Consider the expected profit maximizing inventory placement problem in an N-stage, supply chain facing a stochastic demand for a single planning period for a specialty item with a very short selling season. Each stage is a stocking point holding some form of inventory (e.g., raw materials, subassemblies, product returns or finished products) that after a suitable transformation can satisfy customer demand. Stocking decisions are made before demand occurs. Because of delays, only a known fraction of demand at a stage will wait for shipments. After characterizing an optimal solution, we propose an algorithm for its computation. For the zero fixed cost case, the computations can be done on a spreadsheet given normal demands. For the nonnegative fixed cost case, we develop an effective branch and bound algorithm.
