Abstract not found

Abstract not found

This paper is an invited chapter to appear in Retail Supply Chain Management, Eds. N. Agrawal and S. A.

This paper develops a model of dynamic pricing with endogenous customer behavior. In the model, there is a monopolist who sells a finite inventory over a finite time horizon. The seller adjusts prices dynamically in order to maximize revenue. Customers arrive continually over the duration of the selling season. At each point in time, customers may purchase the product at current prices, remain in the market at a cost in order to purchase later, or exit, and they wish to maximize individual utility. The customer population is heterogeneous along two dimensions: they may have different valuations for the product and different degrees of patience (waiting costs). We study this continuous-time game between the seller and the customers, show that it can be reduced into a single-variable nonlinear program, and characterize the equilibrium that maximizes revenue for the seller. We demonstrate that heterogeneity in both valuation and patience is important because they jointly determine the structure of optimal pricing policies. In particular, when high-value customers are proportionately less patient, markdown pricing policies are effective because the high-value customers would still buy early at high prices while the low-value customers are willing to wait (i.e. they are not lost). On the other hand, when the high-value customers are more patient than the low-value customers, prices should increase over time in order to discourage inefficient waiting. Our results also shed light on how the composition of the customer population affects optimal revenue, consumer surplus, and social welfare. Finally, we consider the long run problem of selecting the optimal initial stocking quantity.

Invited Paper for Production and Operations Management Customer behavior modeling has been gaining increasing attention in the operations man-agement community. In this paper we review current models of customer behavior in the revenue management and auction literatures and suggest several interesting research directions in this area. 1

A flexible product is a menu of two or more alternatives products serving the same market.

We consider revenue management models for pricing a product line with several customer segments, working under the assumption that every customer’s product choice is determined entirely by their reservation price. We model the customer choice behavior by several probabilistic choice models and formulate the resulting problems as mixed-integer programming problems. We study special properties of these formulations and compare the resulting optimal prices of the different probabilistic choice models. We also explore some heuristics and valid inequalities to improve the running time of the mixed-integer programming problems. We illustrate the computational results of our models on real and generated customer data taken from a company in the tourism sector. C&O Research Report: CORR 2007-02

Revenue management models traditionally assume that future demand is unknown, but can be represented by a stochastic process or a probability distribution. Demand is however often difficult to characterize, especially in new or nonstationary markets. In this paper, we develop robust formulations for the capacity allocation problem in revenue management, using the maximin and the minimax regret criteria, under general polyhedral uncertainty sets. Our approach encompasses the following open-loop controls: partitioned booking limits, nested fare classes by origin-destination pairs, Displacement-Adjusted Virtual Nesting, and fixed bid prices. We also characterize the optimal booking policy under interval uncertainty; while partitioned booking limits are optimal under the maximin criterion, some nesting is desirable under the minimax regret criterion. Our numerical analysis reveals that robust controls can outperform the classical heuristics for network revenue management, while achieving the best performance in the worst case. Our models are scalable to solve practical problems, because they combine efficient solution methods (small mixed-integer and linear optimization problems) with very modest data requirements. 1.

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We develop a Markov decision process formulation of a dynamic pricing problem for multiple substitutable flights between the same origin and destination, taking into account customer choice among the flights. The model is rendered computationally intractable for exact solution by its multidimensional state and action spaces, so we develop and analyze various bounds and heuristics. We first describe three related models, each based on some form of pooling, and introduce heuristics suggested by these models. We also develop separable bounds for the value function which are used to construct value- and policy-approximation heuristics. Extensive numerical experiments show the value- and policy-approximation approaches to work well across a wide range of problem parameters, and to outperform the pooling-based heuristics in most cases. The methods are applicable even for large problems, and are potentially useful for practical applications.