analyzing and optimization a two echelon supply chain with uncertainly returned product

high congestion of returned product at remanufacturing facility causes substantial delays and consequently remarketing value losses for time-sensitive and high-tech products with short life cycles, such as electronic equipments. at the remanufacturing site the returned product are inspected and classified according to their quality and processing time in one of the two classes: class 1 being admitted to the remanufacturing process and class 2 jobs that are rejected. in this paper, we provide a two-echelon supply chain; including inventory system and remanufacturing system. we propose an analytical queuing model for the decisions of the acceptance of return products and the maximum capacity of inventory system. the supply chain is modeled as queuing system and analyzed with matrix geometric method. the maximum capacity of inventory system (s) and admission decision value (k) calculated as the total expected discounted profit are maximized.