Inventory rationing and replenishment for an omni-channel retailer

The growth of omni-channel retailing resulted in many new challenges for retailers, especially in relation to the replenishment and allocation of inventories for the different channels. In this paper we consider a brick-and-mortar store that uses its inventory to fulfil both in-store demand as well as online orders. In addition to deciding on replenishment quantities, such a retailer also has to decide how to ration its inventory across the channels. Practically, rationing inventory relates to storing part of the inventory in the backroom to satisfy online demand. The rationing process occurs regularly (e.g. daily) whereas inventory replenishment typically occurs less regular. To analyse this decision process, we model the rationing and ordering decisions as a Markov Decision Problem that maximises the expected profit. Based on the structure of the optimal policies, we determine heuristics that near-optimal results and scale well to retailers with many products.