Annals of Operations Research

, Volume 271, Issue 2, pp 599–617 | Cite as

Mitigating supply risk: an approach with quantity flexibility procurement

  • Bo HeEmail author
  • Yange Yang
Original Research


This paper considers a buyer that procures from its major supplier whose production is subject to random yield risk. To mitigate supply risk, the buyer can procure from another reliable supplier who provides quantity flexibility (QF) contract. Under both deterministic and stochastic demand, we study the buyer’s optimal procurement decisions. We analyze the structural properties of optimal solutions and identify the conditions under which the quantity flexibility procurement policy should be used. We also examine the effect of supply risk, flexibility, wholesale price and demand risk on the procurement decisions. We find that the higher supply risk and demand risk reduce the buyer’s profit but have different impact on the buyer’s order policy. For the QF supplier, it may not obtain more orders by providing larger flexibility to the buyer, on the contrary, doing this may benefit the risky supplier. For the QF supplier or risky supplier, given its competitor’s wholesale price, it can increase its order share by lower wholesale price.


Random yield Dual-sourcing Quantity flexibility Supply chain 



We appreciate for the referee’s comments on this paper, which significantly improved this paper. The authors acknowledge Xia Zhang for her assistance with the computational work in this paper. This work is supported by the National Natural Science Foundation of China (Grant No. 71572021).


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Economics and Business AdministrationChongqing UniversityChongqingChina
  2. 2.China Coal Technology Engineering Group Chongqing Research InstituteChongqingChina

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