4.5 Article

Optimal Pricing Under Multiple-Discrete Customer Choices and Diminishing Return of Consumption

Journal

OPERATIONS RESEARCH
Volume 70, Issue 2, Pages 905-917

Publisher

INFORMS
DOI: 10.1287/opre.2021.2146

Keywords

pricing; customer choice; multiple-discrete continuous choice model

Funding

  1. Natural Sciences and Engineering Research Council of Canada [RGPIN 2020-04213]
  2. Canada Research Chair Program
  3. W. P. Carey Dean's Award for Excellence 2019 Summer Research Grant

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The study examines a utility-based customer-choice model where customers may purchase multiple products. It analyzes the firm's optimal pricing problem and shows that the optimal solution is ordered based on a price-independent index. The study also extends to consider a stochastic model that accounts for customer heterogeneity.
We consider a utility-based customer-choice model where the customer may purchase multiple products and even possibly multiple units of each product. We show that the set of products with strictly positive optimal consumption quantities is one of the ordered sets based on product prices and certain model parameters. We study the firm's optimal pricing problem and present how to find the optimal prices. We show that the optimal solution exhibits a property that the set of products that induces strictly positive consumption quantities under optimal prices is also ordered based on a price-independent index composed of product cost and choice-model parameters. As extensions, we present an alternative formulation that constrains the customer's total expenditure instead of total purchase quantity and develop a solution approach. We also consider a stochastic model that accounts for customer heterogeneity, establishes a connection to the mixed Multinomial Logit (MNL) model, and numerically investigates how the heuristic policy based on the deterministic approximation performs.

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