Choosing an n-Pack of Substitutable Products

48 Pages Posted: 6 Aug 2014 Last revised: 19 Oct 2016

See all articles by Edward Fox

Edward Fox

Southern Methodist University (SMU) - Marketing Department

Laura Norman

affiliation not provided to SSRN

John H. Semple

Southern Methodist University (SMU) - Information Technology and Operations Management Department (ITOM)

Date Written: October 18, 2016

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.

Keywords: Simultaneous Choice, Sequential Choice, Variety

JEL Classification: M31, D11, D12

Suggested Citation

Fox, Edward and Norman, Laura and Semple, John H., Choosing an n-Pack of Substitutable Products (October 18, 2016). Available at SSRN: https://ssrn.com/abstract=2476026 or http://dx.doi.org/10.2139/ssrn.2476026

Edward Fox

Southern Methodist University (SMU) - Marketing Department ( email )

United States

Laura Norman

affiliation not provided to SSRN

John H. Semple (Contact Author)

Southern Methodist University (SMU) - Information Technology and Operations Management Department (ITOM) ( email )

Dallas, TX 75275
United States
214-768-2546 (Phone)
214-768-4099 (Fax)

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