The single-item capacitated lot-sizing problem with backlogging in closed-loop supply chain

This paper proposes a mixed integer programming model for single-item capacitated lot-sizing problem with setup times, safety stock, demand shortages, outsourcing in closed-loop supply chain. the returned products from customers can either be disposed or be remanufactured to be sold as new ones again. The model of this problem is NP-hard and to solve it to verify and validate the efficiency of the SA algorithm, the results are compared with those of the Lingo 8 software. Results suggest that the SA algorithms have good ability of solving the problem.