On a bi-criteria flow shop scheduling problem under constraints of blocking and sequence dependent setup time

In this paper, we propose a bi-criteria optimization model for a flow shop scheduling problem with permutation, blocking and sequence dependent setup time. Indeed, these constraints are the most encountered in the industrial field, which demands high command flexibility. The objective is the minimization of two criteria, in our case the makespan and the total tardiness combined in a single objective function with a weighting coefficient for each criterion. To solve this problem, we propose a mixed integer linear programming method and a set of different metaheuristics. The suggested metaheuristics are; the genetic algorithm, the iterated greedy metaheuristic and the iterative local search algorithm. This last algorithm is proposed in two ways of exploration of the neighborhood. To verify the effectiveness of our resolution algorithms, a set of instances with n jobs and m machines is randomly generated from small instances to relatively large size ones. The analysis of the suggested simulation model allowed us to note that the iterative local search algorithm gives good results compared to the iterative greedy algorithm. Moreover, it was found that the weighting parameter plays an essential role in the problem decision making. However, it was established that it is difficult to find a good solution that minimizes both criteria at once, a suitable compromise will be necessary to be adopted using the weighting coefficient.