Abstract

In this paper, we present a variable block insertion heuristic (VBIH) algorithm to solve the blocking flowshop scheduling problem with the total flowtime criterion. In the VBIH algorithm, we define a minimum and a maximum block size. After constructing the initial sequence, the VBIH algorithm starts with a minimum block size being equal to one. It removes the block from the current sequence and inserts it into the partial sequence sequentially with a predetermined move size. The sequence, which is obtained after several block moves, goes under a variable local search (VLS), which is based on traditional insertion and swap neighborhood structures. If the new sequence obtained after the VLS local search is better than the current sequence, it replaces the current sequence. As long as it improves, it keeps the same block size. However, if it does not improve, the block size is incremented by one and a simulated annealing-type of acceptance criterion is used to accept the current sequence. This process is repeated until the block size reaches at the maximum block size. Furthermore, we present a novel constructive heuristic, which is based on the profile fitting heuristic from the literature. The proposed constructive heuristic is able to further improve the best known solutions for some larger instances in a few seconds. Parameters of the constructive heuristic and the VBIH algorithm are determined through a design of experiment approach. Extensive computational results on the Taillard’s well-known benchmark suite show that the proposed VBIH algorithm outperforms the discrete artificial bee colony algorithm, which is one of the most efficient algorithms recently in the literature. Ultimately, 52 out of the 150 best known solutions are further improved with substantial margins.

Highlights

  • There have been extensive studies about permutation flowshop scheduling (PFSP) in the literature with many important applications in manufacturing and service systems [1,2,3,4]

  • This paper presents a variable block insertion heuristic (VBIH) algorithm to solve the blocking flowshop scheduling problem with the total flowtime criterion

  • Once an initial solution is constructed, the VBIH algorithm begins with a minimum block size of one

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Summary

Introduction

There have been extensive studies about permutation flowshop scheduling (PFSP) in the literature with many important applications in manufacturing and service systems [1,2,3,4]. The traditional PFSP is concerned with scheduling n jobs through m machines in such a way that the same sequence is applied to each machine. Allowing jobs to be waiting in front of machines for their operations words. If any storage capacity amongst machines is not available, the traditional PFSP is said to be blocking flowshop scheduling problem. Algorithms 2016, 9, 71; doi:10.3390/a9040071 www.mdpi.com/journal/algorithms (BFSF) [5]. In this case, a job cannot leave the machine unless the machine is free. A comprehensive review on flowshop scheduling with blocking and no-wait constraint can be found in Hall and Siriskandarajah [7]

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