Job Sequencing with Fuzzy Processing Times using Credibility Theory

Abstract

Abstract
In this paper, a new algorithm to find an optimal sequence of ‘ n ’ jobs that has to be processed through ‘m ’ machines is developed by treating the processing times of jobs on the machines as fuzzy (imprecise) variables. The algorithm is similar to that of Johnson (1954) which considers the processing times as precise in nature. The proposed algorithm makes use of the concepts of ‘Credibility Theory’ due to Liu (2008). An illustration of the proposed algorithm is given by representing the processing times as triangular fuzzy numbers.

Keywords: Credibility measure, credibility distribution, membership function, fuzzy
variable, expectation and variance of fuzzy variable, ranking of fuzzy variable,
sequencing