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In this model, we establish an inventory model to determine the optimal inventory replenishment scheme for the economic production quantity (EPQ) model for imperfect, deteriorating items with sales return service under multiple production and rework setup. In one cycle, production process can produces the products in m production setups and reworks the defective items in one rework setup. The common assumptions in this model are that all units produced are not perfect and shortages are not allowed. The defective/scrap items are produced during the m production setups. The defective items are of two types which are recoverable items and irrecoverable items. The recoverable items are converted into good quality items in rework process and irrecoverable items are considered as scrap (disposable) items. A portion of defective items produced are not successfully screened out internally during the m production setups and passed on to customer, thereby causing defect sales returns and reverse logistic from customers back to the manufacturer. The proposed model is demonstrated numerically and the sensitivity analysis is also carried out to study the behavior of the inventory model.

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The intention of the article is to present an imperfect production process inventory model for deteriorating items where the demand rate depends on advertising cost and price. In this research, an industrial manager produces products in a determined  imperfect replenishment cycles and also in each replenishment cycle, the manufacturer produces items in three imperfect production cycles and one rework setup, (M/P3/R1)  inventory system. Rework is one of the important issues in reverse logistics and green supply chain, because it reduces waste, environmental harms and also the overall inventory cost significantly. Here shortages are  considered under completely backlogging strategy. The major objective is to establish the optimum  advertising cost, optimum cycle time, optimum lot size  quantity and optimum selling price with the intend of minimizing the total inventory cost. A numerical example and a sensitivity analysis are established to validate the theoretical results, and managerial insights for industry managers are provided.