Mathematical programming and three metaheuristic algorithms for a bi-objective supply chain scheduling problem

In this study, a bi-objective optimization problem for a supply chain with different transportation modes is addressed. The first objective function is minimizing costs imposed by production, batching, due date assignment and transportation. The second one is minimizing inventory and tardiness costs. Also, a heuristic rule is developed to choose non-dominated transportation modes. Three metaheuristic algorithms including multi-objective particle swarm optimization (MOPSO), non-dominated sorting genetic algorithm (NSGA-II) and hybrid NSGA-II (HNSGA-II) are customized to solve the problem. In addition, a theoretical improvement in the non-dominated sorting procedure called improved efficient non-dominated sorting (IENS) is proposed. Computational tests are used for comparing and evaluating the proposed methods and algorithms. The results show that IENS reduces running time compared to the modern method of non-dominated sorting, the efficient non-dominated sorting method, and this reduction is statistically significant. Also, the HNSGA-II has an average but robust performance compared to the other two algorithms.