Optimizing the inventory and fulfillment of an omnichannel retailer: a stochastic approach with scenario clustering

We study an inventory optimization problem for a retailer that faces stochastic online and in-store demand in a selling season of fixed length. The retailer has to decide the initial inventory levels and an order fulfillment policy such that the expected total costs are minimized. We approximate the problem by a two-stage stochastic optimization on a reduced number of scenarios. For deciding the representative scenarios, we propose a new similarity measure and a novel technique that combines the framework of Good-Turing sampling and Linear Programming. On randomly generated instances, the proposed algorithm obtains an average cost reduction of 7.56% compared to a state-of-the-art algorithm in the literature. The proposed algorithm works considerably better for short time horizons and a relatively large proportion of in-store customers.