Chance-constrained approach for decentralized supply chain network under uncertain cost

Shuai Huang; Youwu Lin; Jing Zhang; Pei Wang; Shuai Huang; Youwu Lin; Jing Zhang; Pei Wang

doi:10.3934/math.2023616

AIMS Mathematics

2023, Volume 8, Issue 5: 12217-12238. doi: 10.3934/math.2023616

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Research article

Chance-constrained approach for decentralized supply chain network under uncertain cost

Shuai Huang ¹,
Youwu Lin ^{2,3
,
,},
Jing Zhang ⁴,
Pei Wang ^{5
,
,}

1.
School of Management, Guangdong University of Technology, Guangzhou 510520, China
2.
School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin 541004, China
3.
Center for Applied Mathematics of Guangxi (GUET), Guilin 541004, China
4.
Experimental Teaching Center, Guangdong University of Foreign Studies, Guangzhou 510006, China
5.
School of Business, Guangdong University of Foreign Studies, Guangzhou 510006, China

Received: 16 February 2023 Revised: 11 March 2023 Accepted: 13 March 2023 Published: 23 March 2023
MSC : 90C15, 90C33

A decentralized supply chain network under uncertain cost is studied to obtain the optimal decisions of the enterprises in a situation in which the cost is uncertain. The supply chain network members adopt a chance-constrained approach to make decisions. The second-order cone-constrained variational inequality problem is used to construct the chance-constrained supply chain network equilibrium model. Then, the existence and uniqueness properties of the proposed equilibrium model are discussed under some mild assumptions. For the discontinuous functions in the feasible region of the model, the proposed model is converted to a second-order cone complementarity problem. The numerical results show that the uncertainty and risk attitude of retailers and manufacturers have different effects on supply chain network members. When the risk attitude is high, a small change in the risk attitude will significantly change all decisions of supply chain members. If the supply chain member is affected by the uncertainty positively, its profit will increase as its risk attitude increases. Moreover, it is appropriate to adopt a chance-constrained approach when the supply chain members can estimate the distributions of the competitor's strategies.
- decentralized supply chain network,
- variational inequality problem,
- uncertain cost,
- chance-constrained approach,
- existence,
- uniqueness
Citation: Shuai Huang, Youwu Lin, Jing Zhang, Pei Wang. Chance-constrained approach for decentralized supply chain network under uncertain cost[J]. AIMS Mathematics, 2023, 8(5): 12217-12238. doi: 10.3934/math.2023616

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Abstract

A decentralized supply chain network under uncertain cost is studied to obtain the optimal decisions of the enterprises in a situation in which the cost is uncertain. The supply chain network members adopt a chance-constrained approach to make decisions. The second-order cone-constrained variational inequality problem is used to construct the chance-constrained supply chain network equilibrium model. Then, the existence and uniqueness properties of the proposed equilibrium model are discussed under some mild assumptions. For the discontinuous functions in the feasible region of the model, the proposed model is converted to a second-order cone complementarity problem. The numerical results show that the uncertainty and risk attitude of retailers and manufacturers have different effects on supply chain network members. When the risk attitude is high, a small change in the risk attitude will significantly change all decisions of supply chain members. If the supply chain member is affected by the uncertainty positively, its profit will increase as its risk attitude increases. Moreover, it is appropriate to adopt a chance-constrained approach when the supply chain members can estimate the distributions of the competitor's strategies.

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