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

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.