenue management, many industries have tr ied to adopt it. Not far behind the airline industry are the hotel industry and the rental car industry. Cruise lines and tour operators are looking at revenue management too. The movie industry and on the same lines the sporting industry would hugely bene fit from revenue management. 1.4 Thesis Organization The organiza tion of the rest of the thesis is as follows. Chapter 2 reviews the prior work done in the area of airline revenue management. Chapter 3 states the problem of airline revenue management an d also discusses the major assumptions that have been made with their justifications. Chapter 4 discusses the modeling approach and the two main factors namely pricing structure and customer behavior that affect the model. Chapter 5 presents the results fo r a single flight leg model and a n analysis of variance is conducted to verify significant factors. Chapter 6 presents the strategies used in the modeling of a network of three cities with direct and stop over flights between them and also present their re sults Finally Chapter 7 gives the summary and conclusion s and also states the further research that can be done in this area PAGE 15 7 CHAPTER 2 LITERATURE REVIEW This chapter presents an overview of the research done by various authors in the area of re venue management. Most of the material presented in this chapter is adapted from two excellent reviews of airline revenue management by McGill and VanRyzin [1999] and Pak and Piersma [2002]. As stated before the problem h as been more or less divided in to t he seat inventory control problem and the ticket pricing problem. 2.1 Seat Inventory Control The seat inventory control problem involves allocation of finite seat inventory to the demand that occurs over time before the flight is scheduled to depart. H ere the objective is to find the right mix of passengers to maximize the revenue. The problem is approached either as single leg seat inventory control or as network inventory control. 2.1.1 Single Leg Seat Inventory Control Here the flight legs are o ptimized separately. Consider a passenger traveling from A to C through B and offering to pay $800 for his entire journey. That is, traveling from A to C using flight legs from A to B and from B to C. It is assumed that the airline is charging this passeng er $500 for the first flight leg from A to B and $300 for the second flight leg from B to C. Now consider a second passenger traveling from A to B and offering to pay $600 for his journey. If the single leg approach is used, the first passenger can be reje cted on the flight leg from A to B because the second passenger is willing to pay a higher fare on this flight leg and the airline stands to increase its revenue by $100. But by rejecting the first passengers offer, the airline looses an opportunity to cre ate revenue for the combination of the two flight legs. But if the second flight leg from B to PAGE 16 8 C did not get f illed up then it could have been more profitable to accept the first passenger to create revenue for both flight legs. This is the main drawback of the single leg inventory control. Bandla [1998] proposes a solution for such an approach using reinforcement learning. There are two categories of single leg solution methods: static and dynamic solution methods. 2.1.1.1 Static Solution Methods In a static model a booking period is regarded as a single interval and a booking limit for every booking class is set at the beginning of every booking p eriod A drawback of the static solution method is that it considers all the bookings done up to and at a p articular point in time and as we know the booking process is a continuous one. Hence this is not exactly an optimal approach although it is a popular one as it can handle large problems and also multiple leg problems. Littlewood [1972] was the first to propose a solution method for the airline revenue management problem for a single flight leg with two fare classes. His idea was to equate the marginal revenue in each of the two fare classes. He suggests closing down the low fare class when the revenue fr om selling another low fare seat exceeds the expected revenue of selling the same seat at a higher fare. Belobaba [1987] extends Littlewoods rule to multiple fare classes and introduces the term expected marginal seat revenue (EMSR). His method is called EMSRa and incorporates nested protection level, i.e., the number of seats to be sold to each fare class. However his method does not yield optimal booking limits when more than two fare classes are considered. 2.1.1.2 Dynamic Solution Methods Dynamic so lution methods for the seat inventory control problem do not determine a booking control policy at the start of the booking period as the static solution methods do. A dynamic model sets the booking limit for each booking class according to the actual book ings throughout the entire booking process. However a limitation of this approach is that the model developed is computationally intensive. PAGE 17 9 Lee and Hersh [1993] consider a discrete time dynamic programming model. A non homogenous Poisson process models d emand for each fare class. Use of Poisson process gives rise to Markov Decision Process model where in booking requests at time t are independent of the decisions made before time t except available capacity. The entire booking period is divided in to a n umber of decision periods and each request constitutes a period. The decision rule says that a booking request is accepted only if its fare exceeds the expected cost of seats at time t Multiple seat bookings, which are a practical issue in airline seat in ventory control are also considered. Subramanian et al [1999] also formulate and analyze a Markov Decision Process model for airline seat allocation on a single leg flight with multiple fare classes. They have incorporate d cancellations, no shows and overb ooking. Lautenbacher and Stidham [1999] link the dynamic and static approaches of the single leg seat inventory control model. They demonstrate that a common Markov Decision process underlies both the approaches and formulate an omnibus model that yields the static and dynamic models as special cases. 2.1.2 Network Inventory Control Network seat inventory control is aimed at optimizing the complete network of flight legs offered by the airline simultaneously. As explained in the example in Section 2.1.1 Single Leg Seat Inventory Control, consider that the second flight leg from B to C d o not get f illed up The first passenger flying from A to C, was obviously paying more than the second passenger traveling from A to B for the entire journey, but was still rejected. Hence the airline would be flying with an empty seat on flight leg B to C and thereby losing potential revenue on flight leg B to C. In this process the airline increased its revenue by $100. However if the first passenger w as accepted, then the re would be no vacant seats on any of the flight legs and the airline would have increased its revenue by $200 instead. Thus accepting the first passenger would maximize total revenue of both the flight legs. This is network revenue management. Network inv entory control takes in to account the overall revenue the passenger creates from its origin to its destination. PAGE 18 10 Singh [2002] proposes a stochastic approximation approach to such an airline network revenue management problem and solves it using reinforceme nt learning algorithm. 2.2 Ticket Pricing Models It is now common for airline practitioners to view pricing as part of the revenue management process. The reason for this is pretty clear the existence of differential pricing for airline seats is the start ing point of airline revenue management and price is generally the most important determinant of passenger demand behavior. There is also a natural duality between price and seat allocation decisions. If price is viewed as a variable that can be controlled on a continuous basis, raising the price sufficiently high can shut down a booking class. Also when there are many booking classes available, shutting down a booking class can be viewed as changing the price structure faced by the customer. 2.2.1 Dynamic Pricing Models Treatments of revenue management as a dynamic pricing model can be found in the work done by Carvalho and Puterman [2003]. T hey considered a problem of setting prices dynamically to maximize expected revenues in a finite horizon model in which the demand distribution parameters are unknown. The authors suggests a promising pricing policy called the one step look ahead rule where in a Taylor series expansion of the future reward function illustrates the tradeoff between short term revenu e management and future information gains. Chatwin [1999] proposes an optimal dynamic pricing model of perishable products with stochastic demand A finite set of allowable prices is assumed. A continuous time dynamic programming model is employed in whi ch at any given time the state of the model is the number of items in the inventory and the retailers decision is to choose the price to sell at. Demand is assumed to be Poisson with decreasing rate. This model verifies the intuition that optimal price is non increasing in the remaining inventory and non decreasing in the time to go. Gallego and Van Ryzin [1994] suggest a dynamic pricing policy of inventories with stochastic demand Their formulation uses PAGE 19 11 intensity control and obtains structural monotonic results for the optimal price as a function of the stock level and the amount of time left. However they allow only a finite number of prices. Feng and Gallego [1995] investigate the problem of deciding the optimal timing of a single price change from a given initial price to either a given lower or higher second price. They show that the optimal policy is to decrease the initial price as soon as the time to go falls below a time threshold which depends on the number of yet unsold items. While the model i s realistic for retailers of seasonal goods and for certain nonstop flights, it does not extend to multiflight, multileg situation where customers from different itineries compete for the capacity of the flight legs. Feng and Xiao [2000a] generalize the re sults from the above policy by incorporating risk analysis and multiple price changes Also Feng and Gallego [2000] also extend their original work to address the problem of deciding the optimal timing of price change within a given menu of allowable, poss ibly time dependent price paths each of which is associated with a general Poisson process with Markovian, time dependent predictable intensities. Feng and Xiao [2000b] present a continuous time yield management model with multiple prices and reversible changes in price Demand at each price is Poisson with constant intensities. The problem is formulated as an intensity control model and optimal solution in closed form is derived. The model further improves the one proposed in Feng and Gallego [1995] as an exact solution rather than a deterministic one is obtained. Gallego and VanRyzin [1997] also propose a multi product dynamic pricing problem with its application to network yield management. They start with a demand for each product, which is a stochast ic point process with an intensity that is a vector of the prices of the products and the time at which they are offered. An upper bound for the optimal expected revenue is established by analyzing the deterministic version of the problem. From the revie w of the literature done in this chapter it can be summarized that most of the research that has been done is in the area of seat inventory control which again could be categorized in to single leg and network seat inventory control. Whatever little has be en done in the field of ticket pricing has been using mathematical or dynamic programming models that are computationally intensive and time consuming. Also most PAGE 20 12 of these models are fairly complicated and they make simplifying assumptions such as pre deter mined prices, no batch/multiple seat bookings, stochastic demand, fixed number of seats assigned to each fare class, lower fare class requests arrive before higher fare class requests etc Hence the validity of these models is under question and their exac t solutions may not be worked out. In the next chapter we state our research objectives along with the parameters and the assumptions made. PAGE 21 13 CHAPTER 3 RESEARCH STATEMENT In this chapter the problem of network revenue management is stated. The main ob jectives of this research are also discussed. The major assumptions that have been made are explained with their justifications. 3.1 Problem Statement The problem considered in this research constitutes a network of three cities with multiple origin des tination combinations. There are direct and stop over flights in between them. The rev enue generated from the sale of tickets on all flights in their coach class in the network is to be maximized. Passengers request reservations in the coach class of the f light depending upon their preferred itineraries. Every time a passenger requests a reservation the airline checks for the availability of seats for that itinerary. If seats are available, the airline provides the passenger with a fare and the passenger d ecides whether to accept or reject the fare. Customer arrivals are assumed to follow a non stationary Poisson process (an arrival process, which has a rate that varies over time). The objective here is to maximize the revenue generated from sale of seats over the entire network. Also policies to be followed for the sale of tickets on the direct and the stop over flight for the same final destination have to be developed. PAGE 22 14 3.2 Research Assumptions The following parameters have been considered in this res earch Network Details A network of three cities has been considered in this research. Only one way travel between the cities is considered for modeling purposes and no round trip fare option is offered. However the return part of the journey could be model ed a s a percentage of the cost of the first part of the journey and it would be also dependent on the date of the return trip. A request for a booking is always associated with a particular origin destination. For example consider a network of three cities namely Tampa, Atlanta and New York. A flight from Tampa to New York via Atlanta (stop over flight) would be a different origin destination combination from a flight flying directly between Tampa and New York (direct flight). Fair Structure The range of fares for different origin destination combinations is different and is pre determined. Considering the above example the range of fare s for a flight from Tampa to New York via Atlanta would be different from the fare s for a direct flight between the two c ities. Hence the fare structure would vary depending on whether it is a direct flight or with a layover and also factors such as the distance between the cities etc. Arrival Process Many systems are subject to experience arrival loads that can vary dramati cally over the time frame of the simulation. There is a specific probabilistic model for this called the non stationary Poisson process, which provides an accurate way to reflect time varying arrival patterns. Hence the passengers in our model are assumed to arrive with a nonstationary Poisson process and each origin destination combination has its own arrival process. 3.3 Factors and Strategies Considered T hree main factors and three individual strategies will be considered in this model. The fa ctors are pricing str at e gy acceptance probability and customer arrival rate PAGE 23 15 3.3.1 Pricing Str ategy The pri cing strategy basically means the different ways the customer is charged a price. This could be categorized on the basis of the time left to depart ( time rem aining strategy) or up on the number of seats left to be sold, i.e. seats remaining strategy or could be a combination of both called the hybrid strategy 3.3.2 Acceptance Probability Acceptance Probability reflects up on the probability that a customer will purchase a ticket. It could be classified according to the price being offered to the customer or probability w.r.t. price strategy or according to time left to depart called probability w.r.t. time strategy or could be a combination of both called c omposite probability 3.3.3 Customer Arrival Rate Three different customer arrival rates of low, medium and high each suggesting a market with a low demand, medium and high demand for tickets has been experimented with. 3.4 Research Objectives Our obje ctive is to develop a n optimal ticket p ricing policy for the airline industry. Different pricing strategies such as seats remaining, time remaining, and hybrid strategy as well as acceptance strategies such as probability of a customer buying a seat with r espect to time, price or a combination of both are developed and tested using simulation model s Initially the pricing policy is developed for a single flight leg and then for a network of cities to explore the alternatives for direct and indirect flights that airline s can offer to maximize their revenue The comparison of results from these strategies can help in determining the optimal ticket pricing policy for the airline industry. The factors considered and the strategies used is presented in the next chapter and explained in detail with the aid of an example. PAGE 24 16 CHAPTER 4 MODELING AND SOLUTION METHODOLOGY This chapter discusses in detail the main factors that are used in the development of a single leg model. The t hree main factors are the pricing str ategy acceptance probability and customer arrival rate 4.1 Pricing Strategy The pricing str at e gy that we have used in this research is based on the prices being offered online by some popular airlines. Generally it was observed that the price of a f are for a 30 day period varied from 2 times to a maximum of 3 times the cheapest fare. However what is more interesting is as to how these prices are offered to the customers and at what point of time in to the booking period. The pricing str ategy can be e xplained using three different approaches. 4.1.1 Time Remaining Approach At the start of the booking period, when the entire capacity of the aircraft is available and in order to attract more customers to sell as many seats as possible, airlines offer th e cheapest fares. The fares go on increasing as the time to depart nears and the number of seats available becomes less. In such a scenario last minute customers will end up payin g the most expensive fares the airline has to offer. The relationship between time remaining and price offered is a linear one and is shown in Fig ure 2. The equation that describes this relationship is as follows. Price Offered = P max (Time Remaining) j ( 1 ) where, Price Off ered is the price at which the ticket is sold to the customer. PAGE 25 17 P max is the maximum ticket price set by the airline. P min is the minimum ticket price set by the airline. Time Remaining is the time left for the flight to depart. j is a normalizing constan t such that Price Offered will be P min when Time Remaining is 30 days. This equation satisfies our initial condition that price offered is least at the start of the booking period and is the highest when the flight is about to depart. 4.1.2 Seats Rem aining Approach When the entire seat inventory is available at hand and in order to kick star t the booking process, the cheapest fare is offered. The price goes on increasing as the number of seats reduces and the last seat is offered at the highest price Th e relationship which is linear is shown in Figure 3. The equation used is as follows Price Offered = P max (Seats Remaining) k ( 2 ) where in, Seats remaining are the number of seats still availabl e for sale at that time. k is a normalizing constant such that Price Offered will be P max when Seats Remaining will be zero. Price Price Time Remaining Seats Remaining Figure 2. Graph of P ric e O ffered and Figure 3. Graph of P rice O ffered and Remaining T ime Remaining S eats PAGE 26 18 This equation also satisfies the conditions that price offered is lowest when most o f the seats are remaining and vice versa. 4.1.3 Hybrid Approach Both the approaches are logical in their own ways. However consider the case when after a few days in to the booking period, very few or almost no seats are sold. The first approach would ent ail the airline to charge a higher price as the time to depart nears where as the second approach would require the airline to charge a lower price since very few seats were sold. Hence the need for a hybrid model was felt. Th e hybrid approach would charge fares depending on the number of seats sold a s well as the number of days in to the booking period. Here we use the equation Price Offered = P max (Time Remaining) j (Seats Remaining) k ( 3 ) w here j and k are normalizing constants s uch that Price Offered is P max , when Time Remaining is equal to the booking period and Seats Remaining is close to zero. 4.2 Acceptance Probability The probability of a customer accepting or rejecting a seat is called acceptance probab ility and this probability can be classified into three different types depending up on the price and the time at which the customer accepts it and their combination. 4.2.1 Probability with R espect to P rice O ffered If a lower price is offered by the airl ine, the tickets are likely to be sold easily. Hence a very high acceptance probability is assumed when the cheapest fare is offered. However, as the fare increases, the probability of acceptance decreases leading to the lowest probability when the fare of fered is the highest. The equation used is Probability of Acceptance = 100 (Price Offered Cheapest Price)*l ( 4 ) w here l is the normalizing constant such that Probability of Acceptance is 100% when Price Offered is the Cheapest Price. PAGE 27 19 Th is equation will return a 100% probability of acceptance when price offered is the lowest and vice versa. Figure s 4 and 5 show the graphs of the probability of acceptance with respect to the price offered and time remaining respectively Prob. of Prob. of Acceptance Acceptance Price Time Remaining F igure 4 Graph of P rob ability of Figure 5 Graph of P rob ability of Acceptance and P rice O ffer ed A cceptance and T ime R emaining 4.2.2 Probability with R espect to Time R emaining When the bookings open say 30 days before de parture, there is very little rush to buy and hence the probability of acceptance is also very low. However as the date of departure approaches, more customers especially business travelers tend to buy tickets at whatever price. Hence the probability of ac ceptance is greater towards the end. The equation we have used here is Probability of Acceptance = 100 (Time Remaining)*m ( 5 ) This equation follows the initial as well as the final conditions of 100% and 50% probabilit y of acceptance. The graph of time remaining and probability is linear and is shown in Fig. 5. 4.2.3 Composite Probability Both the probability approaches mentioned above are correct in their individual capacity. However consider the case when the bookin gs are just opened and at the same time the lowest fares are offered by the airline. The probability with respect to price PAGE 28 20 would suggest a hi gher probability of acceptance as the ticket price is the lowest; where as the probability with respect to time wou ld suggest a lower probability of acceptance as it is too early in the booking period and the customer is in no particular hurry to book. Hence the need for a composite probability approach that models the customer behavior on the basis of price offered an d time remaining. Here we have used the equation Probability of Acceptance = 100 ( Price Offered Cheapest Price )*l (Time Remaining)*m ( 6 ) This equation satisfies the in itial conditions of higher probability when price offered is the cheapest and Time Remaining is 30 days and vice versa. l and m are the respective normalizing constants. 4.3 Customer Arrival Rate The booking process is assumed to start 30 days in advance and this 30 day period is divided in to 6 time slots of 5 days each. Three different customer arrival rates of low, medium and high have been used and the customers arrive according to non stationary Poisson process. 4.4 Simulation as a T ool There have been several models based on mathematical programming techniques to tackle the airli ne revenue management problem. However, these models are based on many simplifying assumptions such as pre determined prices, no batch/multiple seat bookings, fixed number of seats assigned to each fare class, lower fare class requests arrive before higher fare class requests etc which are not realistic In spite of these assumptions the models are quite complex to build, understand and solve The strategies and policies d eveloped earlier in th is chapter are tested using computer simulation models in this research. T he reason for using simulation is that it allows the models to represent the real world system faithfully. However, the results are based on statistical foundat ions Therefore, while using simulation models one needs to verify and validate them Also, the statistical issues should be resolved properly in order for the results to be valid and meaningful. PAGE 29 21 4. 5 Model Development Using equations ( 1 ) through ( 6 ) we c onsider the development of a single leg airline revenue management model Based on the outcome of this model, we develop a network revenue management model of three cities. Booking period in all the models starts 30 days in advance. Customers arrive accord ing to Poisson process, which has a rate that varies with respect to time (non stationary Poisson process) The number of seats on the aircraft is fixed. A range of fares with an upper limit equal to the maximum price offered and lower limit equal to the minimum price offered is set by the airline. Each arriving customer is offered a ticket price by the airline booking system according to the pricing structure i.e. according to the time remaining, seats remaining and hybrid approach. It is up to the custo mer to decide whether to accept or reject the offered ticket price. This is called acceptance probability Also this decision is a two way by chance probability. If the customer rejects the offer, he exits the booking system. If the customer accepts the o ffer price, a seat is reserved for him /her and the total number of seats available for sale is redu ced by one. The ticket price offered and the total revenue generated at this stage is recorded. Our objective in this model is to maximize revenue within the above mentioned boundaries and conditions. Here we are considering nine different models depending on the pricing structure (seats remaining, time remaining and hybrid approach) and customer behavior (probability with regards to price and time as well as hybrid probability) and their combinations. Also depending on the probability of accepting a ticket, an approximation of the type of destination served by the flight such as a tourist destination, business destination or a mix of both can be obtained. Hen ce the model combinations could be as shown in Table1 In this chapter we have presented the strategies for ticket pricing and probability of accepting the price offered for different types of customers. The corresponding equations were formulated as wel l The numerical analyses of these strategies and their results are present ed in the next chapter. PAGE 30 22 Table 1 Model Combinations Model Type Pricing Strategy based on Type of Destination Seats Rem. & Price Prob. Seats Remaining Time Rem & Price Prob. Time Remaining Hybrid Price & Price Prob. Time and Seats Remaining Mainly Tourist Destination ( e.g. Las Vegas) Seats Rem & Time Prob Seats Remaining Time Rem & Time Prob Time Remaining Hybrid Price & Time Prob Time and Seats Remaining Mainly Business Destination (e.g. Detroit) Seats Rem. &Hybrid Prob. Seats Remaining Time Rem & Hybrid Prob. Time Remaining Hybrid Price & Hybrid Prob Time and Seats Remaining Could be a mix of both (e.g. New York) PAGE 31 23 CHAPTER 5 EXPERIMENT DESIGN AND ANALYSIS OF RESULTS In this chapter the policies and strategies as discussed in the previous section are tested using simulation models and their results are presented. Also a n analysis of variance is performed 5.1 Single Leg Models In this section we have consid ered nine different models with their assumptions and necessary details and have compared their results. For this flight leg a flight capacity of 200 passengers is assumed. The minimum price offered by the a irline is $125 per ticket where as the maximum is $400. The booking of this flight leg starts 30 days in advance A fare offered is for the first part of the round trip and only the forward part of th e journey is modeled The return part can be modeled in a similar fashion The time duration of 30 days i s divided in to 6 time slots of 5 days each. The customer arrivals are assumed to follow Poisson distribution with arrival rates that vary with respect to time Three different arrival rates have been used. The te rminating condition for this model could be either when all the seats are sold out or when the end of the booking period is reached. 5.1.1 Normalizing Constants In this section we describe how we have calculated the values of the normalizing constants j, k, l and m 5.1.1.1 Time Remaining Approa ch Price Offered = P max (Time Remaining) j PAGE 32 24 Initially when we open the bookings, the time remaining is 30 days and price offered is the cheapest price. Hence 125 = 400 (30)* j which gives us a value of j = 9.167 5.1.1.2 Seats Remaining Approach Pr ice Offered = P max (Seats Remaining) k Initially when the booking is opened the entire seat inventory is available and hence th e cheapest fare is offered. Therefore, 125 = 400 (200)* k which gives us k = 1.375 5.1.1.3 Hybrid Approach Price Offered = P max (Time Remaining) j (Seats Remaining) k The total price differential between the minimum and the maximum price offered is (400 125) = 275, the time remaining is 30 days and seats are 200. Case 1. Balanced Weights I f we decide to assign eq ual weight to both the time remaining and seats remaining then we have 275*0.5 = 30 j which gives a value of j = 4.58. Also 275*0.5 = 200 k which gives a value of k = 0.6875. Case 2. Weighted towards Seats Remaining Suppose we decide to assign 20% weight to the time remaining and the remaining 80% weight to the seats remaining, we have 275*0.2 = 30 j which gives j = 1.8333 and 275*0.8 = 200 k which gives k = 1.1 Case 3. Weighted towards Time Remaining. Instead if 80 % weight is attached to the time remai ning and 20 % to seats remaining, then 275*0.8 = 30 j or, j = 7.3333 275*0.2 = 200 k or, k = 0.275 PAGE 33 25 5.1.1.4 Probability of Acceptance with R espect to Price Offered Probability of Acceptance = 100 (Price Offered Cheapest Price)*l The probability of acceptance is set to range between a high level of 100% and a low level of 50%. When price offered is the highest probability o f acceptance is the lowest. This gives us 50 = 100 (400 125)* l or, l = 0.1818. 5.1.1.5 Probability of Acceptance with R espe ct to Time Remaining Probability of Acceptance = 100 (Time Remaining)*m If the time remaining is 30 days then the probability of accepting a ticket is on the lower side considering all the time the custo mer has to choose a flight. Therefore we have, 50 = 100 (30)* m or, m = 1.6667 5.1.1.6 Composite Probability Probability of Acceptance = 100 ( Price Offered Cheapest Price )*l (Time Remaining)*m The probability of acceptance is set at two levels 100 % and 50 % and thei r differential is 50. The price offered differential is 275 and time remaining is 30 days. Thus, Case1. Balanced Weights. The probability of acceptance depending up on the price offered and time remaining is given equal weight. This is an example of a mixe d type of market where the demand by tourists as well as business travelers is equal (e.g. New York) 50*0.5 = 275 l or, l = 0.0909 50*0.5 = 30 m or, m = 0.83 Case2. Weighted Towards Price Offered. Here the price offered is given 80 % weight and time r emaining is given 20 % weight. This is an example of a tourist driven market where majority of the passengers are price conscious tourists (e.g. Las Vegas) 50*0.8 = 275 l which gives l = 0.1454 50*0.2 = 30 m or, m = 0.3333 PAGE 34 26 Table 2 Table of Normalizing Constants and T heir V alue s Equation Criterion Normalizin g Constant Price Offered = P max (Time Remaining) j Time Remaining j = 9.167 Price Offered = P max (Seats Remaining) k Seats Remaining k = 1.375 Price Offered = P max (Time Remaining) j (Seats Remaining) k Time and Seats Remaining j = 4.58 & k = 0.6875 (Equal Weights) j = 1.8333 & k = 1.1 (Weighted T owards Seats) j = 7.3333 & k = 0.275 (Weighted T owards Time) Probability of Acceptance = 100 (Price Offered Cheapest Price)*l Price Offered l = 0.1818 Probability of Acceptance = 100 (Time Remaining)*m Time Remaining m = 1.6667 Probability of Acceptance = 100 (Price Offered Cheapest Price )*l (Time Remaining)*m Price Offered and Time Remaining l = 0.0909 & m = 0.83 (Equal Weights) l = 0.1454 & m = 0.3333 (Weighted T owards Price ) l = 0.0363 & m = 1.3333 (Weighted T owards Time) PAGE 35 27 Case3. Weighted Towards Time Remaining. The time to depart is given more weight (80%) and price offered is given 20 % weight. This example could represent a market where majority of customers are business travelers (e.g. Detroit). 50*0.2 = 275 l or, l = 0.0363 50*0.8 = 30 m or, m = 1.3333 The different policies we discussed so far and their corresponding normalizing constants have been stated in Table 2. 5.1.2 Arrival Rate The customer arrivals follow a non stationary Poisson arrival process with three different arrival rates of low, medium and high. The booking period of 30 days is divided in to 6 time slots of 5 days each and each time slot having a different arrival rate. A low arrival rate can be 0.16, 0.25, 0.33, 0.41, 0.25, 0.33 per hour which corresponds to 4, 6, 8, 10, 6, 8 customers per day. A medium arrival rate can be 0. 2 0, 0. 3 0, 0. 3 5, 0.45, 0.38, 0.3 3 which corresponds to 5 7 8 11, 9, 8 customers per day. A high arrival rate is 0. 35 0.4 0 0. 45 0. 48 0. 30 and 0. 35 which is 8 9 10 11 7 and 8 arrivals per day. The arrival rates can be summarized from the following table. Table 3 Arrival Rates Arrival Rate(Number of cu stomers per day for every 5 days) Type 0 5 days 5 10 days 10 15 days 15 20 days 20 25 days 25 30 days Total Customers Low 4 6 8 10 6 8 210 Medium 5 7 8 11 9 8 240 High 8 9 10 11 7 8 265 The arrival rates are also calculated in terms of number of custome rs per hour as Arena software is unable to accept the arrival rate in terms of customers per day. If the number of customers per day is 6, then 6/24 = 0.25 would be the arrival rate per hour. PAGE 36 28 Table 4 Comparison of Single Leg Models for Low A rrival R at e Model Type Customer Arrivals Tickets Purchased Customers balked (high price) Customers lost due to no seats Seats Vacant Average Revenue ($) Half Width ** ($) Avg. Ticket Price($) Time Seats get Full* Type of Destination Seats Rem & Price Prob 207 162 44 0 37 38,274 570 235 n/a Time Rem & Price Prob 207 151 56 0 49 39,431 585 261 n/a Hybrid Price & Price Prob 207 157 49 0 43 38,915 575 247 n/a Mainly tourist destination e.g. Las Vegas Seats Rem & Time Prob 207 160 46 0 40 37,685 754 234 n/a Time Rem & Time Prob 207 160 46 0 40 46,086 668 287 n/a Hybrid Price & Time Prob 207 160 46 0 40 39,343 732 245 n/a M ainly business destination e.g. Detroit Seats Rem & Hybrid Prob 207 162 45 0 38 38,203 723 235 n/a Time Rem & Hybrid Prob 207 153 54 0 47 40,802 598 267 n/a Hybrid Price & Hybrid 207 159 47 0 41 43,511 636 273 n/a Could be a mix of both e.g. New York days into the booking period **based on 95% Confidence Interval PAGE 37 29 Table 5 Comparison of Single Leg Models for Medium A rrival R ate Model Type Customer Arrivals Tickets Purchased Customers balked (high price) Customers lost due to no seats Seats Vacant Average Revenue ($) Half Width ** ($) Avg. Ticket Price($) Time Seats get Full* Type of Destination Seats Rem & Price Prob 2 41 182 59 0 18 45,396 633 249 n/a Time Rem & Price Prob 241 177 64 0 23 46,116 624 261 n/a Hybrid Price & Price Prob 241 180 61 0 20 45,778 616 254 n/a Mainly tourist destination e.g. Las Vegas Seats Rem & Time Prob 243 188 54 0 12 47,731 808 253 n/a Time Rem & Time Prob 241 186 54 0 14 53,328 677 286 n/a Hybrid Price & Time Prob 241 186 54 0 14 48,301 786 259 n/a Mainly business destination e.g. Detroit Seats Rem & Hybrid Prob 243 189 54 0 11 47,954 752 254 n/a Time Rem & Hybrid Prob 241 182 59 0 18 49,852 649 274 n/a Hybrid Price & Hybrid 241 185 55 0 15 51,104 669 275 n/a Could be a mix of both e.g. New Yo rk *days into the booking period **based on 95% Confidence Interval PAGE 38 30 Table 6 Comparison of Single Leg Models for H igh A rri val R ate Model Type Customer Arrivals Tickets Purchased Customers balked (high price) Customers lost due to no seats Seats Vacant Average Revenue ($) Half Width ** ($) Avg. Ticket Price($) Time Seats get Full* Type of Destination Seats Rem & Price Pr ob 279 197 73 9 0 51,285 370 259 17 Time Rem & Price Prob 280 199 56 24 0 47,255 310 237 23 Hybrid Price & Price Prob 280 198 66 16 0 49,603 275 250 20 Mainly tourist destination e.g. Las Vegas Seats Rem & Time Prob 279 198 69 12 0 51,569 354 260 22 Time Rem & Time Prob 279 198 69 12 0 52,986 303 267 21 Hybrid Price & Time Prob 279 198 69 12 0 51,853 317 261 21 Mainly business destination e.g. Detroit Seats Rem & Hybrid Prob 280 198 70 0 2 51,532 341 260 n/a Time Rem & Hybrid Prob 280 198 64 0 2 49,998 313 252 n/a Hybrid Price & Hybrid 280 198 68 0 2 51,808 289 261 n/a Could be a mix of both e.g. New York days into the booking period **based on 95% Confidence Interval PAGE 39 31 5.2 Results and Analysis Using the above values of j, k, l and m t he nine models are run for a replication length of 30 days and 10 0 replications each for low, medium and high arrival rates. The number of replications have been calculated to obtain a half width of less than 2% of the revenue generated and has been explai ned in Appendix B. The results are shown in Tables 4 5 and 6 respectively and are average for 10 0 replications. The first column indicates the model type as explained in detail in Table 1 and the last column gives the exact time in to the booking period w hen the seats get full. Tourists are mostly price conscious people and hence tend to book their flights well in advance. Hence their acceptance probability of a ticket would be mostly based on price. From Table 4 we observe that for the tourist destination any of the three models could be used as the average revenue generated is pretty much the same The half widths of all the three revenue generated values overlap and hence, there is no significant difference between the three values. Since a verage ticket price is the least for Seats Rem & Price Prob model this could be the optimal strategy. Also out of the three m odels the Seats Rem & Price Prob model sells the most seats Business travelers generally tend to book late in the booking period and price i s not really the deciding factor for them Hence their acceptance probability of a ticket would be mostly based on time. From Table 4 we observe that for the business destination, the revenue generated by all the three models is significantly different as their half widths do not overlap Time Rem and Time Prob generates the most revenue as price is charged according to time remaining and business customers tend to book late when the price is higher Also average ticket price is the most for this model. Hyb rid Price & Time Prob model generates the second most revenue and Seats Rem & Time Prob the least revenue. Numbers of seats remaining vacant are the same in all the models. For a mixed type of destination which would have both tourist and business travele rs the probability of acceptance would be based on both time and price offered. The revenue generated by Seats Rem & Hybrid Prob and Time Rem & Hybrid Prob is not significantly different as their half widths overlap. But the revenue generated by Hybrid Pr ice and Hybrid Prob is significantly different from the other two models. This model generates the most revenue as price offered is according to both time and seats remaining PAGE 40 32 and both types of customers tourists and business book on this flight. Also the average ticket price is not very high and hence, this could be the optimal policy. Time Rem & Hybrid Prob generates the second most revenue. Average ticket price is the slightly less for Time Rem & Hybrid Prob, but since less customers book this flight ave rage revenue generated is less. The most number of customers purchasing tickets is in the Seats Rem & Hybrid Prob model, but as the average ticket price is least the revenue generated is also the least. Similar conclusions can be drawn from Table 5 an d 6 with the only exception that for the high arrival rate the Seats Rem and Price Prob generates the most revenue for the tourist destination. This could be attributed to the high rate of arrival which fills up the seats faster when the ticket price is low. All t hese results have been summarized according to the arrival rate and destination type in Table 7. Table 7 Best Pricing Strategy Destination Type Arrival Rate Tourist Business Mixed Low Seats Rem & Price Prob Time Rem & Time Prob Hybrid Pric e & Hybrid Prob Medium Seats Rem & Price Prob Time Rem & Time Prob Hybrid Price & Hybrid Prob High Seats Rem. & Price Prob Time Rem & Time Prob Hybrid Price & Hybrid Prob 5.2.1 Sensitivity Analysis To test the sensitivity of the results obtained from our model we have taken a second example and verified if the results and conclusions drawn are consistent with the original example In this second example we have assumed a flight capacity of 300 passengers with the lower price limit being set at $200 an d the higher limit at $425. The booking period was kept at 30 days and t wo arrival rate s (low and medium) w ere adjusted correspondi ng to the increase in flight capacity. The adjusted low arrival rate gives 0.35, 0.45, 0.53, 0.50, 0.38 and 0.43 customers pe r hour or 8, 11, 13, 12, 9 and 10 customers per day. The adjusted medium arrival rate gives 0.38, 0.45, 0.50, 0.63, 0.55 and 0.50 customers per hour or 9, 11, 12, 15, 13 and 12 customers per day. A ll the nine PAGE 41 33 models were run for 1 00 replication s for the ad justed low and medium rate of arrival s The revenues generated by the hybrid probability models were used for verifying the sensitivity of the results. The revenue generated by the original example and this second example are shown in Table 8 and 9. Table 8 Revenues for Low and A djusted L ow R ate of A rrival Model Type Revenue G enerated by O riginal E xample ($) Revenue G enerated by S econd E xample ($) Seats Remaining & Hybrid Probability 38,203 (13.8%)* 60,866(8.8%)* Time Remaining & Hybrid Probability 40,80 2 (6.6)* 62,326(6.3%)* Hybrid Price & Hybrid Probability 43,511 66,267 proportion by which this revenue is less than the maximum revenue Table 9 Revenues for Medium and A djusted M edium R ate of A rrival Model Type Revenue G enerated by O riginal E xample ( $) Revenue Generated by S econd E xample ($) Seats Remaining & Hybrid Probability 47,954(6.5%)* 72,228(7.2%)* Time Remaining & Hybrid Probability 49,852(2.5%)* 74,940(3.3%)* Hybrid Price & Hybrid Probability 51,104 77,465 *proportion by which this revenu e is less than the maximum revenue From Table 8 it can be observed that the hybrid price policy generates the most revenue followed by the time remaining model T he seats remaining model generates the least revenue for both the examples. The percentage lo ss in the revenue compared with the best policy is given in parentheses for both the examples. It can be seen that the relative performance of all the policies in the second example is consistent with that of original problem Similar observations can be drawn from Table 9. The outcome of the second example reinforces our belief that the strategies that have been modeled are robust with regard to assumptions that have been made regarding ticket pricing, plane capacity and arrival population. PAGE 42 34 5. 2.1 Analysi s of Variance In order to compare the results produced by different simulations runs and to find out the impact the parameters that are varied (controls) have on the results (response) we perform analysis of variance also called ANOVA. The hybrid price and hybrid probability model is considered as a sample example. We believe that t here are two factors that if varied will give significant changes in the revenue generated These two factors are the price offered and probability of acceptance. The price offer ed and probability of acceptance are determined by the following equations, Price Offered = P max (Time Remaining) j (Seats Remaining) k Probability of Acceptance = 100 (Price Offered Cheapest Price )*l (Time Remaining) *m where j, k, l and m are normalizing constants as shown in Table 2 Another factor we believe most certainly has an impact on the revenue generated is the arrival rate and hence we intend to conduct an analysis of the significant factors at all three l evels of the arrival rate. However for the sake of our proposal we have used the low rate of arrival. Table 10 Controls and Their Levels Control Level 1 Level 2 Level 3 Pricing Strategy Weighted towards Seats Remaining Balanced Weights Weighted towards T ime Remaining Acceptance Probability Weighted Towards Price Offered Balanced Weights Weighted Towards Time Remaining Arrival Rate Low Medium High The ANOVA for this 2 factorial, 3 level design is performed using Minitab software for 10 replicates at ea ch level for the low arrival rate The analysis of variance is as follows. Multilevel Factorial Design Factors: 2 Replicates: 10 Base runs: 9 Total runs: 90 Base blocks: 1 Total blocks: 1 PAGE 43 35 Number of levels: 3, 3 Analysis of Variance for Revenue Generated, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P Pricing Strategy 2 133526695 133526695 66763348 6.69 0.002 Acceptance Prob 2 1071964396 1071964396 535982198 53.72 0.000 Pricing Strategy*Accept Prob 4 25370324 25370324 6342581 0.64 0.638 Error 81 808115814 808115814 9976738 Total 89 2038977229 From the above a nalysis we see that the F value s for Pric ing Strategy (6.69) and the F value for Acceptance Probability ( 53.72 ) are greater than F 0.05 2, 81 ( 3.15 ) Hence we can conclude that both Pricing Strategy and Acceptance Probability are significant factor s and their interaction Pric ing Strategy Acceptance Probability is not significant as its F value (0.64) is less than 3.15 The ANOVA for the medium and high arrival rate s also indicate similar results. They have been attached in the Appendix portion of this doc ument. From Table 3 we can observe that the t ime remaining and probability based on time strategy generates the most revenue ($ 4 6,086 ). However in all models other than the hy brid model either the pricing strategy or acceptance probability can be adjusted but not both. In the sample hybrid model which we have used for the purpose of calculations, high revenue of $5 2,755 can be obtained by setting the pricing strategy and acceptance probability at level 3 as shown in Table 10 This is done using the Process Analyzer part of the Arena simulation software. Hence the hybrid price and hybrid probability model out performs all the other models in terms of revenue generated. Other strategies where the p robab ility of acceptance is based on the price offered are mor e or less meant for the price conscious leisure travelers (tourists) who tend to book their tickets much in advance when the price offered is the lowest where as the strategies where the probability of acceptance is based on time are applicable to the busi ness travelers who dont mind paying a high fare as long as they get to their destination at the right time. Such customers usually tend to book their tickets late in the boo k ing period. The hybrid price and hybrid probability strategy covers the scenarios mentioned above into one model. PAGE 44 36 In the next chapter we will develop some new strategies for a network of three cities with direct and stop over flights and suggest the optimal strategy to be used. PAGE 45 37 CHAPTER 6 NETWORK MODEL S This chapter discusses the main factors used in the development of the network model of three cities. The main factors to be considered here are the pricing of all the flight legs, their acceptance probability and also different arrival patterns of customers. 6.1 Flight Networ k A network of three cities is considered as shown in F igure 6. There are four origin destinations, Tampa Atlanta (1 2), Atlanta New York (2 3) and Tampa New York (1 3) and Tampa Atlanta New York (1 2 3). Their assumed flight capacities and price ranges ar e shown in Table 11 3 New York Table 11 Flight Capacities and Price Ranges Atlanta 2 1 Tampa Figure 6 Flight Network 6.2 Pricing Strategy The pricing strategy for the individual flight legs 1 2 and 2 3 will remain the same as in the single leg approach as these customers are flying only on these single leg s and do not have a connecting flight. Hence the pricing for these flight legs will be dependent upon the time remaining, seats remaining and their combination. As observed in Chapter Origin Destination Flight Capacity Min Price Max Price 1 2 200 100 275 2 3 125 100 225 1 3 150 150 350 1 2 3 125 100 300 PAGE 46 38 5 there could be nine different combination equations for each flight le g and here we have used only the hybrid combinations as it was found that the combination of time and seats remaining model gives the maximum revenue These have been summarized in Table 10. However for a customer flying from Tampa to New York can either b ook on the direct flight (1 3) or the connecting flight with a stop over in Atlanta (1 2 3). Hence the problem comes down to pricing the origin destinations 1 3 and 1 2 3. 6.2 1 Pricing Strategy for Tampa New York (1 3) Direct Flight The pricing for Tamp a New York direct flight (1 3) is assumed to be independent of the seats remaining on the indirect route (1 2 3). Here we have assumed flight leg 1 3 to be independent and h ence the price offered for 1 3 would be similar to the single flight legs 1 2 and 2 3. It can be either dependent on time remaining, seats remaining or their combination. Here also we have used the hybrid equations and these have been summarized in Table 1 2 6.2 .2 Pricing Strategy for Tampa New York (1 2 3) Indirect Flight The indirec t flight 1 2 3 is offered to generate extra revenue from the vacant seats on flight legs 1 2 and 2 3. But at the same time it has to be made sure that this flight does not diminish the revenue generated by the direct flight. Thus, t he price offered for the indirect flight has to be dependent on the seats available for that flight leg, seats remaining on the direct flight and the price offered for th e direct flight Two s trategies have been used. Strategy1. In the first strategy the price offered when the b ooking begins is the cheapest and there after increases as the seats remaining on the direct flight decrease. The equation developed for this approach is, Price Offered 123 = Price Offered 13 (Seats Remaining 12 3 )* j ( 150 Seats Remaining 13 )* k ( 7 ) Initially, when the booking starts we have 100 = 150 (125)*j (150 150)*k Which gives us j = 0.4 PAGE 47 39 Towards the end of the booking process, Price Offered 123 = 350 (1)*j (15 0 1)*k 300 = 350 0.4 149*k which gives us k = 0.3328 Strategy2. It was observed from the websites of some popular airlines that when the bookings were opened the indirect flight was priced much higher than the direct flight. The explanation for th is strategy could be that the airline wants to sell the seats on the direct flight first and then the remaining demand is absorbed of by the indirect flight. Hence, the price offered for the indirect flight when the booking is opened is the highest and t he ticket price decreases as the booking period advances. The equation developed for this approach is Price Offered 123 = Price Offered 13 (Seats Remaining 12 3 )* j ( 50 Seats Remaining 13 )* k (8) Initially the booking starts and all the seats are available, the cheapest price will be offered for 1 3 and price offered for 1 2 3 will be max. Thus, 300 = 150 125* j (50 150)* k which is 100 k 125 j = 150 Also towards the en d the following condition could prevail, 100 = 350 1* j (50 1)* k which is 49 k + j = 250 Equating the above two equations we can solve for j and k. j = 2.8353 and k = 5.0441 6.3 Acceptance Probability Strategy Acceptance probability equations fo r the individual flight legs 1 2 and 2 3 will remain the same as in the single leg approach as these customers are flying only on these single legs and do not have a connecting flight. These are dependent on the time remaining to depart, price offered or t heir combination. Here we have used only their hybrid combination and it has been stated in Table 1 3 A customer flying from Tampa to New York can either book on the direct flight (1 3) or the connecting flight with a stop over in Atlanta (1 2 3). Hence th e question is whether to accept itinerary 1 3 or 1 2 3 or not to accept the fare at all. The acceptance probability cannot be based on time as both PAGE 48 40 Table 1 2 Normalizing Constants for Pricing Strategy Flight Leg Equation Criterion Normalizing Constant 1 2 Price Offered12 = P max12 (Time Remaining) j (Seats Remaining12) k Time and Seats Remaining j = 2.9166 & k = 0.4375 (Equal Weights) 2 3 Price Offered23 = P max23 (Time Remaining) j (Seats Remaining23) k Time and Seats Remaining j = 2.0833 & k = 0.5 (Equal Weights) 1 3 Price Offered 1 3 = P max 13 ( Time Remaining )*j (Seats Remaining 1 3)*k Time and Seats Remaining j = 3.3333 & k = 0.6666 (Equal Weights) Table 1 3 Normalizing Constants for Acceptance Strategy Flight Leg Equatio n Criterion Normalizing Constant 1 2 Probability of Acceptance12 = 100 (Price Offered12 Cheapest Price12 )*l (Time Remaining)*m Price Offered and Time Remaining l = 0.14 & m = 0.83 (Equal Weights) 2 3 Probability of Acceptance23 = 100 (Price Offer ed23 Cheapest Price )*l (Time Remaining)*m Price Offered and Time Remaining l = 0.2 & m = 0.83 (Equal Weights) PAGE 49 41 flights are assumed to depart at the same point in time. Hence the only deciding factors are the price differential between the direct and stop over flight and the inability to buy even the cheapest fare offered for the Tampa New York. 6.3.1 Probability of Not Buying As mentioned before the customer will decide not to fly Tampa New York (1 3 or 1 2 3) if he is not able to even purchase the lowest offered fare which could b e either 1 3 or 1 2 3. Hence two equations are used to determine whether th e customer will accept the fare. Case 1. Acceptance Probability if the lower price offered is 1 3 Probability of Acceptance T NY = 100 (Price Offer ed13 Cheapest Price13)*l ( 9 ) If price offered is maximum, acceptance probability is lower. Hence, 50 = 100 (350 150)*l Which gives l = 0.25 Case 2. Acceptance Probability if the lower price offered is 1 2 3 Probability of Acceptance T NY = 100 (Pri ce Offered123 Cheapest Price123)*m ( 10 ) Similar to Case1 we have 50 = 100 (300 100) *m and m = 0.25 6.3.2 Price Differential If the price difference between the direct and the indirect route is $50 or less than $50, it is assumed that the customer would rather fly direct route than the stop over route. However there would still be some passengers who would want to save that $50 and we have assumed them to be 10% of this population. If the price differential is $150 or greater than $150, it is assumed the customers would rather fly the stop over route and save some money. However there w ould still be some passengers who would want to fly directly and we have assumed them to be 10% of this population. PAGE 50 42 If the price differential is between $50 and $150 then the acceptance probability equation is Probability of Acceptance = 10 + (Price Diff erential 50) *0.8 ( 11 ) This equation suggests that lower the differential, lower is the probability of flying the indirect route and higher the differential, higher is the probability of flying the indirect route. 6.4 Arrival Distr ibution The customer arrivals are assumed to follow Poisson distribution with arrival rates that vary with respect to time and different arrival rates have been used for each origin destination. As in the single leg models the booking period of 30 days is divided in to 6 time slots of 5 days each and each time slot having a different arrival rate. Three different arrival patterns have been experimented with The first pattern shows a mixed type of market with both tourist and business concentration. The se cond pattern signifies a business market with customers not really price conscious and booking towards the end of the booking period. This is shown by an increase in the customer arrival rate towards the end of the booking process. The third pattern shows a tourist market where the customer arrivals are concentrated towards the beginning of the booking process as price conscious tourists generally tend to book at the start. The three different arrival patterns for on flight leg (1 2) are shown in Figures 7 and the arrival rates are shown in Table 1 4 6.5 Model Development The booking of all flight legs is assumed to start 30 days in advance and all flights depart at the same point in time. The fare s offered are for the first part of the round trip and onl y the forward part of th e journey is modeled and return part can be modeled in similar way. The pricing and acceptance of fares on flight legs 1 2 and 2 3 follows the same assumptions and parameters used in the single leg approach. The hybrid price and hyb rid probability strategies have been used. Now when a customer for the Tampa New York itinerary enters the booking process, two separate fares namely 1 3 and 1 2 3 are PAGE 51 43 offered to him. If the customer cannot afford even the minimum of the two offered fares he leaves the system. If the customer can afford to purchase either of the fares, then the question is whether he will fly the direct or the indirect route. If the price differential between the direct and the indirect fares is less than or equal to $50, h e is assumed to buy the direct flight fare (1 3). However there will be some passengers who would still fly the indirect route (1 2 3) and we have assumed them to be 10% of this population. If the price differential is $150 or more than $150 the customer is assumed to fly the indirect route. And there will be some passengers (10%) who would want to avoid the indirect route and still fly directly. If the price differential is between $50 and $150, the lower the differential, lower is the probability of flyi ng the indirect route and higher the differential, higher is the probability of flying the indirect route. 6.5.1 Blocking of Seats in 1 2 3 In this model we have also attempted to exclusively sell the seats on the direct route (1 3) when the booking pr ocess starts, by blocking the seats on the indirect route (1 2 3) till a certain number of seats on the direct route are sold and then opening up the seats to be sold on the indirect route. This exclusive reservation of seats on the direct route is done fo r 50% (75 seats), 33% (50 seats), 16% (25 seats) and zero seats out of the total flight capacity of 150 seats. The models developed have been run for a replication length of 30 days and 200 replications each for the three different arrival patterns and usi ng both the pricing strategies for Price Offered 123 By setting the number of replications at 168, the half width for the total revenue generated is less than 1% of its value. The method for calculating the number of replications is shown in Appendix B. T he results are shown in Table 1 5 1 6 and 1 7 6.6 Results and Analysis In Table 12 the first column indicates the percentage of seats initially reserved for the direct flight 1 3. This implies that the indirect flight between the destinations (1 2 and 2 3 in our example) will not be opened until certain percentage of direct flight seats is sold. The model was run with 50% (75 seats), 33% (50 seats) and 16% (25 seats) of the PAGE 52 44 Table 1 4 Arrival Rates and Pattern Arrival Rate (Number of customers pe r day for every 5 days) Itinerary Arrival Pattern 1 Arrival Pattern 2 Arrival Pattern 3 Total No of Customers Total Flight Capacity Tampa Atlanta 4, 6, 8, 10, 6, 8 4, 6, 6, 8, 8, 10 10, 8, 8, 6, 6, 4 213 200 Atlanta New York 2, 5, 7, 8, 6, 4 2, 4, 5, 6, 7, 8 8 7, 6, 5, 4, 2 155 125 Tampa New York 5, 7, 8, 11, 9, 8 5, 7, 8, 8, 9, 11 11, 9, 8, 8, 7, 5 232 150 Arrival Pattern 2 (12) 0 2 4 6 8 10 12 0 10 20 30 40 Days Number of Customers Arrival Pattern 3 (12) 0 2 4 6 8 10 12 0 10 20 30 40 Days Number of Customers Figure 7 Arrival Pattern Arrival Patern 1 (12) 0 2 4 6 8 10 12 0 10 20 30 40 Days Number of customers PAGE 53 45 Table 1 5 Results for Arrival Pattern 1 half width Strategy 1 Strategy 2 % Seats Reserved for 1 3 Flight Leg Rev enue Generated Av erage Ticket Pr Seats Vacant Customer Balked Flight Leg Rev enue Generated Average Ticket Pr Seats Vacant Customers Balked 1 2 $ 23,560 $ 179 48 76 1 2 $ 23,738 $ 180 35 77 2 3 14,013 158 16 67 2 3 13,675 157 5 67 1 3 30,611 243 24 1 3 26,989 236 36 1 2 3 4,533 230 16 95 1 2 3 6,753 208 5 94 50 (75 seats) Total 72,719 (829)* Total 71,157 (775)* 1 2 23,643 180 45 77 1 2 23,886 182 29 77 2 3 13,967 159 13 68 2 3 13 ,289 158 1 67 1 3 31,835 245 20 1 3 27,692 238 13 1 2 3 5,161 216 13 88 1 2 3 8,805 226 1 86 33 (50 seats) Total 74,608 (826)* Total 73,674 (764)* 1 2 23,576 182 41 76 1 2 23,506 182 29 76 2 3 14,093 162 8 69 2 3 13,077 158 0 64 1 3 33,437 247 15 1 3 29,614 240 27 1 2 3 5,784 197 8 78 1 2 3 9,391 222 0 76 16 (25 seats) Total 76,892 (782)* Total 75,589 (701)* 1 2 24,102 185 35 77 1 2 23,957 185 23 78 2 3 14,076 164 4 69 2 3 12,218 158 0 63 1 3 34, 689 247 9 1 3 31,336 240 20 1 2 3 6,327 181 4 64 1 2 3 10,406 217 0 63 0 Total 79,196 (739)* Total 77,920 (684)* PAGE 54 46 Table 1 6 Results for Arrival Pattern 2 half width Strategy 1 Strategy 2 % Seats Reserved for 1 3 Flight Leg Rev enue Generated Average Ticket Pr Seats Vacant Customer Balked Flight Leg Rev enue Generated Average Ticket Pr Seats Vacant Customers Balked 1 2 $ 24,071 $ 182 47 77 1 2 $ 23,977 $ 182 38 77 2 3 14,757 163 13 67 2 3 14,457 162 6 66 1 3 30,433 245 25 1 3 27,784 239 34 1 2 3 4,792 229 13 95 1 2 3 5,813 195 6 95 50 (75 seats) Total 74,054 (858)* Total 71,995 (785)* 1 2 24,356 184 42 77 1 2 24,435 185 28 77 2 3 14,470 165 11 68 2 3 13,673 163 1 65 1 3 31,393 247 23 1 3 27,447 239 35 1 2 3 5,436 208 11 88 1 2 3 8,850 224 1 86 33 (50 seats) Total 75,656 (821)* Total 74,406 (702)* 1 2 24,284 186 38 77 1 2 24,379 187 25 77 2 3 14,751 168 6 68 2 3 13,166 164 0 63 1 3 33,006 249 17 1 3 29,160 241 29 1 2 3 5,940 190 6 78 1 2 3 9,717 220 0 77 16 (25 seats) Total 77,982 (802)* Total 76,424 (684)* 1 2 24,491 189 33 78 1 2 24,511 189 20 78 2 3 14,424 170 2 67 2 3 12,307 164 0 63 1 3 34,701 249 11 1 3 30,867 241 22 1 2 3 6,627 177 2 64 1 2 3 10,79 0 216 0 58 0 Total 80,244 (738)* Total 78,477 (666)* PAGE 55 47 Table 1 7 Results for Arrival Pattern 3 half width Strategy 1 Strategy 2 % Seats Reserved for 1 3 Flight Leg Rev enue Generated Average Ticket Pr Seats Vacant Customer Balked Flight Leg Rev en ue Generated Average Ticket Pr Seats Vacant Customers Balked 1 2 $ 21,381 $ 167 52 80 1 2 $ 21,501 $ 168 38 80 2 3 13,041 149 17 70 2 3 12,678 149 5 69 1 3 29,329 233 24 1 3 25,598 225 36 1 2 3 4,534 224 17 96 1 2 3 6,979 205 5 95 50 (75 seats) Total 68,286 (811)* Total 66,758 (735)* 1 2 21,650 169 47 80 1 2 21,743 170 31 80 2 3 13,037 151 13 71 2 3 12,318 149 1 68 1 3 30,578 235 20 1 3 26,423 227 34 1 2 3 5,201 209 13 86 1 2 3 8,819 217 1 84 33 (50 seats) Total 70,468 (77 1)* Total 69,305 (675)* 1 2 21,827 171 41 80 1 2 21,977 172 26 80 2 3 13,001 152 9 71 2 3 11,726 148 0 66 1 3 32,145 236 14 1 3 28,167 229 27 1 2 3 5,960 195 9 73 1 2 3 9,682 212 0 72 16 (25 seats) Total 72,935 (753)* Total 71,554 (649)* 1 2 21,841 174 36 81 1 2 22,050 175 22 81 2 3 12,998 155 3 70 2 3 10,810 148 0 62 1 3 33,772 236 7 1 3 30,576 231 17 1 2 3 6,795 178 3 57 1 2 3 10,689 205 0 57 0 Total 75,407 (651)* Total 74,127 (637)* PAGE 56 48 sea ts being reserved The entire table is divided in to two parts, the results for strategy 1 and 2 which is nothing but the two equations we have developed for Price Offered 123 From Table 1 5 we see that the revenue generated progressively increases as the number of seats reserved for the dir ect flight goes on decreasing. R eserving seats for the direct flight does not increase the revenue and the model with no seats reserved gives the maximum revenue. This is true for both the strategies. When the two strat egies are compared, strategy 1 outperforms strategy 2 in terms of the total revenue generated. However this difference in the revenue generated is not significant for arrival pattern s 1 and 3 (Tables 1 5 and 1 7 respectively) as the half widths for the avera ge re venue generated overlap. But this difference is significant for the arrival pattern 2 as seen from Ta ble 1 6 For strategy 1, t he average ticket price s and revenue generated for leg 1 2 and 2 3 remain constant irrespective of the blocking The revenue generated for direct and indirect flights increases as the number of seats blocked goes on reducing. This could be due to the fact that when the most number of seats are blocked (75 seats) the direct flight seats get sold out faster as the ticket price i s lower initially. Also, when the indirect flight b ookings are opened, certain number of seats on the direct flight has been sold and the direct flight is more costly than the indirect flight Therefore there is more demand to purchase the indirect flight thereby reducing the revenue generated for the direct flight. But as the blocking of seats goes on reducing and as the bookings for direct and indirect flight are opened at the same time this direct flight revenue increases Average ticket price for the indirect flight when more number of seats are blocked (75 seats) is higher resulting in less customers buying and hence, lower revenues. But when no seats are blocked the average ticket price is much lower resulting in more demand and hence more revenue g enerated. This combined increase in the revenue of direct and indirect flight results in a higher total revenue generated when no seats are blocked. Similar conclusions can be dram from strategy 2. The best pricing strategy to be used for different type of markets can be summarized according to Table 1 8 In this chapter we have seen a flight network of three cities. Pricing strategies and customer acceptance strategies for the four origin destinations have been discussed. PAGE 57 49 Further, the sale of the indirect flight seats was blocked until a percentage of the direct flight seats we re sold. These strategies were tested for the three different patterns of arrival. T he results suggested the optimal strategy to be followed. In the final conclusion chapter of this t hesis, we will summarize the entire thesis and discuss the future extensions that can be carried out. Table 1 8 Best Pricing Strategy for Network Model Arrival Pattern Mixed Business Tourist Strategy to be followed Strategy 1 or 2 Strategy 1 Strate gy 1 or 2 PAGE 58 50 CHAPTER 7 CONCLUSION S In this chapter we will briefly summarize the research undertaken in this thesis and also state the scope for future research. 7.1 Summary and Conclusions In this research, a very important p roblem faced by the airline industry namely ticket pricing was considered. Different strategies such as pricing strategy, customer acceptance probability strategy and factors such as customer arrival rates and arrival distribution were considered. I nitiall y the pricing policy for a single flight leg was developed Three different pricing strategies namely time remaining, seats remaining and their combination were devel oped. Also, customer behavior such as probability of acceptance based on price offered and the time remaining to depart was studied. The pricing strategies were tested using simulation models for three different customer arrival rates. Following conclusions were drawn. F or a tourist destination where the probability of acceptance was based on p rice the pricing according to seats remaining was the optimal policy. This policy gave a lower average ticket price and higher revenues thus benefiting both the customer and the airline. F or a business destination where the acceptance probability was bas ed on time pricing according to time remaining generated the most revenue. For a mixed type of destination where the acceptance probability was based on both time to depart and the price offered the pricing according to both seats remaining and time rem aining outperformed all the other strategies. PAGE 59 51 We also investigated the impact of offering indirect (stop over) flights on the revenue generated by considering a network of three cities where travel can be made both direct and with a stop over. T wo differ ent strategies were developed. According to the first strategy the pricing for both the direct and indirect flight s was cheapest at the start of the booking period and ended with the last ticket being sold at the maximum price. The second strategy suggeste d a reverse path with the indirect flight being sold at the maximum price at the start of the booking period and the price reducing there after This was done to discourage the selection of indirect flights early in the booking process The first strategy always outperformed the second strategy in terms of revenue generated with their difference being significant for an arrival pattern resembling a business destination and insignificant for arrival patterns for the tourist and mixed destinations. Also the effect of blocking of indirect route until a certain proportion of seats o n the direct route were sold was investigated. It was observed that this approach did not increase the revenue T he model with no seats blocked generated the most revenue. The sing le leg models for the low and medium rate of arrival were tested using another example with a different price range, flight capacity and corresponding arrival rates. The results were found to be consistent indicating the robustness of the model s we have de veloped. Thus, an attempt was made in this research to develop a set of ticket pricing policies that could benefit the airline industry. 7.2 Scope for Further Research Some of the extensions that can be undertaken to make this research more widely us eful are : 1. It is known that every airline overbook s its flight s to compensate for cancellations, no shows etc This extra revenue obtained from overbooking could contribute to the overall revenue generated. Hence, the factors such as cancellations, no shows and overbooking could be integrated with the policies that have been developed in this research. The impact of these factors on the relative performance of different strategies can be investigated. PAGE 60 52 2. These days airlines offer fare prices to customer s by tak ing in to account the fares offered by the ir competitors. This competition aspect in the airline industry with regards to ticket pricing could be considered. Game theory based models could probably be used to investiga te this aspect of the problem. The othe r related aspect that could be studied is the impact of alliance or code sharing Code sharing provide s a way for both major carriers and established regional carriers to expand their customer base by feeding in to each others flight networks. 3. The ticke t pricing strategies that we have developed are with the expectation of one customer buying one ticket. Discount could be given to large groups buying together and hence, this aspect of g roup bookings may impact the revenue generated specially in low deman d markets PAGE 61 53 REFERENCES 1. Bandla, N. Yield Management Using Reinforcement Learning Approach. Masters Thesis IMSE Dept., University of South Florida, Tampa, Fl, 1998. 2. Belobaba, P. Airline Yield Management: An Overview of Seat Inventory Control. Transportation Science Vol. 21, No. 2, 1987. 3. Belobaba, P. Application of a Probabilistic Decision Model to Airline Seat Inventory Control. Operations Research Vol. 37, No. 2, 1989. 4. Carvalho, A and Puterman, M. Dynamic Pricing and Learning over Short T erm Horizons. Working Paper Statistics Dept. and Saunder School of Business, University of British Columbia, Canada, 2003. 5. Chatwin, R. Optimal Dynamic Pricing of Perishable Products with Stochastic Demand and a Finite Set of Prices. European Journal of O perational Research Vol. 125, No. 1, 1999. 6. Feng, Y and Gallego, G. 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PAGE 63 55 APPENDICES PAGE 64 56 Appendix A Analysis of Variance A 1 The A nalysis of V ariance for the M edium R ate of A rrival Multilevel Factorial Design Factors: 2 Replicates: 10 Base runs: 9 Total runs: 90 Base blocks: 1 Total blocks: 1 Number of levels: 3, 3 General Linear Model: Revenue Generate versus Price Offered, Probability Factor Type Levels Values Pricing Strategy fixed 3 1, 2, 3 Acceptance Probabi lity fixed 3 1, 2, 3 Analysis of Variance for Revenue Generated, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P Pricing Strategy 2 116590110 116590110 58295055 4.57 0.013 Accept ance Prob 2 1685751160 1685751160 842875580 66.01 0.000 Pricing Strat*Accept 4 13230612 13230612 3307653 0.26 0.903 Probability Error 81 1034331612 1034331612 12769526 Total 89 2849903494 S = 3573. 45 R Sq = 63.71% R Sq (adj) = 60.12% From the above analysis we see that the F values for pricing strategy (4.57) and acceptance probability (66.01) are greater than F 0.05, 2, 81 (3.15). Hence we can conclude that both Pricing Strategy and Acceptance Probability are significant factors and their interaction Pricing Strategy*Acceptance Probability is not significant as its F value (0.26) is less than 3.15. A 2 The analysis of Variance for the H igh R ate of A rrival. Multilevel Factorial Design Factors: 2 Replicates: 10 Base runs: 9 Total runs: 90 Base blocks: 1 Total blocks: 1 Number of levels: 3, 3 PAGE 65 57 Appendix A (continued) General Linear Model: Revenue Generate versus Price Offered, Probability Factor Type L evels Values Price Offered fixed 3 1, 2, 3 Probability fixed 3 1, 2, 3 Analysis of Variance for Revenue Generated, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P Pricing Strategy 2 135062050 135062050 33765512 4.30 0.002 Acceptance Prob 2 1502155964 1502155964 751077982 64.49 0.000 Pricing Strat*Accept 4 1220663 1220663 305166 0.03 0.999 Probability Error 81 943289950 943289950 11645555 Total 89 2454497317 S = 3412.56 R Sq = 61.57% R Sq (adj) = 57.77% From the above analysis we see that the F values for pricing strategy (4. 30 ) and acceptance probability (6 4 49 ) are greater than F 0.05, 2, 81 (3.15). Hence we can conc lude that both Pricing Strategy and Acceptance Probability are significant factors and their interaction Pricing Strategy*Acceptance Probability is not significant as its F value (0. 03 ) is less than 3.15. PAGE 66 58 Appendix B Method for C alculating the N umber of R eplications The equation used for calculating the number of replications to obtain a specific value of half width is n = n 0 h 0 2 / h 2 [ Kelton, Sadowski and Sadowski, 200 2] where, n = number of replications n 0 = number of initial replication h 0 = half width from the initial replications h = half width required If the total revenue generated from 10 replication is 39,941 and the half width is 2,329, to obtain a half width of 2% of 39,941 which is 798, we have n = 10* (2,329 / 798) 2 n = 85.17 w hich we can round off to 100 replications. Similarly, i f the total revenue generated from 10 replication is 79,885 and the half width is 3 279 to obtain a half width of 1% of 79,885 which is 798 we have n = 10 ( 3,279 / 798 ) 2 n = 168 xml version 1.0 encoding UTF8 standalone no record xmlns http:www.loc.govMARC21slim xmlns:xsi http:www.w3.org2001XMLSchemainstance xsi:schemaLocation http:www.loc.govstandardsmarcxmlschemaMARC21slim.xsd leader nam Ka controlfield tag 001 001498145 003 fts 006 med 007 cr mnuuuuuu 008 041209s2004 flua sbm s0000 eng d datafield ind1 8 ind2 024 subfield code a E14SFE0000557 035 (OCoLC)57719360 9 AJU6740 b SE SFE0000557 040 FHM c FHM 090 T56 (ONLINE) 1 100 Joshi, Kapil. 0 245 Modeling alternate strategies for airline revenue management h [electronic resource] / by Kapil Joshi. 260 [Tampa, Fla.] : University of South Florida, 2004. 502 Thesis (M.S.I.E.)University of South Florida, 2004. 504 Includes bibliographical references. 516 Text (Electronic thesis) in PDF format. 538 System requirements: World Wide Web browser and PDF reader. Mode of access: World Wide Web. 500 Title from PDF of title page. Document formatted into pages; contains 66 pages. 520 ABSTRACT: Ever since the deregulation of the airline industry in 1978, fierce competition has made every airline try and gain a competitive edge in the market. In order to accomplish this, airlines are turning to advanced optimization techniques such as revenue management. Revenue management is a way for airlines to maximize capacity and profitability by managing supply and demand through price management. Over the last few years research in the field of revenue management has steadily progressed from seat inventory control techniques such as single leg seat inventory and network inventory control to ticket pricing techniques. Ticket pricing techniques involve setting ticket prices according to the time remaining to depart and inventory level conditions at that point in time. These models can be solved either by dynamic or mathematical programming.However, these models in addition to having increased complexity are based on several assumptions which may not be valid in real life situations thereby limiting there applicability. In this research, we have developed computer simulation models using Arena software as a tool to solve airline revenue management problems. Different models based on factors such as customer behavior, which would involve the probability of a customer accepting a ticket and relevant pricing methods such as seats remaining and time remaining have been developed with the objective of reaching an optimal revenue management policy. Initially, the strategies have been developed and tested for a single flight leg for different types of destinations such as tourist, business and mixed tourist and business.It was found that models where pricing was based on seats remaining generated the most revenue for the tourist destinations, time remaining for the business destinations and pricing based on time and seats remaining for the mixed type. Two different strategies, one where the ticket price for the indirect (stopover) flight increases as more seats for direct flight are sold and the second where the ticket price for the indirect flight decreases have been developed for a network of three cities with direct and stopover flights. It was found that the first strategy works well for the business destination. There was no significant difference between the two strategies for the other two destinations. Also, the model was run where a set percentage of seats on the direct flight are sold prior to the opening of indirect flight bookings (blocking). It was found that blocking of seats did not increase the total revenue generated. 590 Adviser: Khator, Suresh. 653 network. pricing. ticket. yield. simulation. 690 Dissertations, Academic z USF x Industrial Engineering Masters. 773 t USF Electronic Theses and Dissertations. 4 856 u http://digital.lib.usf.edu/?e14.557 