Simulation-Based Booking Limits for Airline Revenue Management

Bertsimas, Dimitris; Boer, Sanne de

doi:10.1287/opre.1040.0164

Cited by 120 publications

(85 citation statements)

References 28 publications

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“…Williamson (1992) nicely summarizes many of these techniques. Other key work includes Bertsimas and Popescu (2003) and Bertsimas and de Boer (2005). For references to both MDP and math programming research, see Talluri and van Ryzin (2004b).…”

Section: Introductionmentioning

confidence: 99%

“…The approach is inspired by methods that decompose network problems into single-leg problems, replacing fares with suitable displacement adjusted fares (e.g., van Ryzin 2004b, Bertsimas andde Boer 2005). The individual two-leg problems are then solved using our time-decomposition approach (or another method, if so desired), and the resulting policies are reconstituted to obtain a policy for the original network problem.…”

Section: Introductionmentioning

confidence: 99%

“…Bertsimas and de Boer (2005) describe a procedure designed to obtain a nested booking-limit policy. They rely on stochastic-gradient techniques as well as a carefully devised procedure to estimate derivatives by finite differences.…”

Section: Introductionmentioning

confidence: 99%

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Some Decomposition Methods for Revenue Management

Cooper

Homem-de-Mello

2007

Transportation Science

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W orking within a Markov decision process (MDP) framework, we study revenue management policies that combine aspects of mathematical programming approaches and pure MDP methods by decomposing the problem by time, state, or both. The "time decomposition" policies employ heuristics early in the booking horizon and switch to a more-detailed decision rule closer to the time of departure. We present a family of formulations that yield such policies and discuss versions of the formulation that have appeared in the literature. Subsequently, we describe sampling-based stochastic optimization methods for solving a particular case of the formulation. Numerical results for two-leg problems suggest that the policies perform well. By viewing the MDP as a large stochastic program, we derive some structural properties of two-leg problems. We show that these properties cannot, in general, be extended to larger networks. For such larger networks we also present a "state-space decomposition" approach that partitions the network problem into two-leg subproblems, each of which is solved. The solutions of these subproblems are then recombined to obtain a booking policy for the network problem.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Some Decomposition Methods for Revenue Management

Cooper

Homem-de-Mello

2007

Transportation Science

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“…Another class of methods use gradients generated via simulation. Bertsimas and de Boer [8] proposed a stochastic gradient procedure for discrete demand case and van Ryzin and Vulcano [32] gave a similar approach for continous demand. Recent books by Talluri and van Ryzin [30] and Phillips [25] provide an excellent treatment of NCC problem and further literature review on the subject.…”

Section: Review Of Related Literaturementioning

confidence: 99%

New stochastic linear programming approximations for network capacity control problem with buy-ups

Büke

Yildirim²,

Kuyumcu

2007

J Revenue Pricing Manag

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“…One possible approach for revenue management problems is to establish booking limits that capture what portion of the available product inventory should be reserved for different customer classes. Recently, Karaesmen and van Ryzin (2004), Bertsimas and de Boer (2005), and van Ryzin and Vulcano (2006) have proposed stochastic gradient algorithms that are somewhat similar to our approach for establishing the booking limits. Stochastic gradient algorithms have been successfully applied in other settings as well.…”

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confidence: 99%

Incorporating Pricing Decisions into the Stochastic Dynamic Fleet Management Problem

Topaloğlu

Powell

2007

Transportation Science

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T his paper shows how to coordinate the decisions on pricing and fleet management of a freight carrier. We consider a setting where the carrier announces its prices at the beginning of a certain time horizon and the load arrivals over this horizon depend on the announced prices. Assuming that the vehicle fleet is managed according to a particular class of fleet management models, we present a tractable method to obtain sample path-based directional derivatives of the objective function with respect to the prices. We use this information to search for a good set of prices. Numerical experiments show that our approach yields high-quality solutions. Extensive literature has evolved around the problem of managing a fleet of vehicles to serve the loads occurring at different locations in a transportation network. Yet relatively little attention has been directed to the problem of determining what prices to charge. Due to the competitive nature of the freight transportation industry, lower prices can increase the number of loads over different traffic lanes (origindestination pairs), but the correct prices have to consider not only the profit-maximization problem over each traffic lane, but also the downstream effects that arise when the vehicles become empty and have to be repositioned to other locations.In this paper, we address the question of how to coordinate the decisions on pricing and fleet management of a freight carrier. Let 1 T be the set of time periods in the planning horizon and at the beginning of time period 1, the carrier decides what prices to charge over the next T time periods. These prices vary by traffic lanes, and may or may not vary by time. The objective is to find a set of prices that maximize the total expected profit over the planning horizon. We explicitly model the random load arrivals and the price-demand interactions by letting the number of loads over each traffic lane be a random variable whose distribution depends on the price. Assuming that the carrier makes its fleet management decisions by using the stochastic fleet management model previously developed by Godfrey and Powell (2002), we provide a tractable algorithm to obtain sample path-based directional derivatives of the objective function with respect to the prices. Starting from given prices, we use this information to search for better ones.Fleet management models have their roots in some of the earliest applications of linear programming and min-cost network-flow algorithms; see Fulkerson (1954), Ferguson andDantzig (1955), White and Bomberault (1969) and White (1972). These early models essentially formulate the problem over a statetime network, where the nodes represent the supply of vehicles at different locations at different time periods, the arcs represent the vehicle movements, and where the load availabilities act as upper bounds on the arcs. They are referred to as deterministic models because they assume that the load arrivals over the entire planning horizon are known in advance and they incorporate the uncertai...

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Simulation-Based Booking Limits for Airline Revenue Management

Cited by 120 publications

References 28 publications

Some Decomposition Methods for Revenue Management

Some Decomposition Methods for Revenue Management

New stochastic linear programming approximations for network capacity control problem with buy-ups

Incorporating Pricing Decisions into the Stochastic Dynamic Fleet Management Problem

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