Minimizing the total tardiness and the total carbon emissions in the permutation flow shop scheduling problem

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.