Assortment Optimization Under the Paired Combinatorial Logit Model

C ustomer cancellations and no-shows have an important impact on the performance of an airline's revenue management system. In this study, we study airline network revenue management problems with customer cancellations and no-shows, considering two types of demand models: independent-demand and choice-based-demand models. In independent-demand models, the booking request rates for different products are independent of the assortment of products offered by the airline (exogenous), whereas in choice-based-demand models they depend on the airline's assortment (endogenous). The stochastic problems of optimizing the booking policies for the two demand models are not tractable because of the high-dimensional state space. Therefore, for each model, we use the corresponding deterministic, continuous-time, and continuous-state model, known as the fluid model. A booking policy based on the fluid solution can be implemented for the original stochastic, discrete model. This fluid policy is shown to be asymptotically optimal when the arrival rates become high and the seat capacities become large. In the independent-demand setting, an optimal fluid solution can be computed by solving a convex optimization problem for which efficient algorithms exist, whereas for some choice-based-demand models, the fluid control problems are known to be intractable. We also develop mixed fluid policies for the independent-demand setting, taking advantage of the real-time booking state, to improve the performance over the fluid policy. In a factorial experiment of 20 small-sized single-leg problems, the revenue loss under one of the mixed fluid policies is demonstrated to be less than 1% of the optimal value for all problems.

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“…, Zhang et al. ). There is a substantial body of research on solving fluid control problems for the choice‐based‐demand model.…”

Section: Discussionmentioning

confidence: 99%

Network Revenue Management with Cancellations and No‐Shows

Dai

Kleywegt

Xiao

2019

Production and Operations Management

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“…Usually, a particular choice model was first analyzed on its own, and subsequently in conjunction with certain constraints on capacity, allowable prices, consideration set structures, etc. We expect that more work will appear in the coming years on this, using less common choice models such as the paired combinatorial logit model (Zhang et al (2017)).…”

Section: Discussionmentioning

confidence: 99%

A review of choice-based revenue management: Theory and methods

Strauss

Klein

Steinhardt

2018

European Journal of Operational Research

131

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“…In this paper, we assume that customers' choice behavior is captured by the PCL model, which can accurately capture the substitution effects among products [16][17][18]. Throughout this paper, the deterministic utility of product 𝑖 is captured through 𝛼 𝑖 − 𝛽𝑝 𝑖 , where 𝛼 𝑖 is a known constant to measure the quality of this product, and 𝛽 > 0 is the price-sensitivity parameter to capture the utility variation when the selling price changes.…”

Section: Modeling Frameworkmentioning

confidence: 99%

“…To solve the above problem, we first linearize the objective function by using the characteristic of the PCL model that there are exact two products under each nest. To do so, we follow the similar approach used in [17][18]. Letting 𝜌 𝑖𝑗 = (exp(𝛼 𝑖 /𝛾 𝑖𝑗 ) + exp (𝛼 𝑗 /𝛾 𝑖𝑗 )) 𝛾…”

Section: Solution Approachmentioning

confidence: 99%

“…The authors show that the uniqueness of the optimal prices can be achieved under certain conditions based on the concept of P-matrix and develop the corresponding solution algorithms. Recently, Reference [17] shows that the assortment optimization problem under the PCL model is NP-hard even when there are no capacity constraints and develop a general approximation framework based on iterative variable fixing and coupled randomized rounding. Later, Reference [18] proposes another approximate algorithm based on approximations to the knapsack problem when there is a known capacity constraint.…”

Section: Introductionmentioning

confidence: 99%

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Capacitated Assortment Optimization with Pricing under the Paired Combinatorial Logit Model

Zhang¹,

Zhong²,

Gao³

et al. 2018

2018 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM)

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In this paper, we investigate the capacitated assortment optimization problem with pricing under the paired combinatorial logit model, whose goal is to identify the revenue-maximizing subset of products as well as their selling prices subject to a known capacity limit. We model customers' purchase behavior using the paired combinatorial logit model, which allows for covariance among any pair of products. We formulate this problem as a non-linear mixed integer program. Then, we propose a two-step approach to obtain the optimal solution based on solving a mixed integer program and Lambert-W function. To further improve its performance, we design a greedy heuristic algorithm and a greedy randomized adaptive search procedure to obtain highquality solutions so as to balance the tradeoff between accuracy and computational efficiency. A series of numerical experiments are conducted to gauge the efficiency and quality of our proposed approaches.

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Assortment Optimization Under the Paired Combinatorial Logit Model

Cited by 29 publications

References 24 publications

Network Revenue Management with Cancellations and No‐Shows

Network Revenue Management with Cancellations and No‐Shows

A review of choice-based revenue management: Theory and methods

Capacitated Assortment Optimization with Pricing under the Paired Combinatorial Logit Model

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