Abstract
In this paper, we study the resolution of a permutation flow shop problem with sequence-independent setup time. The objective is to minimize the maximum of job completion time, also called the makespan. In this contribution, we propose three methods of resolution, a mixed-integer linear programming (MILP) model; two heuristics, the first based on Johnson’s rule and the second based on the NEH algorithm; and finally two metaheuristics, the iterative local search algorithm and the iterated greedy algorithm. A set of test problems is simulated numerically to validate the effectiveness of our resolution approaches. For relatively small-size problems, it has been revealed that the adapted NEH heuristic has the best performance than that of the Johnson-based heuristic. For the relatively medium and large problems, the comparative study between the two metaheuristics based on the exploration of the neighborhood shows that the iterated greedy algorithm records the best performances.
Highlights
We measure the deviation of the solution found from the optimal solution given by the mixed-integer linear programming (MILP), for relatively small instances, where CHmai x represents the solution found by the heuristic Hi and Cbmeasxt represents the value found by the MILP
We limit ourselves to such number of problems; our objective is to highlight the effectiveness of resolution heuristics and their relevance to solve this problem
We have conducted a comparative study between the exact mixed-integer linear programming method and two heuristics, one is based on Johnson’s rule, and the other is based on NEH algorithm
Summary
We propose these three classes for solving the flow shop with permutation problem (PFSP) under the constraint of sequence-independent setup time (SIST) In this case, the SIST constraint depends on the technology nature of the machine, as well as the means used to prepare it for the execution of a new job. Ese activities can be carried out by robots or manipulators independent of the processed jobs in the machine In this perspective, we present a study to contribute to the resolution of this problem which forms an essential manufacturing case to be encountered in the new industrial technology. We present a study to contribute to the resolution of this problem which forms an essential manufacturing case to be encountered in the new industrial technology We continue in this line of research and propose a model in MILP and two metaheuristics for solving the PFSP-SIST problem
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