Optimizing production and inventory decisions in a supply chain with lot size, production rate and lead time interactions

Lead time decision involves interactions both supply side and demand side in a supply chain with different interests. A Stackelberg game framework is presented in this paper to model the interactions between a manufacturer and a retailer, in which the lead time demand is distribution free and only the mean and variance are known. Then, a minimax approach is applied to tackle the model, and an efficient iterative algorithm has been developed to solve the model. The numerical examples are employed to illustrate the solution procedure and analyze the double marginalization in the decentralized decision scenario. In addition, a transfer payment contract is proposed to coordinate the supply chain, through which the decentralized Stackelberg game decision can a results show that the contract can flexibly allocate the system's cost between the two sides of the supply chain, and both sides in the supply chain become strictly better off through the collaboration.

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