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

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.