This research presents three profit sharing models of a key item in a two-echelon supply chain production. The first model maximizes the supplier’s profit while allowing the producer to take his own optimal inspection sampling policy. The second model is developed exclusively to the supplier’s advantage. The last model adopts a collaborative strategy that permits both parties to negotiate an inspection policy, and aims to maximize total profit. In this two-echelon supply chain, the supplier determines the item quality by selecting a quality level of process setup, as well as the cycle time to reset this quality level. There is a tradeoff between total setup cost and the resulting quality of the key items. The interrupted geometric distribution is used to describe the item manufacturing quality for various cycle time setups. Furthermore, it is assumed that the inspection will not be perfect. The supplier must bear the loss from its downstream producer’s type I inspection error, and the producer will in turn undertake the risk of selling flawed products to customers. The application of the proposed models is illustrated via an example with interrupted geometric distributions
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