A linguistic approach to non-identical parallel processor scheduling with fuzzy processing times

Abstract

This study presents an application of non-identical parallel processor scheduling under uncertain operation times. We have been motivated from a real case scheduling problem that contains some uncommon welding operations to be processed by workers in an automotive subcontract company. Here each operator may weld each job but in different processing times depending on learning effect because of operator’s ability and experience, and batch sizes. To determine the crisp operation times in such a fuzzy environment, a linguistic reasoning approach (with a 75-“If- Then” rules) considering the learning effect is proposed in the study. Since the fuzzy linguistic approach allows the representation of expert information more directly and adequately, it can be more possible to make realistic schedules under uncertainty. With the objective to balance the workload among all operators, the longest processing time heuristic algorithm is been used and measured average makespan. For evaluating the effectiveness of this approach, it is compared with the scheduling method that use the random operation times generated from a uniform distribution. Results showed that the proposed fuzzy linguistic scheduling approach has balanced the workload of operators with a standard deviation of 0.37 and improved the Cmax value as 16%. A general conclusion can be drawn the proposed approach is able to generate realistic schedules and especially useful to solve non-identical parallel processor scheduling problem under uncertainty. An important contribution of this study is that Mamdani inference method with learning effect is the first time used to obtain the crisp processing times of non-identical processors by the help of a rule base with expert knowledge.