# zbMATH — the first resource for mathematics

Revenue management under a general discrete choice model of consumer behavior. (English) Zbl 1168.91427
Summary: 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 reserve management problem in which the buyers’ choice behavior is modeled explicitly. The choice model is very general, simply specifying the probability of purchase for each fare product as a 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 for this problem has a quite simple form. Namely, it consists of identifying an ordered family of “efficient” subsets $$S_1,\dots, S_m$$, and at each point in time opening one of these sets $$S_k$$, where the optimal index $$k$$ is increasing in the remaining capacity $$x$$ and decreasing in the remaining time. That is, the more capacity (or less time) available, the further the optimal set is along this sequence. We also show that the optimal policy is a nested allocation policy if and only if the sequence of efficient sets is nested, that is $$S_1\subseteq S_2\subseteq\dots\subseteq S_m$$. Moreover, we give a characterization of when nesting by fare order is optimal. 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.

##### MSC:
 91B38 Production theory, theory of the firm 91B42 Consumer behavior, demand theory 90C39 Dynamic programming
Full Text: