Fuzzy programming for multiobjective job shop scheduling with fuzzy processing time and fuzzy duedate through genetic algorithms

In this paper, by considering the imprecise or fuzzy nature of the data in real-world problems, job shop scheduling with fuzzy processing time and fuzzy duedate is introduced. On the basis of the agreement index of fuzzy duedate and fuzzy completion time, multiobjective fuzzy job shop scheduling problems are formulated as three-objective ones which not only maximize the minimum agreement index but also maximize the average agreement index and minimize the maximum fuzzy completion time. Having elicited the linear membership functions for the fuzzy goals of the decision maker, we adopt the fuzzy decision of Bellman and Zadeh. By incorporating the concept of similarity among individuals into the genetic algorithms using the Gannt chart, a genetic algorithm which is suitable for solving the formulated problems is proposed. As illustrative numerical examples, both 6×6 and 10×10 three-objective job shop scheduling problems with fuzzy duedate and fuzzy processing time are considered, and the feasibility and effectiveness of the proposed method are demonstrated by comparing with the simulated annealing method.