Specially Structured Flow Shop Scheduling Models with Processing Times as Trapezoidal Fuzzy Numbers to Optimize Waiting Time of Jobs

Abstract

This paper presents a two-stage flow shop fuzzy scheduling approach under uncertain situations. The processing times are demonstrated by the trapezoidal membership function. An exact algorithm is proposed with an objective to achieve a schedule that minimizes the total waiting time of jobs in a specially structured model where the AHR of processing times is not on the whole arbitrary but must satisfy a definite condition. Most of the literature in scheduling focuses on minimizing the make-span. The significance of the desired objective and the effectiveness of the proposed algorithm are exhibited in comparison to Johnson (Naval Res Logist Quar 1(1):61–68, [1]), Palmer (Oper Res 16:101–107, [2]), NEH (Int J Manag Sci11(1):91–95, [3]), Nailwal et al. (Int J Indus Eng Comput 7:671–680, [4]) and Goyal and Kaur (Mater Today: Proc, [5]) heuristic approaches. The results obtained show the best out of the five as well whenever the objective of minimizing waiting times is concerned.