Working in collaboration with Spain-based retailer Zara, we address the problem of distributing, over time, a limited amount of inventory across all the stores in a fast-fashion retail network. Challenges specific to that environment include very short product life-cycles, and store policies whereby an article is removed from display whenever one of its key sizes stocks out. To solve this problem we first formulate and analyze a stochastic model predicting the sales of an article in a single store during a replenishment period as a function of demand forecasts, the inventory of each size initially available and the store inventory management policy just stated. We then formulate a mixed-integer program embedding a piece-wise linear approximation of the first model applied to every store in the network, allowing us to compute store shipment quantities maximizing overall predicted sales, subject to inventory availability and other constraints. We report the implementation of this optimization model by Zara to support its inventory distribution process, and the ensuing controlled pilot experiment performed to assess the model's impact relative to the prior procedure used to determine weekly shipment quantities. The results of that experiment suggest that the new allocation process increases sales by 3 to 4%, reduces transshipments, and increases the proportion of time that Zara's products spend on display within their life-cycle. Zara has been using this process for all of its products worldwide since June 2007.

(joint work with Felipe Caro, UCLA)