A simple proof for optimality of (s,S) policies in infinite horizon inventory systems

A simple proof for optimality of (s,S) policies in infinite horizon inventory systems

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Article ID: iaor19932100
Country: Israel
Volume: 28
Issue: 4
Start Page Number: 802
End Page Number: 810
Publication Date: Dec 1991
Journal: Journal of Applied Probability
Authors:
Keywords: programming: dynamic
Abstract:

The classical proofs for the existence of a stationary (s,S) inventory policy that minimizes the total discounted or average cost over an infinite horizon are lengthy because they depend heavily on the optimality results for corresponding finite-horizon models. This note presents a simpler alternative. Since optimal stationary (s,S) policies are relatively simple to characterize, it is easy to construct a solution to the optimality equation which is satisfied by an (s,S) policy on an equivalent variant thereof. For the discounted model, the proof characterizes an (s,S) policy that is optimal for all initial inventory positions. This policy can be generated by a simple existing algorithm. For the average-cost model, the optimality proof is completed with some additional arguments, which are simple but novel, to overcome the normal difficulties encountered in models with unbounded one-step expected costs.

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