Some Scheduling Problem with Fuzzy Resource Constraints

Abstract

Resource constrained scheduling problems cover a wide range of problems which captures many variations of the model. But in realistic situations, many uncertainties exist and the fuzzy methodology is employed to deal with situations that are expressed in vague or ambiguous terms. In this paper, the available resource limit of each job is flexible as we propose the following bi criteria scheduling problem: There are n jobs to be processed on one of identical parallel machines. Each job has unit processing time and its processing requires the number of resource types. Resource requirement of each job for each type of resource is fixed but available limit of each type of resource to be used by job processing in each unit time interval is flexible. That is, fuzzy limit with membership function describing non-decreasing satisfaction degree about setting limit quantity. Under above setting, maximum completion time is to be minimized and minimal satisfaction degree about upper limits of resource quantity of all types to be maximized. But usually we cannot optimize two objectives at a time. So we seek non-dominated schedule after defining dominance between schedules by proposing an efficient algorithm.