Solving Machine Scheduling Problem under Fuzzy Processing Time using the Simulated Annealing Method

In this paper, we describe the problem of sequencing a set of n jobs on single machine was considered to minimize multiple objectives function (MOF). The objective is to find the approximate solutions for scheduling n independent jobs to minimize the objective function consists from asum of weighted number of earlyjobs and weighted number of tardy jobs with fuzzy processing time.This problem is denoted by: (1/ / 𝑁ℎ𝑗𝐸𝑗 + 𝑁𝑤𝑗 𝑇𝑗 𝑛 𝑗 =1 𝑛 𝑗 =1 ). To resolve it we proposed the Average High Ranking (AHR) method to obtain a processing time generated from fuzzy processing time, calculate the costs and reach to total penalty cost. Since our problem is Strongly NP-hard in normal form, we used Simulated Annealing. It solved the problem with up to 12000 jobs in 30 seconds.