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Job-Shop Scheduling Problem

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Encyclopedia of Optimization

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The job-shop problem may be formulated as follows. Given are n jobs j = 1,..., n and m machines M 1,..., M m . Job j consists of a sequence

of n j operations which must be processed in the given order, i.e. O i + 1, j cannot start before O ij is completed for i = 1,..., n j −1. Associated with each operation O ij there is a processing time p ij and a machine μ ij ∈{M 1,..., M m }. O ij must be processed for p ij time units on machine μ ij . Each job can be processed by at most one machine at a time and each machine can process only one operation at a time. If not stated differently preemptions of operations are not allowed. One has to find a feasible schedule which minimizes the makespan.

It is assumed that all processing times are nonnegative integers and that all jobs and machines are available at starting time zero. Furthermore, if not stated differently, machine repetition is allowed, i.e. μi + 1, j = μ ij is possible.

For a precise formulation of the job-shop problem, let be the...

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Authors and Affiliations

  1. Fachber. Math./Informatik Univ. Osnabrück, 49069, Osnabrück, Germany

    Peter Brucker

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  1. Peter Brucker
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Editors and Affiliations

  1. Dept. Chemical Engin., Princeton Univ., Princeton, NJ, 08544-5263, USA

    Christodoulos A. Floudas

  2. Center for Applied Optim. Dept. Industrial and Systems Engin., Univ. Florida, Gainesville, FL, 32611, USA

    Panos M. Pardalos

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© 2001 Kluwer Academic Publishers

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Brucker, P. (2001). Job-Shop Scheduling Problem . In: Floudas, C.A., Pardalos, P.M. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/0-306-48332-7_239

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  • DOI: https://doi.org/10.1007/0-306-48332-7_239

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-7923-6932-5

  • Online ISBN: 978-0-306-48332-5

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