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A branch and bound procedure for the reentrant permutation flow-shop scheduling problem

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Abstract

This investigation considers a reentrant permutation flow-shop (RPFS) scheduling problem whose performance criterion is makespan. A reentrant flow-shop (RFS) refers to situations in which every job must be processed on machines in the order, M 1, M 2, ..., M m , M 1, M 2, ..., M m , ..., and M 1, M 2, ..., M m . Every job can be decomposed into several layers each of which starts on M 1 and finishes on M m . In the RFS case, if the job ordering is the same on any machine at each layer, then no passing is said to be allowed, since no job is allowed to pass any former job. The RFS scheduling problem in which no passing is allowed, is called an RPFS problem. A branch and bound algorithm is presented and an example is also given to illustrate the solution procedure. To compare the proposed algorithm, a series of computational experiments are done on randomly generated test problems and the results show that the developed algorithm is efficient.

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Abbreviations

n :

Total number of jobs for processing at time zero

m :

Total number of machines in the shop

L :

Total number of levels of each job

J i :

Job number i, 1≤i≤n

J i(q) :

Job scheduled at the qth position in the processing sequence, 1≤q≤n

M k :

Machine number k, 1≤k≤m

O lk i :

Operation of J i on M k at layer l, 1≤i≤n, 1≤l≤L, 1≤k≤m

P lk i :

Processing time of O lk i, 1≤i≤n, 1≤l≤L, 1≤k≤m

C lk i(q) :

Completion time of J i(q) on M k at layer l, 1≤q≤n, 1≤l≤L, 1≤k≤m

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Authors and Affiliations

  1. Department of Industrial Engineering and Management, Far East College, 49 Junghua Road, Shinshr Shiang, Tainan, 744, Taiwan

    Jen-Shiang Chen

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  1. Jen-Shiang Chen
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Correspondence to Jen-Shiang Chen.

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Chen, JS. A branch and bound procedure for the reentrant permutation flow-shop scheduling problem. Int J Adv Manuf Technol 29, 1186–1193 (2006). https://doi.org/10.1007/s00170-005-0017-x

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  • DOI: https://doi.org/10.1007/s00170-005-0017-x

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