Partial Backorder Inventory System: Asymptotic Optimality and Demand Learning

45 Pages Posted: 15 Apr 2024

See all articles by Zhaoxuan Wei

Zhaoxuan Wei

Institute of Operations Research and Analytics, NUS

Andrew Lim

National University of Singapore (NUS) - Department of Decision Sciences; National University of Singapore (NUS) - Department of Finance; National University of Singapore (NUS) - Institute for Operations Research and Analytics

Hanqin Zhang

National University of Singapore (NUS) - NUS Business School

Date Written: March 26, 2024

Abstract

We develop a stochastic inventory system which accounts for the limited patience of backlogged customers. While limited patience is a feature that is closer to the nature of unmet demand, our model also unifies the classic backlogging and lost-sales inventory systems which are special cases of the one we propose. We establish the uniform (asymptotic) optimality of the base-stock policy when both demand and patience distributions are known. When the backlogged demands become unobservable, we introduce a novel policy family that operates without backlogged demands information, and prove that it can approach the cost efficiency of the optimal policy in the system when the demand and patience distributions are known. Finally, we consider an online inventory control problem in which backlogged demand is unobservable and demand and patience distributions are also not known, and develop a UCB-type algorithm that yields a near-optimal policy. The regret bounds given by the algorithm are provably tight within the planning horizon, and are comparable to the state-of-the-art results in the literature, even in the face of partial and biased observations and weaker system ergodicity.

Keywords: partial backorder, inventory control, hidden backorder, censored demand, online learning

JEL Classification: C44, C61

Suggested Citation

Wei, Zhaoxuan and Lim, Andrew E. B. and Zhang, Hanqin, Partial Backorder Inventory System: Asymptotic Optimality and Demand Learning (March 26, 2024). Available at SSRN: https://ssrn.com/abstract=4772763 or http://dx.doi.org/10.2139/ssrn.4772763

Zhaoxuan Wei (Contact Author)

Institute of Operations Research and Analytics, NUS ( email )

3 Research Link
117602
Singapore

Andrew E. B. Lim

National University of Singapore (NUS) - Department of Decision Sciences ( email )

NUS Business School
Mochtar Riady Building, 15 Kent Ridge
Singapore, 119245
Singapore

National University of Singapore (NUS) - Department of Finance ( email )

Mochtar Riady Building
15 Kent Ridge Drive
Singapore, 119245
Singapore

National University of Singapore (NUS) - Institute for Operations Research and Analytics ( email )

Singapore

Hanqin Zhang

National University of Singapore (NUS) - NUS Business School ( email )

1 Business Link
Singapore, 117592
Singapore

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