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This paper develops an integrated fuzzy two-layer supply chain for manufacturers and retailers with defective and non-defective types of products. The manufacturer produces up to a specific time, including both faulty and non-defective items, and post-screening only the non-defective item sends to the retailer. The strategy of the retailer is to do the screening of items received from the manufacturer. Subsequently, the perfect quality items use to fulfill the demand of the customer, and the defective items are reworked. The retailer considers that customer demand is time and reliability dependent. The proposed supply chain considers probabilistic deterioration for the manufacturer and retailers. The optimum solution of the given model is evaluated for both the cases of crisp and fuzzy environments on the strategies such as production rate, unit production cost, idle time, screening, rework, etc. Managerial insights and the effect of parameters on the optimal inventory under fuzziness are presented.

Two-echelon imperfect production supply chain with probabilistic deterioration rework and reliability under fuzziness