# An Iterated Greedy Algorithm for Solving the Blocking Flow Shop Scheduling Problem with Total Flow Time Criteria

pp. 301-308

ISSN: 2008-4889

http://IJIEPR.iust.ac.ir/

An Iterated Greedy Algorithm for Solving the Blocking Flow Shop Scheduling Problem with Total Flow Time Criteria D. Khorasanian & G. Moslehi*

Danial Khorasanian is an M.S. Student of Department of Industrial Engineering, Isfahan University of Technology, Isfahan, Iran Ghasem Moslehi is a Professor of Department of Industrial Engineering, Isfahan University of Technology, Isfahan, Iran

KEYWORDS

Constructive heuristic, Iterated greedy algorithm, Blocking flow shop, Total flow time

ABSTRACT

In this paper, we propose an iterated greedy algorithm for solving the blocking flow shop scheduling problem with total flow time minimization objective. The steps of this algorithm are designed very efficient. For generating an initial solution, we develop an efficient constructive heuristic by modifying the best known NEH algorithm. Effectiveness of the proposed iterated greedy algorithm is tested on the Taillard's instances. Computational results show the high efficiency of this algorithm with comparison state-of-the-art algorithms. We report new best solutions for 88 instances of 120 Taillard's instances. © 2012 IUST Publication, IJIEPR, Vol. 23, No. 4, All Rights Reserved.

1. Introduction

The flow shop scheduling problem is one of the most popular machine scheduling problems with extensive engineering relevance, representing nearly a quarter of manufacturing systems, assembly lines and information service facilities in use nowadays [1]. In the general flow shop model, it is assumed that the buffers have unlimited capacity. However, in many real flow shop environments, the buffers may have limited capacity due to technological requirements or process characteristics [2]. A special case of these environments is the flow shop with zero capacity buffers that the related problem is known as the blocking flow shop scheduling problem (BFSP). Since there are no buffers between machines, no intermediate queues of jobs are allowed in the production system for their next operations [3]. In BFSP, the completed job on a machine may block it until the next downstream machine is free. Grabowski *

Corresponding author: Ghasem Moslehi Email: . moslehi@cc.iut.ac.ir Paper first received July. 05, 2012, and in revised form Oct. 9, 2012.

and Pempera [4] present a real life example in the production of concrete blocks that does not allow storage in some stages. A detailed review of studies and applications of the BFSP can be found in [2]. It has been proved that the BFSP with makespan criteria and more than two machines is strongly NP-hard [2]. Also, Rock [5] showed that the BFSP with total flow time criteria and two machines is strongly NP-hard. In recent years, the BFSP has attracted much attention among researchers. Since the problem is strongly NPhard for large numbers of jobs and machines, as is usual in real systems, it is more practical to use heuristics and metaheuristics to solve it. The simplest heuristics are constructive procedures, which use rules to assign a priority index to each job, in each step, to build a sequence. Most studies of the BFSP have dealt with makespan criteria. Among the proposed constructive heuristics for the BFSP with makespan criteria, one can refer to Profile Fitting (PF) [6], MinMax (MM) [7], MME [7], PFE [7], NEH2 [8]. The most important proposed constructive heuristic for the BFSP with total flow time criteria is NEH-WPT [9]. Most of the proposed heuristics for the BFSP have

D. Khorasanian & G. Moslehi

An Iterated Greedy Algorithm for Solving the Blocking Flow Shop…

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been developed by modifying the best known NEH [10] heuristic. As we know, the NEH algorithm is as follows [10]: Step 1: Sort the jobs according to the non-increasing sums of their processing times and let the obtained sequence ( (1),, (n )) ....

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