A heuristic based on quadratic approximation for dual sourcing problem with general lead times and supply capacity uncertainty

Abstract

We study a single-product, periodic-review dual sourcing inventory system with demand and supply uncertainty, where the replenishment lead times can be arbitrary and the expedited supplier has a shorter lead time with a higher unit price than the regular supplier, unmet demand is fully backlogged. Even for the general dual sourcing problem without supply risks, the optimal stochastic policy has been unknown for over 50 years and several simple heuristics have been proposed in the literature. Moreover, the consideration of supply uncertainty brings another challenge, where the objective functions characterized by the dynamic programming recursions are not convex in the ordering quantities. Fortunately, a powerful transformation skill is recently proposed to successfully address the problem above and shows that the value-to-go function is $L^{♮}$ convex. In this article, we design a Linear Programming greedy (LP-greedy) heuristic based on the quadratic approximation of $L^{♮}$ convex value-to-go function and convert the problem into a convex optimization problem during each period. In an extensive simulation study, two sets of test instances from the literature are employed to compare the performance of our LP-greedy heuristic with that of some well-known policies in dual sourcing system, including Tailored base-surge, Dual index, Best vector base-stock. In addition, to assess the effectiveness of our heuristic, we construct a lower bound to the exact system. The lower bound is based on an information-relaxation approach and involves a penalty function derived from the proposed heuristic. We show that our proposed LP-greedy heuristic performs better than other heuristics in the dual sourcing problem and it is nearly optimal (within 3%) for the majority of cases.

Keywords:

• Dual sourcing
• lead times
• supply capacity uncertainty
• inventory control
• heuristic

Acknowledgement

The authors thank Editors and anonymous reviewers for their valuable suggestions that helped to significantly improve the paper.

Additional information

Funding

This research was partly supported by the Natural Science Foundation of China (71802096, 71502026, 71871047, 71431004, 71872033), Humanity and Social Science Youth foundation of Ministry of Education of China (18YJC630223), China Postdoctoral Science Foundation (2018M633292), Major Projects of the National Social Science Foundation (16ZZD049), Postdoctoral Foundation of Jinan University, Research Center on Low-carbon Economy for Guangzhou Region and the Institute of Enterprise Development at Jinan University.

Notes on contributors

Wenbo Chen

Wenbo Chen is an associate professor at the International Business College and Institute of Supply Chain Analytics, Dongbei University of Finance and Economics. He received his Ph.D. in Management Science & Engineering from Shanghai Jiao Tong University in 2018. His research has focused on dynamic programming, inventory control and supply chain management.

Huixiao Yang

Huixiao Yang is a postdoctoral fellow at the Department of Business Administration and Research Center on Low-carbon Economy for Guangzhou Region & the Institute of Enterprise Development at Jinan University, and a visiting scholar at The Hong Kong University of Science and Technology. He received his Ph.D. in management science & engineering from Shanghai Jiao Tong University in 2017. His research has focused on supply chain management and inventory management.