Convergence Results and Approximations for Optimal (<i>s</i>, <i>S</i>) Policies

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 → ∞. 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 → ∞ to the minimal average cost.

• 저널Management Science · 20(11) · 1432–1438
• 토픽Supply Chain and Inventory Management · Management Information Systems
• DOI10.1287/mnsc.20.11.1432
• 저자Arie Hordijk, Henk Tijms