Solution to the Continuous Time Dynamic Yield Management Model

Liang, Yigao

doi:10.1287/trsc.33.1.117

Cited by 67 publications

(23 citation statements)

References 11 publications

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“…In the following example, it is possible to obtain an optimal policy; see Stone and Diamond (1992) or Liang (1999). However, by focusing on a simple example we are able to demonstrate clearly the possible drawbacks of updating suboptimal policies.…”

Section: Is Re-solving Better?mentioning

confidence: 90%

“…Recent studies have considered more realistic models for the demand process. Such work on Markovdecision-process-type models of single-leg flights includes Stone and Diamond (1992), Lee and Hersh (1993), Lautenbacher and Stidham (1999), Liang (1999), Subramanian et al (1999), and Zhao and Zheng (2001). If a single-leg flight is in question and the arrival process has independent increments, then natural monotonicity properties can be exploited to make the computation and storage of optimal policies possible.…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic Behavior of an Allocation Policy for Revenue Management

Cooper

2002

Operations Research

143

124

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Revenue management has become an important tool in the airline, hotel, and rental car industries. We describe asymptotic properties of revenue management policies derived from the solution of a deterministic optimization problem. Our primary results state that, within a stochastic and dynamic framework, solutions arising out of a single well-known linear program can be used to generate allocation policies for which the normalized revenue converges in distribution to a constant upper bound on the optimal value. We also show similar asymptotic results for expected revenues. In addition, we describe counterintuitive behavior that can occur when allocations are updated during the booking process (updating allocations can lead to lower expected revenue). These results add to the understanding of allocation policies and help to make concrete the statement that simple policies from easy-to-solve formulations can be relatively effective, even when analyzed in the more realistic stochastic and dynamic framework.

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Section: Is Re-solving Better?mentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

Asymptotic Behavior of an Allocation Policy for Revenue Management

Cooper

2002

Operations Research

143

124

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“…Lee and Hersh [26] introduced and analyzed a discrete-time, Markov model that allows for an arbitrary order of arrivals. For further work on single-leg allocation problems, see Brumelle et al [14], Kleywegt and Papastavrou [24], Lautenbacher and Stidham [25], Liang [27], Stone and Diamond [38], Subramanian et al [39] and Zhao [48]. For analysis of multiple-leg (network) allocation problems, see Cooper [15], Curry [16], Dror et al [18], Glover et al [22], Simpson [36], Talluri [40], Talluri and van Ryzin [41], [42] and Williamson [43], [44].…”

Section: Introduction and Overviewmentioning

confidence: 99%

Revenue Management Under a General Discrete Choice Model of Consumer Behavior

Talluri¹,

Ryzin²

2004

mnsc

141

158

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Customer choice behavior, such as "buy-up" and "buy-down", is an important phenomenon in a wide range of revenue management contexts. Yet most revenue management methodologies ignore this phenomenon -or at best approximate it in a heuristic way. In this paper, we provide an exact and quite general analysis of this problem. Specifically, we analyze a single-leg yield management problem in which the buyers' choice behavior is modeled explicitly. The choice model is perfectly general and simply specifies the probability of purchasing each fare product as function of the set of fare products offered. The control problem is to decide which subset of fare products to offer at each point in time. We show that the optimal policy is of a simple form. Namely, it consists of 1) identifying the ordered family of "nondominated" subsets S 1 , ..., S m , and 2) at each point in time opening one of these sets S k , where the optimal index k is increasing in the remaining capacity x. That is, the more capacity we have available, the further the optimal set is along this sequence. Moreover, we show that the optimal policy is nested if and only if the ordered sets are increasing, that is S 1 ⊆ S 2 ⊆ ... ⊆ S n , and we give a complete characterization of when nesting by fare order is optimal. We then show that two important models, the independent demand model and the multinomial logit model (MNL), satisfy this later condition and hence nested-by-fare-order policies are optimal in these cases. We also develop an estimation procedure for this setting based on the expectation-maximization (EM) method that jointly estimates arrival rates and choice model parameters when no-purchase outcomes are unobservable. Numerical results are given to illustrate both the model and estimation procedure.

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“…Liang [99] also considers a problem related to Gallego and van Ryzin [62], except that the author allows for multiple fare classes with different demand intensity functions, which are inhomgeneous Poisson processes with no specific order arrival. As before, the demand depends on both the price and the inventory that is available.…”

Section: 31mentioning

confidence: 99%