Estimation and optimization problems in revenue management with customer choice behavior

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Ding, Weijun
Kleywegt, Anton J.
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The first part of the thesis studies the parameter estimation problem in revenue management with discrete choice models. Revenue management models that include customer choice behavior have among others two types of parameters: (1) customer arrival rates and (2) choice parameters. In most applications, revenue managers have access to censored arrival data only. We first consider the conditions under which the arrival rates and choice parameters are identifiable. We then propose an algorithm to recover any non-homogeneous arrival rate. The estimation from the proposed algorithm theoretically converges to the true parameter. The numerical experiments also show that the algorithm has good practical performance. The second part of the thesis focuses on the revenue management problem with buy-down effects. The buy-down effects refer to the phenomenon that a product becomes more attractive if it is the cheapest available within certain subset of the assortment set, than if it is not the cheapest available within that subset. We consider the dynamic assortment optimization problem under discrete choice model with buy-down effects and propose a sales based linear programming (SBLP) formulation as a deterministic approximation to the original stochastic problem. Both the number of the decision variables and the number of constraints in the SBLP formulation are polynomial of the number of products. We give an efficient algorithm that converts an SBLP solution to a CDLP solution. We then consider the extension where the no-purchase alternative is random. We propose a polynomial algorithm to solve the assortment optimization with 100% buy-down effects or general buy-down effects.
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