Optimal Policies for a Dual-Sourcing Inventory Problem with Endogenous Stochastic Leadtimes

Operations Research, 2017, 65(2):379-395

47 Pages Posted: 25 Apr 2016 Last revised: 8 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

Paul Zipkin

Duke University - Fuqua School of Business

Date Written: April 24, 2016

Abstract

We consider a single-product, two-source inventory system with Poisson demand and backlogging. Inventory can be replenished through a normal supply source, which consists of a two-stage tandem queue with exponential production time at each stage. We can also place an emergency order by skipping the first stage, for a fee. There is no fixed order cost. There are linear order, holding and backorder costs. Through a new approach, we obtain optimal ordering policies for the discounted or long-run average cost, and also characterize near-optimal heuristic policies. The approach consists of four steps. The first step is to establish an equivalent system, in the sense that it has the same optimal policy as the original system. The second step is to construct a tandem queueing system, where costs are charged in accord with the equivalent system's cost structure. The third step derives an optimal control of the service rate at each server so as to minimize the tandem queue's system-wide cost. The fourth and final step is to translate the queue's optimal policy to an optimal policy for the equivalent system and hence the original system.

Keywords: dual-source, stochastic lead time, optimality equation, queueing system

Suggested Citation

Song, Jing-Sheng Jeannette and Xiao, Li and Zhang, Hanqin and Zipkin, Paul, Optimal Policies for a Dual-Sourcing Inventory Problem with Endogenous Stochastic Leadtimes (April 24, 2016). Operations Research, 2017, 65(2):379-395, Available at SSRN: https://ssrn.com/abstract=2769658 or http://dx.doi.org/10.2139/ssrn.2769658

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

Paul Zipkin

Duke University - Fuqua School of Business ( email )

Box 90120
Durham, NC 27708-0120
United States

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