Optimal ordering policies for periodic-review systems with a refined intra-cycle time scale

Optimal ordering policies for periodic-review systems with a refined intra-cycle time scale

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Article ID: iaor20084269
Country: Netherlands
Volume: 177
Issue: 2
Start Page Number: 872
End Page Number: 881
Publication Date: Mar 2007
Journal: European Journal of Operational Research
Authors:
Keywords: programming: dynamic
Abstract:

Chiang recently proposed a dynamic programming model for periodic-review systems in which a replenishment cycle consists of a number of small periods (each of identical but arbitrary length) and holding and shortage costs are charged based on the ending inventory of small periods. The current paper presents an alternative (and concise) dynamic programming model. Moreover, we allow the possibility of a positive fixed cost of ordering. The optimal policy is of the familiar (s, S) type because of the convexity of the one-cycle cost function. As in the periodic-review inventory literature, we extend this result to the lost-sales periodic problem with zero lead-time. Computation shows that the long-run average cost is rather insensitive to the choice of the period length. In addition, we show how the proposed model is modified to handle the backorder problem where shortage is charged on a per-unit basis irrespective of its duration. Finally, we also investigate the lost-sales problem with positive lead-time, and provide some computational results.

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