Supply coordination with penalty policy in the assembly system under uncertain delivery time

Successful supply chain management requires a cooperative integration between all the partners. We study an assembly system with two suppliers and one manufacturer under uncertain delivery time. The model is established and optimal solution is given under decentralized decision. We find the cost function of two suppliers is convex, and there exists the unique Nash equilibrium between the two suppliers. Then the optimal decision under centralized decision is analyzed, which is regarded as a benchmark for supply coordination. Additionally, the total cost of the assembly system is jointly convex in agreed delivery times. To achieve supply coordination we develop a penalty policy to coordinate the assembly system under uncertain delivery time. Finally we provide numerical and sensitivity analysis and the result show our penalty policy is reasonable and effective.