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 a reference is removed from display whenever one of its key sizes stocks out. We first formulate and analyze a stochastic model predicting the sales of a reference 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. Secondly, we formulate a mixed-integer program embedding a piece-wise linear approximation of the first model applied to every store in the network and allowing to compute store shipment quantities maximizing overall predicted sales, subject to inventory availability and other constraints. We report the implementation of this optimization model b...