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In this paper, we explore the challenge of assortment planning in the context of quick-commerce, a rapidly-growing business model that aims to deliver time-sensitive products. In order to achieve quick delivery to satisfy the immediate demands of online customers in close proximity, personalized online assortments need to be included in brick-and-mortar store offerings. With the presence of this physical linkage requirement and distinct multinomial logit (MNL) choice models for online consumer segments, the firm seeks to maximize overall revenue by selecting an optimal assortment of products for local stores and by tailoring a personalized assortment for each online consumer segment. We refer to this problem as quick-commerce assortment planning (QAP). We employ an integer programming approach to solve this NP-hard problem to global optimality. Specifically, we propose convexification techniques to handle its combinatorial and nonconvex nature. We capture the consumer choice of each online segment using a convex hull representation. By exploiting the geometry behind Luce's choice axiom, we provide a compact polyhedral characterization of the convex hull under various operational constraints that are not totally-unimodular. Furthermore, we conduct a polyhedral study on the relation between assortment decisions for products to offer and choice probabilities of products under the MNL model.Our methodology, coupled with a modified choice probability ordered separation algorithm, yields formulations that provide a significant computational advantage over existing methods. Through comprehensive numerical studies, we emphasize the significance of aligning offline and online assortment decisions and underscore the perils associated with inaccurately specifying customer behavior models.
Chen et al. (Fri,) studied this question.