Dynamic programming algorithms for multi-stage safety stock optimization

Dynamic programming algorithms for multi-stage safety stock optimization

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Article ID: iaor19982601
Country: Germany
Volume: 19
Issue: 4
Start Page Number: 261
End Page Number: 271
Publication Date: Jan 1997
Journal: OR Spektrum
Authors:
Keywords: programming: dynamic
Abstract:

The task of multi-stage safety stock optimization is very complex. Therefore, simplifying models with specific assumptions are considered. In this paper, the inventory system is controlled by a base-stock policy where each stockpoint of the inventory system follows a periodically reviewed order-up-to policy. End item demands are assumed to be normally distributed. To reduce the occurrences or size and duration of internal and external stockouts, appropriate service level constraints are specified for all items. Applying such a control policy within systems of serial, convergent or divergent structure, solution properties hold which reduce the solution set to a limited number of cut-levels. Dynamic programming allows us to evaluate the relevant alternatives with little computational effort. For the serial system, both a forward and a backward recursion with different types of service levels are presented and extended to a backward algorithm for divergent and a forward algorithm for convergent systems. Bounds for the complexity of the algorithms are discussed and numerical examples are presented to demonstrate differences in size and allocation of safety stocks according to the prespecified type of service level.

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