Joint supplier selection and order lot-sizing problem of remanufacturable items with price and transportation cost discounts

Sometimes due to the inefficient transportation and inspection methods or improper storage، some items sent to the buyer are damaged that they might be reused by some types of remanufacturing. However، the defective items are naturally purchased at a lower price than the perfect ones. In this paper، a mixed-integer linear programming model is proposed for the multi-period joint supplier selection and order lot-sizing problem concerning both the percentage of defective as well as the remanufacturable items in which besides the purchase price، the transportation costs are also discounted according to the number of departure vehicles. The order lot-size is optimized with respect to three factors including the purchase price discount، the capacity of supplier''s vehicles and the carrying costs. To assess the validity of the proposed model، a numerical example from the recent literature is solved through the GAMS modeling language and the sensitivity of the model parameters is analyzed. The results confirm that considering simultaneously the three proposed objectives، i. e.، - purchase costs، transportation and ordering costs، and carrying costs، could result in an decrement of almost 20% in the total costs. Furthermore، suppliers can achieve a more chance of selection by delivery of the smaller percentage of defective items.