Convergence Results and Approximations for Optimal (s, S) Policies

Arie Hordijk and Henk Tijms
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Arie Hordijk: Mathematisch Centrum, Amsterdam, Holland

Management Science, 1974, vol. 20, issue 11, 1432-1438

Abstract: In this paper we consider the dynamic inventory model with a discrete demand and no discounting. We verify a conjecture of Iglehart about the asymptotic behaviour of the minimal total expected cost. To do this, we give for the denumerable state dynamic programming model a number of conditions under which the minimal total expected cost for the n-stage model minus n times the minimal average cost has a finite limit as n -> \infty . For a positive demand distribution we establish a turnpike theorem which states that for all n sufficiently large the optimal n-stage policy (s n , S n ) is average cost optimal. Further, we show that the computation of the (s n , S n ) policies supplies monotonic upper and lower bounds on the minimal average cost. Also, the average cost of the (s n , S n ) policy lies between the corresponding bounds. For a positive demand distribution these bounds converge as n -> \infty to the minimal average cost.

Date: 1974
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