Two parameter-tuned metaheuristic algorithms for the multi-level lot sizing and scheduling problem

This paper addresses the problem of lot sizing and scheduling problem for n-products and m-machines in flow shop environment where setups among machines are sequence-dependent and can be carried over. Many products must be produced under capacity constraints and allowing backorders. Since lot sizing and scheduling problems are well-known strongly NP-hard, much attention has been given to heuristics and metaheuristics methods. This paper presents two metaheuristics algorithms namely, Genetic Algorithm (GA) and Imperialist Competitive Algorithm (ICA). Moreover, Taguchi robust design methodology is employed to calibrate the parameters of the algorithms for different size problems. In addition, the parameter-tuned algorithms are compared against a presented lower bound on randomly generated problems. At the end, comprehensive numerical examples are presented to demonstrate the effectiveness of the proposed algorithms. The results showed that the performance of both GA and ICA are very promising and ICA outperforms GA statistically.