Flow Shop Scheduling Problem

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Dublin Institute of Technology

Conference papers School of Marketing


Flow Shop Scheduling Problem: a Computational Study
Amr Arisha
Dublin Institute of Technology,, amr.arisha@dit.ie

Paul Young
Dublin City University

Mohie El Baradie
Dublin City University

Follow this and additional works at: http://arrow.dit.ie/buschmarcon Part of the Other Operations Research, Systems Engineering and Industrial Engineering Commons Recommended Citation Arish, A., Young, P., El Baradie, M.:Flow Shop Scheduling Problem: a Computational Study.Sixth International Conference on Production Engineering and Design for Development (PEDD6),Cairo, Egypt, pp 543 – 557.

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A. Arisha, P. Young, and M. EL Baradie
School of Mechanical & Manufacturing Engineering, Dublin City University Dublin 9, Ireland Email: amr.arisha@gmail.com

ABSTRACT: A computational study has been developed to obtain optimal / near optimal solution for the flow shop scheduling problem with make-span minimization as the primary criterion and the minimization of either the mean completion time, total waiting time or total idle time as the secondary criterion. The objective is to determine a sequence of operations in which to process ‘n’ jobs on ‘m’ machines in same order (flow shop environment) where skipping is allowed. The Simulation approach for deterministic and stochastic flow shop scheduling has been developed. It reads and manipulates data for 500 jobs on 500 machines. Different factorial experiments present a comparative study on the performance of different dispatching rules, such as FCFS, SPT, LPT, SRPT and LRPT with respect to the objectives of minimizing makespan, mean flow time, waiting time of jobs, and idle time of machines. The proposed model is evaluated and found to be relatively more effective in finding optimal/ near optimal solutions in many cases. The influence of the problem size in computational time for this model is discussed and recommendations for further research are presented. KEYWORDS: Optimization. Flow Shop Scheduling, Simulation, Dispatching Rules, and Enumerative

1. INTRODUCTION The purpose of this paper is twofold: (1) to provide a simulation program able to find the optimum / near optimum sequence for general flow shop scheduling problem with make-span minimization as main criteria; (2) to compare different dispatching rules on minimizing multiple criteria. Numerous combinatorial optimization procedures have been proposed for solving the general flowshop problem with the maximum flow time criterion. Many researches have been successful in developing efficient solution algorithms for flowshop scheduling and sequencing [1, 2, 3, 4, 5, 6, 7 and 8] using up to 10 machines. Dannenbring [2] found that for small size shop problems his heuristic outperformed others in minimizing the make-span for 1280 flowshop scheduling problems. Ezat and El Baradie carried a simulation study for pure flowshop scheduling with makespan minimization as a major criterion for n ψ90 on m ψ90 [9]. In This paper study general flow shop scheduling problem with make-span minimization as main criteria for n ψ 250 and m ψ 250 with different ranges of random numbers generated (0-99) for processing times matrix.

2. THE FLOWSHOP SCHEDULING PROBLEM The flowshop problem has interested researchers for nearly half a century. The flowshop problem consists of two major elements: (1) a production system of ‘m’ machines; and (2) a set of ‘n’ jobs to be processed on these machines. All ‘n’ jobs are so...
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