| Summary: | Working in collaboration with Spain-based retailer Zara, we address the problem of dis-
tributing over time a limited amount of inventory across all the stores in a fast-fashion retail
network. Challenges speci¯c 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 ¯rst 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 ¯rst
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 by Zara to support its inventory distribu-
tion process, and the ensuing controlled ¯eld experiment performed to assess the impact of that
model relative to the prior procedure used to determine weekly shipment quantities. The results
of that experiment suggest that the new allocation process tested increases sales, reduces tran-
shipments, and increases the proportion of time that an important category of Zara's products
spends on display.
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