A Multi-Criteria Decision Making for the Unrelated Parallel Machines Scheduling Problem

Wei-Shung Chang,Chiuh-Cheng Chyu

doi:10.4236/jsea.2009.25042

Wei-Shung Chang, Chiuh-Cheng Chyu

Open Access

https://doi.org/10.4236/jsea.2009.25042

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Abstract

In this paper, we propose a multi-criteria machine-schedules decision making method that can be applied to a produc-tion environment involving several unrelated parallel machines and we will focus on three objectives: minimizing makespan, total flow time, and total number of tardy jobs. The decision making method consists of three phases. In the first phase, a mathematical model of a single machine scheduling problem, of which the objective is a weighted sum of the three objectives, is constructed. Such a model will be repeatedly solved by the CPLEX in the proposed Multi-Objective Simulated Annealing (MOSA) algorithm. In the second phase, the MOSA that integrates job clustering method, job group scheduling method, and job group – machine assignment method, is employed to obtain a set of non-dominated group schedules. During this phase, CPLEX software and the bipartite weighted matching algorithm are used repeatedly as parts of the MOSA algorithm. In the last phase, the technique of data envelopment analysis is applied to determine the most preferable schedule. A practical example is then presented in order to demonstrate the applicability of the proposed decision making method.

Highlights

Parallel machine scheduling problems have been extensively studied in the literature and widely used in many manufacturing environments, such as the drilling operation in a PWB line [1] and glass etch polishing process in the TFT-LCD manufacture
We propose a multi-criteria machine-schedules decision making method that can be applied to a production environment involving several unrelated parallel machines and we will focus on three objectives: minimizing makespan, total flow time, and total number of tardy jobs
We proposed an interactive simulated annealing algorithm aimed at searching for a set of near Pareto optimal solutions to the unrelated parallel machine scheduling problem with three objectives: minimizing total completion time, total flow time, and total number of tardy jobs

Summary

Introduction

Parallel machine scheduling problems have been extensively studied in the literature and widely used in many manufacturing environments, such as the drilling operation in a PWB line [1] and glass etch polishing process in the TFT-LCD manufacture. In many real-life situations, the used machines are not always identical in performance. They are different because they were purchased at different times or for different considerations. The layout of unrelated parallel machines is more common than identical parallel machines in real manufacturing environments. The unrelated parallel machine scheduling problem (UPMSP) is more difficult than the identical case. Since the latter belongs to NP hard [2], the UPMSP is NP hard. For further knowledge and recent findings regarding the UPMSP, we refer to [3,4]

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