This thesis addresses the problem of pricing perishable inventories such as airline seats and hotel rooms. It also analyzes the airline seat allocation problem when two airlines compete on a single-leg flight. Finally, several existing models for seat allocation with multiple fares on a single-leg flight are compared. The pricing framework is consistent with modern yield management tools which utilize restrictions such as weekend stayover to segment the market. One model analyzed considers a restriction which is irrelevant to one set of consumers, but which the others find so onerous that they will not purchase a restricted ticket at any price. If the consumers who do not mind the restriction are less price sensitive than those who find the restriction onerous, then the thesis shows that there is an optimal policy for a monopolist which will sell fares at no more than three price levels. When two restrictions are allowed in the model, if one is more onerous than the other in the sense that the set of consumers who would not buy a ticket with the first restriction is a subset of those who would not buy it with the second restriction, then the restrictions are said to be nested. If the sets of consumers who would not buy tickets with the first restriction is disjoint from those who would not buy with the second restriction, then the restrictions are said to be mutually exclusive. If two restrictions are either nested or mutually exclusive, then a monopolist needs at most four price levels with three types (i.e. combinations of restrictions) of product. With two general restrictions, the monopolist may need five price levels with four types of product. The pricing model is applied to restrictions which are based on membership in a particular organization. For example, employees of an airline are frequently eligible for special fares. Some airlines provide special fares for government employees or for employees of certain corporations. An analysis is given to help airlines understand the costs and benefits of such arrangements. A model of two airlines competing on a single-leg flight is developed for the case where the airlines have fixed capacity and fixed price levels for two types of fares-full and discount. The airlines compete by controlling the number of discount fares which they sell. The split of the market between the airlines is modelled in two different ways. First, the airlines might share the market for a fare class proportionally to their allocation of seats to that fare class. In this case, under certain conditions, there exists an equilibrium pair of booking limits for the discount fare such that each airline will protect the same number of seats for the full fare customers, even when the demands are random and stochastically dependent. The second market sharing model assumes that the two airlines share the market demand equally. In this case, when the demands are deterministic, then there is an equilibrium solution where each airline will protect enough seats to split equally the market for the full fares. Finally, three existing seat allocation models for multi-fare single-leg flights with stochastically independent demands are compared. It is shown that the optimality conditions for each of these models are analytically equivalent, thus providing a unified approach to this problem.

This thesis addresses the problem of pricing perishable inventories such as airline seats and hotel rooms. It also analyzes the airline seat allocation problem when two airlines compete on a single-leg flight. Finally, several existing models for seat allocation with multiple fares on a single-leg flight are compared. The pricing framework is consistent with modern yield management tools which utilize restrictions such as weekend stayover to segment the market. One model analyzed considers a restriction which is irrelevant to one set of consumers, but which the others find so onerous that they will not purchase a restricted ticket at any price. If the consumers who do not mind the restriction are less price sensitive than those who find the restriction onerous, then the thesis shows that there is an optimal policy for a monopolist which will sell fares at no more than three price levels. When two restrictions are allowed in the model, if one is more onerous than the other in the sense that the set of consumers who would not buy a ticket with the first restriction is a subset of those who would not buy it with the second restriction, then the restrictions are said to be nested. If the sets of consumers who would not buy tickets with the first restriction is disjoint from those who would not buy with the second restriction, then the restrictions are said to be mutually exclusive. If two restrictions are either nested or mutually exclusive, then a monopolist needs at most four price levels with three types (i.e. combinations of restrictions) of product. With two general restrictions, the monopolist may need five price levels with four types of product. The pricing model is applied to restrictions which are based on membership in a particular organization. For example, employees of an airline are frequently eligible for special fares. Some airlines provide special fares for government employees or for employees of certain corporations. An analysis is given to help airlines understand the costs and benefits of such arrangements. A model of two airlines competing on a single-leg flight is developed for the case where the airlines have fixed capacity and fixed price levels for two types of fares-full and discount. The airlines compete by controlling the number of discount fares which they sell. The split of the market between the airlines is modelled in two different ways. First, the airlines might share the market for a fare class proportionally to their allocation of seats to that fare class. In this case, under certain conditions, there exists an equilibrium pair of booking limits for the discount fare such that each airline will protect the same number of seats for the full fare customers, even when the demands are random and stochastically dependent. The second market sharing model assumes that the two airlines share the market demand equally. In this case, when the demands are deterministic, then there is an equilibrium solution where each airline will protect enough seats to split equally the market for the full fares. Finally, three existing seat allocation models for multi-fare single-leg flights with stochastically independent demands are compared. It is shown that the optimality conditions for each of these models are analytically equivalent, thus providing a unified approach to this problem. / Business, Sauder School of / Graduate

When a customer requests a discount fare, the airline must decide whether to sell the seat at the requested discount or to hold the seat in hope that a customer will arrive later who will pay more. I model this situation for a single leg flight with multiple fare classes and customers who arrive according to a semi-Markov process (possibly nonhomogeneous). These customers can request multiple seats (batch requests) and can be overbooked. Under certain conditions, I show that the value function decreases as departure approaches. If each customer only requests a single seat or if the requests can be partially satisfied, then I show that there are optimal booking curves which decrease as departure approaches. I provide counterexamples to show that this structural property of the optimal policy does not hold in general. When customers are allowed to cancel I show that booking curves exist and may be monotone in certain cases. I also consider the situation where the customer's request size and fare offered are not known, but their joint probability distribution is available, and show that under certain conditions existence of booking curves obtains, and that under further assumptions, they are monotone. Finally, the theoretical results are used in realistic numerical examples, which are compared to certain deterministic upper bounds and revenues obtained under heuristic policies. The airline yield management problem described above is an instance of a generic revenue management problem, which, in turn, can be cast into a finite horizon semi-Markov dynamic optimal control problem. I provide examples of other applications of revenue management.

When a customer requests a discount fare, the airline must decide whether to sell the seat at the requested discount or to hold the seat in hope that a customer will arrive later who will pay more. I model this situation for a single leg flight with multiple fare classes and customers who arrive according to a semi-Markov process (possibly nonhomogeneous). These customers can request multiple seats (batch requests) and can be overbooked. Under certain conditions, I show that the value function decreases as departure approaches. If each customer only requests a single seat or if the requests can be partially satisfied, then I show that there are optimal booking curves which decrease as departure approaches. I provide counterexamples to show that this structural property of the optimal policy does not hold in general. When customers are allowed to cancel I show that booking curves exist and may be monotone in certain cases. I also consider the situation where the customer's request size and fare offered are not known, but their joint probability distribution is available, and show that under certain conditions existence of booking curves obtains, and that under further assumptions, they are monotone. Finally, the theoretical results are used in realistic numerical examples, which are compared to certain deterministic upper bounds and revenues obtained under heuristic policies. The airline yield management problem described above is an instance of a generic revenue management problem, which, in turn, can be cast into a finite horizon semi-Markov dynamic optimal control problem. I provide examples of other applications of revenue management. / Business, Sauder School of / Graduate

Keywords. Hub-to-hub network, bid-price control, certainty equivalent control, combinatorial optimization, structures, primal-dual, revenue management, airline network, monotone thresholds, supermodularity/submodularity, L♮ concavity, Lagrange dual. / The subject of this study is the revenue management problem in hub-to-hub airline networks. The network consists of two hubs and a connecting flight between them with spoke cities expanding outwards. The airline produces various itineraries within the network, and its flights compete with each other for limited flight capacities during a fixed booking period. Although stochastic dynamic network revenue management has been theoretically established, in reality its implementation is still heavily dependent on linear programming-based heuristics. Simpson (1989) and Williamson (1992) proposed bid price control, which is now widely adopted by major airlines. Bertsimas and de Boer (2003) proposed certainty equivalent control, which has been little studied by RM researchers. In this thesis, bid price control is first explained, and then the structural properties of the hub-to-hub network are investigated. Using the Lagrange dual-function and the primal-dual relationship, it is shown that the threshold values used in bid price control have some monotone properties in the network's capacity states. The certainty equivalent control is then applied to the hub-to-hub network. By linking the network revenue management problem with a maximum-weight circulation problem in network flow, the optimal value function is shown to be supermodular in certain capacity dimensions, and submodular in other dimensions. This leads to the monotonicity of CEC thresholds on some short-haul itineraries. The notion of L ♮ concavity developed by Murota and Shioura (2005) is applied to this work, and it is shown that even the CEC thresholds on some two-leg or three-leg long-haul itineraries are monotonically increasing or decreasing in certain legs' capacities. It is hoped that the new structural properties found in this thesis can lead to a reduction of the computational work in the implementation of both the bid price control and the certainty equivalent control in the hub-to-hub airline network. / He, Hongzhi. / Adviser: Zhang Shuzhong. / Source: Dissertation Abstracts International, Volume: 72-04, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 111-118). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.