Distributionally Robust Omnichannel Stocking Decisions in Quick Fulfillment Systems

This work is inspired by the daily operations of Hema supermarket, which is a recently established “new retail” model by Alibaba Group, China. In a Hema supermarket store, a single SKU may be presented with demand in the form of multiple channels. The challenge facing Hema is to stock inventory between the warehouse and the store-front in advance of uncertain demand that arises in several consecutive time frames, each 30 minutes long. Using historical sales data provided by Alibaba, we construct a distributionally robust optimization model, wherein we are to make a stocking decision robust to an adversary's choice of coupling of (marginal) demand distributions by channel and by time frame. The adversary's decision amounts to designing a random mathematical program with equilibrium constraints (MPEC). And we provide both a structural analysis of the adversary's choice of coupling as well as an efficient procedure to find this coupling. Though the distributionally robust stocking problem is non-concave in general, we provide sufficient conditions on the cost parameters for which this problem is concave, and hence tractable. Finally, in data experiments, we compare and contrast the performance of our distributionally robust solution with the performance of a Newsvendor-like solution implemented at Alibaba on various SKUs of varying sales volume and number of channels. The results indicate that the distributionally robust solutions generally outperform the Newsvendor-like solution. Interestingly, in all experiments, the distributionally robust inventory problems presented by the historical data provided by Hema are in fact concave