In the conventional scheduling problem, the parameters such as the processing time for each job and due dates are usually assumed to be known exactly, but in many real-world applications, these parameters may very dynamically due to human factors or operating faults. During the last decade, several works on scheduling problems have used a fuzzy approach including either uncertain or imprecise data. A fuzzy logic based tool for multi-objective Hybrid Flow-shop Scheduling with Multi-processor Tasks (HFSMT) problem is presented in this paper. In this study, HFSMT problems with a fuzzy processing time and a fuzzy due date are formulated, taking Oğuz and Ercan’s benchmark problems in the literature into account. Fuzzy HFSMT problems are formulated by three-objectives: the first is to maximize the minimum agreement index and the second is to maximize the average agreement index, and the third is to minimize the maximum fuzzy completion time. An efficient genetic algorithm(GA) is proposed to solve the formulated fuzzy HFSMT problems. The feasibility and effectiveness of the proposed method are demonstrated by comparing it with the simulated annealing (SA) algorithm in the literature.
Lagrangian relaxation approach to minimize makespan for hybrid flow shop scheduling problem with unrelated parallel machines
