Optimizing omnichannel assortments and inventory provisions under the multichannel attraction model

Assortment optimization presents a complex challenge for retailers, as it depends on numerous decision factors. Changes in assortment can result in demand redistribution with multi-layered consequences. This complexity is even more pronounced for omnichannel retailers, which have to manage assortments across multiple sales channels. Choice modeling has emerged as an effective method in assortment optimization, capturing customer shopping behavior and shifts in demand as assortments change. In this paper, we utilize the multichannel attraction model – a discrete choice model specifically designed for omnichannel environments – and generalize it for the case of a retailer managing both an online store and a network of physical stores. We integrate assortment decisions with optimal inventory decisions, assuming stochastic demand. Our model shows that overlooking the demand variability can result in suboptimal assortment decisions due to the demand pooling effect. We derive complexity results for the assortment optimization problem, which we formulate as a mixed-integer second-order cone program. We then develop two heuristic algorithms based on different relaxations of the formulated optimization problem. Furthermore, we conduct an extensive numerical analysis to provide managerial insights. We find that an increasing coefficient of variation of demand has a dual effect on optimal assortment sizes, initially causing a decrease in online assortment size due to rising costs, followed by an increase in online assortment size because of the demand pooling effect. Finally, we evaluate the potential benefits of omnichannel assortment optimization compared to assortment optimization in siloed channels.