An Optimal Returned Policy for a Reverse Logistics Inventory Model with Backorders

Environmental responsibility plays a significant role in the firm’s agendas nowadays. In this paper, we address the environmental operations of reverse logistics. Here we developed an integrated supply chain model with coordinated production and remanufacturing due to time-dependent rates. To study the problem we consider the demand to be satisfied with newly manufactured produced and the remanufactured products, so there is no difference between manufactured and remanufactured items. The shortages are allowed and excess demand is backlogged as well. The returned items are collected from the end user to be remanufactured. Optimal expression is obtained for the acceptable returned quantity, maximum inventory level, production and remanufacturing scheduling period, and the total average cost. Illustrative examples, which explain the application of the theoretical results as well as their numerical verifications, are given. The sensitivity of these solutions to change in underling parameter values is also discussed.