Fuzzy LPT Algorithms for Flexible Flow Shop Problems with Unrelated Parallel Machines for a Continuous Fuzzy Domain

A flexible flow shop problem can be considered as a generalization of a pure flow shop problem in which the jobs have to go through the stages in the same order. We consider a flexible flow shop problem with unrelated machines and setup times, where the processing times depend on the chosen machine and setup times are sequence-dependent. While for classical problems the processing times for each job are assumed to be known exactly, in many real-world situations processing times vary dynamically due to human factors or operating faults. In this paper, fuzzy concepts are used in an LPT algorithm for managing uncertain scheduling. Given a set of jobs together with a membership function for the standard processing times, the fuzzy LPT algorithms construct a solution by means of a membership function for the final makespan. The proposed algorithms provide a more flexible method of scheduling jobs than conventional scheduling methods. The results show that the fuzzy LPT algorithms give a deviation from the optimal makespan value of about five percent for the small-size test problems. In addition, the fuzzy LPT algorithm by using the average values of the total operating times at the last stage (denoted by FLPT) gives a good solution for both smalland large-test problems.