Optimal Dual-Sourcing Policies for Backlogging and Lost-sales Inventory Systems with Uncertain Lead Times and Order Tracking

68 Pages Posted: 10 Aug 2022

See all articles by Jing-Sheng Jeannette Song

Jing-Sheng Jeannette Song

Duke University - Fuqua School of Business

Li Xiao

School of Business, Southern University of Science and Technology, China

Hanqin Zhang

National University of Singapore (NUS) - NUS Business School

Date Written: August 7, 2022

Abstract

This paper studies how companies use order-tracking information to more effectively execute their dual-sourcing strategies. We consider dual-sourcing inventory systems under either backlogging or lost-sales assumptions. The normal source consists of a two-stage tandem queue with Erlang distributed processing times at each stage while the emergence source skips the first stage. We show the optimal policy is characterized by two constant thresholds and one emergency-source-state-dependent switching curve. To derive this result, we first reduce the state space by a state transformation; then construct an auxiliary system so that the resulting dynamic program becomes tractable, and show its value function satisfies supermodularity, convexity, and the exchange axiom property that appears to be new to inventory research; finally use a sample-path analysis to show the optimal policy derived from the auxiliary system is also optimal for the original system under a certain condition. Using partial or no order-tracking information, several heuristic policies are developed when the condition fails. We next assess the value of order-tracking information and demonstrate its significant value through numerical studies. Also, the value of full information is more substantial in the backlogging setting than in the lost-sales setting.

Keywords: dual-source, inventory policy, dynamic programming, tandem queue, Erlang distribution

Suggested Citation

Song, Jing-Sheng Jeannette and Xiao, Li and Zhang, Hanqin, Optimal Dual-Sourcing Policies for Backlogging and Lost-sales Inventory Systems with Uncertain Lead Times and Order Tracking (August 7, 2022). Available at SSRN: https://ssrn.com/abstract=4183683 or http://dx.doi.org/10.2139/ssrn.4183683

Jing-Sheng Jeannette Song

Duke University - Fuqua School of Business ( email )

100 Fuqua Drive
Duke University
Durham, NC 27708
United States

HOME PAGE: http://people.duke.edu/~jssong/

Li Xiao (Contact Author)

School of Business, Southern University of Science and Technology, China ( email )

Hanqin Zhang

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

1 Business Link
Singapore, 117592
Singapore

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