Technical Note—Constant-Order Policies for Lost-Sales Inventory Models with Random Supply Functions: Asymptotics and Heuristic

Jinzhi Bu (), Xiting Gong () and Dacheng Yao ()
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Jinzhi Bu: Institute for Data, Systems, and Society, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Xiting Gong: Department of Decision Sciences and Managerial Economics, CUHK Business School, Chinese University of Hong Kong, Shatin, New Territories, Hong Kong
Dacheng Yao: Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190 Beijing, China

Operations Research, 2019, vol. 68, issue 4, 1063-1073

Abstract: We consider an infinite-horizon lost-sales inventory model where the supply takes positive lead times and is a random function of the order quantity (e.g., random yield/capacity). The optimal policy for this model is computationally intractable, and no heuristic has been proposed in the literature. In this paper, we focus on a simple class of constant-order policies (COPs) that place the same order in every period regardless of the system state. Under some assumptions on the random supply function, we prove that the best COP is asymptotically optimal with large lead times, and the optimality gap converges to zero exponentially fast in the lead time. We also prove that if the mean supply capacity is less than the mean demand, then the best COP is also asymptotically optimal with large penalty costs; otherwise, the long-run average cost of the best COP asymptotically increases at the rate of the square root of the penalty cost. Further, we construct a simple heuristic COP and show that it performs very close to the best COP. Finally, we provide a numerical study to derive further insights into the performance of the best COP.

Keywords: inventory; lost sales; random supply function; constant-order policy; lead time; penalty cost (search for similar items in EconPapers)
Date: 2019
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