Supply chain coordination and risk sharing with considering internal and external quality fault and return policy

This paper studies a supply chain quality coordination and risk-sharing problem. We find when the supply chain is coordinated under internal and external quality fault existing, it can be obtained the optimal profit, order quantity and risk sharing of the supply chain parties for each. And when the supply chain is coordinated and the item has not been sold, the supplier should allow the seller return his order item with wholesale price. The total optimal expected profit is smaller when internal and external quality fault is appeared but the risking share is larger. The risk sharing is positively correlated with the fault rate but is non-correlated with the return policy. The risk sharing of the supply chain is also positively correlated with the wholesale price, retail price and the seller is not zero risk sharing
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