  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.
