Coordinating supply chains with uncertain production cost by incomplete contracts

ABSTRACT

Production cost affects heavily supply chain coordination, but it is uncertain in many cases. We consider a supply chain consisting of a manufacturer and a retailer, where the unit production cost is uncertain when the firms sign a procurement contract. We derive the optimal decisions and profits for the centralised and decentralised cases. We show that production cost uncertainty exaggerates the supply chain’s incentive conflict, but may increase the expected profit in the centralised decision case. Then we design an incomplete contract, which sets a wholesale price and an order quantity in the first stage, which the firms can re-negotiate after the production cost is realised in the second stage. We prove that such an incomplete contract can lead to the first best outcome. We further consider the case with asymmetric cost information and show that the incomplete contract can also coordinate the supply chain. Furthermore, we discuss how the degree of contract incompleteness, re-negotiation freedom, and residual control rights affect the supply chain performance. The results reveal that the hold-up problem is prone to occur with improper contract incompleteness, re-negotiation freedom, and residual control rights, while the incomplete contract we propose can effectively avoid the problem.

KEYWORDS:

• Supply chain coordination
• uncertain production cost
• incomplete contracts
• re-negotiation
• Nash bargaining

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under (grant numbers 71661167009, and 71711530714), NSFC/RGC under grant number 3-RAA7, and Beijing Logistics Informatics Research Base. Cheng was also supported in part by The Hong Kong Polytechnic University under the Fung Yiu King-Wing Hang Bank Endowed Professorship in Business Administration.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by National Natural Science Foundation of China [grant number 71661167009,71711530714]; Fung Yiu King-Wing Hang Bank Endowed Professorship in Business Administration; Beijing Logistics Informatics Research Base; NSFC/RGC [grant number 3-RAA7].

Notes on contributors

Shouting Zhao

Shouting Zhao is a lecturer in Logistics School, Beijing Wuzi University. She received her Ph.D. in Logistics Management and Engineering from Beijing Jiaotong University. Her research is focused on supply chain coordination, contract design and e-commerce.

Juliang Zhang

Juliang Zhang is Professor in School of Economics and Management, Beijing Jiaotong University. He received his Ph.D. in Operations Research from Chinese Academy of Sciences. His areas of research include supply chain management, behaviour management, and inventory control.

T. C. E. Cheng

T. C. E. Cheng is Dean of Faculty of Business, and Professor of Management, at The Hong Kong Polytechnic University. He obtained a Ph.D. in Operations Research from the University of Cambridge. His research interests are in supply chain management, e-business and e-commerce, quality management, and scheduling science.