Multi-location assortment optimization under lead time effects

We have investigated the assortment planning problem for an online retailer that has multiple ful llment centers to maximize its expected pro t. Each ful llment center is responsible for a customer segment which has its own customer pro le, and each customer segment's demand is governed by a multinomial logit model (MNL), resulting in a mixtures of MNL (MMNL) model. A demand is primarily met by the responsible ful llment center, if available. However, if a product is not available in the responsible ful llment center, the demand can be met by ful llment centers in other regions at an additional shipping cost paid by the rm. The shipping cost depends on the distance between regions, so it varies by origin and destination. We assume that each customer has access to the entire assortment in all ful llment centers. To solve this problem, di erent from the literature, we have formulated the problem using a conic quadratic mixed integer programming approach. Later, the conic formulation is strengthened with valid inequalities. We have provided a numerical study to test the performance of our formulation against other formulations. Results show that our conic formulation together with the valid inequalities delivers outstanding performance compared to others in the literature. We also validated our approach using data from a local chain that operates in Northwestern part of Turkey.