Bulk versus Sequential Product Returns: Algorithms and Insights for Assortment Planning

Abstract

In this paper, we present, study and compare two distinct customer choice frameworks crafted to model the step-by-step process through which consumers order products, and then subsequently decide which to keep and which to return based on their realized preferences. The first of the two models that we consider is the so-called Sequential Returns model conceived by Wagner and Martínez-de Albéniz (2020), wherein customers sequentially order products one-by-one, deciding when to stop their search process by trading off their realized utility for the product at-hand with the inconveniences of returning this item and ordering a substitute. The second model is our own creation, which we derive by tweaking the randomutility-based framework of the sequential model so as to capture what we refer to as "bulk" ordering behavior. That is, we develop the Bulk Returns model, wherein customers are allowed to order all of the products that interest them upfront, ultimately keeping their most preferred, and returning the rest. First and foremost, we set out to study the now-classic assortment optimization problem, where the goal is to select the profit-maximizing subset of products to make available for purchase, when demand is governed by either of the two returns models, and the retailer incurs a refurbishing cost for each item that is returned. For the Sequential Returns model, we provide an optimal polynomial-time algorithm for the setting where the return costs are homogeneous across products, noting that this result improves upon the previous-best PTAS of Wagner and Martínez-de Albéniz (2020). Additionally, we present a novel hardness result for a constrained variant of the assortment problem. For the Bulk Returns model, we show that its corresponding assortment problem is NP-Hard, and present a PTAS based on a carefully-crafted knapsack-based approximation. We then augment the bulk framework to allow for multiple customer types, each distinguished by the extent to which returning items is deemed to be an inconvenience. For this multi-type extension, we present two nuanced approximate-dynamic-programming-based approaches. We conclude our analysis by offering both theoretical and empirical comparisons of the two returns model so as to better understand what sorts of returns behavior should be enforced or encouraged by retailers. Our cornerstone result along this line is that we are able to show that the sequential model surprisingly leads to universally higher profits. In the numerical experiments that follow, we set out to quantify these gains and understand if the high-level managerial insights derived from our theoretical analysis persist when we augmented our returns disutility/cost framework to add more of an air of realism.

Keywords: consumer choice, return, assortment optimization, approximation schemes