In this paper, we consider the permutation flow shop scheduling problem and aim to minimize the total tardiness as well as the total carbon emissions. We present a formulation of the problem through a mixed-integer programming model. To solve the problem, we develop a multi-objective decomposition-based heuristic (MODBH) algorithm, working based on job insertion, as well as a multi-objective VNS algorithm. Furthermore, a multi-objective iterated greedy algorithm is utilized to validate the efficiency of the developed methods. Using extensive computational experiments, we indicate that the MODBH algorithm has a significant superiority to the other developed solution approaches. Furthermore, the multi-objective VNS algorithm shows better performance than the multi-objective iterated greedy algorithm.

Keywords