three metaheuristic algorithms for solving the multi-item capacitated lot-sizing problem with product returns and remanufacturing

this paper proposes a new mixed integer programming model for multi-item capacitated lot-sizing problem with setup times, safety stock and demand shortages in closed-loop supply chains. the returned products from customers can either be disposed or be remanufactured to be sold as new ones again. due to the complexity of problem, three meta-heuristics algorithms named simulated annealing (sa) algorithm, vibration damping optimization (vdo) algorithm and harmony search (hs) algorithm have been used to solve this model. additionally, taguchi method is conducted to calibrate the parameter of the meta-heuristics and select the optimal levels of the algorithm’s performance influential factors. to verify and validate the efficiency of the proposed algorithms in terms of solution quality, the obtained results were compared with those obtained from lingo 8 software for a different problem. finally, computational results of these algorithms were compared and analyzed by producing and solving some small, medium and large-size test problems. the results confirmed the efficiency of the hs algorithm against the other methods.