Solving flow shop problem with permutation and sequence independent setup time

Abstract

In this paper, we study one of the frequently encountered issues in manufacturing industry, that is the flow shop scheduling problem. We present a mixed-integer linear programming model to solve n job and m machine flow shop process with permutation and sequence independent setup time. The objective is to minimize the maximum completion time for all jobs, called makespan. In addition to the mixed-integer linear programming model, two other algorithms are used in this investigation. The first one consists of the Johnson’s rule which will be adapted to solve more than two-machines flow shop problems. The second one is based on the NEH heurstic. Simulations are conducted for different instances by varying the number of jobs and machines. The proposed algorithms are compared to the optimal solution given by the mixed-integer linear programming model. It was revealed that the adapted NEH heuristic presents best performance than the heuristic based on Johnson’s rule.