Fixed-interval order-up-to policies and myopic optimal warehouse stock allocation for one-warehouse multiple-retailer systems

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We consider a centralized two-level distribution system that consists of one warehouse and multiple retailers. The retailers are non-identical and face independent Poisson demand. The system adopts a fixed-interval order-up-to policy, in which the warehouse and retailers each order in a fixed interval to raise the echelon inventory position to a fixed base stock level. Shortages in the system are fully backlogged but transshipments between retailers are not allowed. The fixed-interval order-up-to policy has been studied in the literature under virtual allocation that reserves a unit of warehouse stock immediately after a unit of demand occurs. We consider an inventory control system that is different in two aspects. First, the warehouse implements myopic optimal allocation that allocates stock to retailers only at points of delivery to minimize system cost. Second, the warehouse adopts a non-stationary base stock policy to order stock for retailers according to their replenishment schedules. We develop methods to exactly evaluate and fully optimize this inventory control system. In a numerical study, we demonstrate that myopic optimal allocation reduces system cost by an average of 5.89% with a range from 1.45% to 10.13% as compared to virtual allocation. In addition, we develop an iterative procedure to alleviate the problem of dimensionality for myopic optimal warehouse stock allocation and a close-to-optimal heuristic solution that can significantly reduce computation.