Valid inequalities for the capacitated lot-sizing problem in a hybrid manufacturing and remanufacturing system

This paper investigates an existing model of capacitated lot-sizing problem in a hybrid manufacturing and remanufacturing system (HMRS) which is computationally hard to solve. Therefore, three classical families of valid inequalities are proposed to solve this problem. The efficiency of the proposed method are tested on numerical example available in the literature and compared with the existing method. The computational results show that the exact method provides better performance than the existing method in terms of LP gaps and the best feasible solution. Besides, the proposed method are also tested on a large number of test data sets, where the time-invariant cost parameters are considered. The findings demonstrate that these valid inequalities have significantly outperformed the original formulation with regard to LP gaps, solution times and the number of times the LP relaxation of a formulation found the integer optimal solution. Lastly, the concluding remarks and some future research directions are discussed.