Choosing ann-Pack of Substitutable Products
Edward Fox, Laura Norman, John Semple
Management Science · 2018 · Volume 64 · Issue 5
Abstract
We develop a framework to model the shopping and consumption decisions of forward-looking consumers. Assuming that the consumer’s future utility for each product alternative can be characterized by a standard random utility model, we use dynamic programming to determine the optimal consumption policy and the maximum expected value of consuming any n substitutable products selected while shopping (an n -pack). We propose two models. In the first ( canonical ) model, we assume that an alternative is consumed on each successive consumption occasion and obtain a closed-form optimal policy and a closed-form value function. Given a consumer’s preferences for the product alternatives in an assortment, we then show how to identify that consumer’s optimal n -pack using a simple swapping algorithm that converges in at most n swaps. In the second ( generalized ) model, we introduce an outside option so that a product alternative need not be consumed on each consumption occasion. We obtain a closed-form value function for the generalized model and show that its optimal n -pack is related to that of the canonical model using a special type of majorization. Additional structural properties and implications of each model are explored, as are other applications. The online appendix is available at https://doi.org/10.1287/mnsc.2017.2729 . This paper was accepted by Vishal Gaur, operations management.
Keywords
dynamic programming, decision analysis, utility/preference applications, multinomial logit, assortment optimization
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