Problems with Fuzzy Allowable Time Constraints between Two Machines Scheduling

Abstract

We have already introduced many fuzzy concepts to scheduling problems and discussed so called fuzzy scheduling problems. In This paper we introduce fuzzy allowable time concept newly to two identical machines and fuzzy ready times and deadlines are associated to each job, i.e., membership representing a satisfaction degree of start times and completion time are considered to each job and minimal one of them is to be maximized. Further among jobs ,there exists a 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 of both minimal degree at a time if possible ,but usually there exists no schedule maximizing both of them and so we seek no dominated Schedules. In real world scheduling Problems, priorities of jobs may change over time. A less important job today may be of high importance tomorrow and vice-versa.