Two-machines Scheduling Problem with Fuzzy Allowable Time Constraint

We have already introduced many fuzzy concepts to scheduling problem and discussed so called fuzzy scheduling problems. In this paper, we introduce fuzzy allowable time concept newly to two identical machine problem, which is a fuzzy version of M. R. Garey and D. S. Johnson. That is, there are two identical machines and fuzzy ready times and deadlines are associated to each job, i.e., membership function representing a satisfaction degree of start times and completion times are considered to each job and minimal one of them is to be maximized. Further among jobs, there exists fuzzy precedence relation, which is a fuzzy relation with membership function representing satisfaction degree of precedence order of each job pair and again minimal one of them is to be maximized. The aim is to maximize both minimal degrees at a time if possible, but usually there exists no schedule maximizing both of them, and so we seek nondominated schedules.