Applied Mathematics & Information Sciences

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A supply chain of one producer and one retailer is considered in this paper. The production process produces items in lots with random fraction defective to satisfy the retailer with a deterministic demand. When a lot is completed, a random sample is drawn to sentence the produced lot. If the number of defective items in the sample is less than or equal to the specified acceptance number, the lot is accepted and sold at a regular price. On the other hand, if the lot is rejected, it is sold at a reduced price. The retailer is protected by a limit on the incoming quality. That is, the retailer dictates a certain Acceptable Quality Level, which must be respected by the producer. The objective of the model is to determine the optimal production run, sample size, and acceptance number simultaneously, to maximize the expected total profit made by the producer. The decision variables in this model are the production lot size, the sample size, and the acceptance number.