Title

Choosing an n-Pack of Substitutable Products

Publication Date

8-6-2014

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.

Document Type

Article

Keywords

Simultaneous Choice, Sequential Choice, Variety

Disciplines

Marketing

DOI

10.2139/ssrn.2476026

Source

SMU Cox: Marketing (Topic)

Language

English

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