Operations Management under Consumer Choice Models with Multiple Purchases

Abstract

This paper investigates the effects of multiple purchases that arise in both brick-and-mortar retailing and online e-tailing. The product choice and consumer surplus depend not only on what to purchase but also on how many units to purchase. We incorporate the effects of multiple purchases into the multinomial logit model and a mixture of multinomial logit models, respectively. In the new choice framework with the effects of multiple purchases, consumers first form a consideration set, and then select one product at its optimal purchase quantity with the largest utility from the consideration set. For the joint assortment and pricing optimization problem with homogenous fixed cost, we show that a multi-purchase-willingness-ordered assortment is optimal under certain condition and propose a polynomial-time algorithm to find the optimal solution for general cases. We also give an approximate method for the joint optimization problem with heterogeneous fixed costs. For the joint assortment and pricing optimization problem with heterogenous consumers, we develop a fully polynomial time approximation scheme by transforming the joint optimization problem with discrete price levels into a constrained assortment problem. We combine the alternating optimization algorithm with the expectation maximization algorithm to overcome the non-concavity and missing data issues in estimation. An empirical study on the JD.com data shows that incorporating the effects of multiple purchases into discrete choice models can significantly improve model fitting and prediction accuracy, while ignoring the effects of multiple purchases may lead to substantial losses.