An integrated supply chain model for deteriorating items considering delay in payments, imperfect quality and inspection errors under inflationary conditions

In this article, an integrated production-distribution model is presented for a manufacturer and retailer supply chain under inflationary conditions, permissible delay in payments, deterioration, imperfect production process and inspection errors. We assume that the first-stage inspection of the manufacturer is not perfect and makes inspection errors of Type 1 and Type 2. The second-stage inspection of the manufacturer is at the end of production period without inspection errors. Also, the demand is linear function of time. Once the retailer receives the lot, a 100% screening process of the lot is conducted without inspection errors, and the screening process and demand proceed simultaneously. The main objective is to determine the optimal inspection time and the optimal number of cycle such that the present value of the total cost is minimized. Finally, a numerical example and sensitivity analyses are provided to illustrate the proposed model using a proper algorithm.