Consider a central depot that supplies several locations experiencing random demands. Periodically, the depot may place an order for exogenous supply. Orders arrive after a fixed leadtime, and are then allocated among the several locations. Each allocation reaches its destination after a further delay. We consider the special case where the penalty-cost/holding-cost ratio is constant over the locations. Several approaches are given to approximate the dynamic program describing the problem. Each approach provides both a near-optimal order policy and an approximation of the optimal cost of the original problem. In addition, simple but effective allocation policies are discussed.
Federgruen, Awi, and Paul Zipkin. "Allocation policies and cost approximations for multilocation inventory systems." Naval Research Logistics 31, no. 1 (1984): 97-129.
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