Heuristics, Metaheuristics and Approximate Methods in Planning and Scheduling by Ghaith Rabadi

Author:Ghaith Rabadi
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

7.3 Unrelated Parallel Machine Scheduling Problem with Multi-Objectives

The unrelated parallel machine scheduling problem with minimization of total weighted tardiness and total weighted completion time, , may be described as a set of N independent jobs to be processed without preemption on any of the M unrelated parallel machines. Each machine m is capable of processing only one job at a time. It is assumed that all jobs are available at time zero. Job j has a processing time on machine m represented as p jk , a due date d j , a completion time C j , and a weight w j . In addition, a weighted tardiness penalty is incurred for each time unit of tardiness T j , given by T j  = max (0, C j  − d j ). is the total weighted tardiness and is the total weighted completion time of all the n independent jobs. Hence the problem can be formally stated as: find a schedule S that minimizes the objective functions f 1(S) = and f 2(S) = .

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