Joint Initial Stocking and Transshipment—Asymptotics and Bounds
David D. Yao, Sean X. Zhou, Weifen Zhuang
Production and Operations Management · 2016 · Volume 25 · Issue 2
Abstract
A common problem faced by many firms in their supply chains can be abstracted as follows. Periodically, or at the beginning of some selling season, the firm needs to distribute finished goods to a set of stocking locations, which, in turn, supply customer demands. Over the selling season, if and when there is a supply-demand mismatch somewhere, a re-distribution or transshipment will be needed. Hence, there are two decisions involved: the one-time stocking decision at the beginning of the season and the supply/transshipment decision throughout the season. Applying a stochastic dynamic programming formulation to a two-location model with compound Poisson demand processes, we identify the optimal supply/transshipment policy and show that the optimal initial stocking quantities can be obtained via maximizing a concave function whereas the contribution of transshipment is of order square-root-ofT. Hence, in the context of high-volume, fast-moving products, the initial stocking quantity decision is a much more important contributor to the overall profit. The bounds also lead to a heuristic policy, which exhibits excellent performance in our numerical study; and we further prove both the bounds and the heuristic policy are asymptotically optimal whenTapproaches infinity. Extension to multiple locations is also discussed.
Keywords
inventory, transshipment, stochastic dynamic programming, bounds, asymptotic optimality
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