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

Forthcoming, Operations Research

44 Pages Posted: 2 Nov 2017 Last revised: 27 Nov 2019

See all articles by Jinzhi Bu

Jinzhi Bu

Massachusetts Institute of Technology (MIT)

Xiting Gong

The Chinese University of Hong Kong

Dacheng Yao

Academy of Mathematics and Systems Science, Chinese Academy of Sciences

Date Written: November 26, 2019

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 (COP) 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 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

Suggested Citation

Bu, Jinzhi and Gong, Xiting and Yao, Dacheng, Constant-Order Policies for Lost-Sales Inventory Models with Random Supply Functions: Asymptotics and Heuristic (November 26, 2019). Forthcoming, Operations Research. Available at SSRN: https://ssrn.com/abstract=3063730 or http://dx.doi.org/10.2139/ssrn.3063730

Jinzhi Bu

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

Xiting Gong (Contact Author)

The Chinese University of Hong Kong ( email )

Room 906, 9/F, Cheng Yu Tung Building
12 Chak Cheung Street, Shatin, N.T.
Hong Kong
China

HOME PAGE: http://www.bschool.cuhk.edu.hk/staff/gong-xiting/

Dacheng Yao

Academy of Mathematics and Systems Science, Chinese Academy of Sciences ( email )

No. 55, Zhong Guan Cun East Road
Haidian District
Beijing, Beijing 100190
China

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