In this study, the problem of scheduling jobs on unrelated parallel machines with sequence-dependent setup times under due-date constraints is considered to minimize the total cost of tardiness and earliness. A new mathematical model is presented for considered problem and due to the complexity of the problem; an integrated meta-heuristic algorithm is designed to solve the problem. The proposed algorithm consists of genetic algorithm as the basic algorithm and simulated annealing method as local search procedure that follows the genetic algorithm to improve the quality of solutions. The performance of the proposed algorithm is evaluated by solving a set of test problems. The results show that the proposed integrated algorithm is effective.
This paper deals with unrelated parallel machines scheduling problem with sequence dependent setup times under fully fuzzy environment to minimize total weighted fuzzy earliness and tardiness penalties, which belongs to NP-hard class. Due to inherent uncertainty in Processing times, setup times and due dates of jobs, they are considered here with triangular and trapezoidal fuzzy numbers in order to take into account the unpredictability of parameters in practical settings. Although this study is not the first one to study on fuzzy parallel machines scheduling problem, it advances this area of research in three fields: (1) it selects a fuzzy environment to cover the whole area of the considered problem not just part of it, and also, it chooses an appropriate fuzzy method based on an in-depth investigation of the effect of spread of fuzziness on the variables; (2) It introduces a mathematical programming model for the addressed problem as an exact method; and (3) due to NP-hardness of the problem, it develops an existing algorithm in the literature for the considered problem through extensive simulated experiments and statistical tests on the same benchmark problem test by proposing a genetic algorithm (GA) and a modified simulated annealing (SA) methods to solve this hard combinatorial optimization problem. The result shows the superiority of our modified SA.
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