Operations Management under Consumer Choice Models with Multiple Purchases
72 Pages Posted: 15 Oct 2020 Last revised: 11 May 2022
Date Written: August 1, 2020
In this paper we investigate the effects of multiple purchases that could arise in both brick-and-mortar retailing and 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 multiple purchases into consumer choice behavior and study a series of associated operations problems.
Under the new choice framework that integrates the multiple purchases with discrete choice models, consumers first form a consideration set, then decide purchase quantity for each product within the consideration set and lastly select one product from the consideration set with determined purchase quantity in mind. We show that the joint assortment and pricing optimization problem in the presence of fixed costs can be decoupled into multiple pricing problems of different assortment sizes, each of which can be transformed into a scalar optimization problem. We also propose an approximation with provable guarantee for heterogeneous fixed costs. We further incorporate consumer heterogeneity into our choice model with the multiple purchases. By transforming the joint assortment and pricing problem with discrete price levels into a constrained assortment problem, we derive a fully polynomial time approximation scheme with time complexity growing exponentially in the number of consumer segments.
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 could lead to substantial losses.
Suggested Citation: Suggested Citation