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Flexible job shop scheduling with blockages

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Abstract

Motivated by an application in rail car maintenance, we study a variant of makespan-minimizing flexible job shop scheduling with work centers (FJc). In standard FJc a work center contains parallel machines, i.e. any machine in the work center is accessible whenever idle. In our variant, a work center consists of a linearly ordered set of machines with restricted accessibility, i.e. a busy machine blocks access to all succeeding machines. In rail car maintenance, the machines of a work center are located sequentially along a track. Therefore, a rail car waiting before or after some maintenance step can neither reach nor leave an idle machine if another rail car blocks the access path on the track. We call the resulting problem FJc with blockages. It turns out to be weakly \(\fancyscript{N\!\!\!P}\)-hard even for a single work center with two machines, and strongly \(\fancyscript{N\!\!\!P}\)-hard for a single work center. We derive a mixed integer linear optimization model, we present heuristic as well as exact solution methods, and we discuss computational results. In particular, we observe that our implementation of a branch&bound procedure is quite competitive with the commercial solvers Cplex 12.4 and Gurobi 5.0.

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Acknowledgments

We like to thank the Franz Kaminski Waggonbau GmbH in Hameln, Germany, for motivating and supporting practical discussions. Furthermore, we are grateful to the anonymous reviewers for the helpful comments on an earlier draft of the paper.

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Authors and Affiliations

  1. Institute of Mathematical Optimization, Technical University Braunschweig, Braunschweig, Germany

    R. S. Hansmann, T. Rieger & U. T. Zimmermann

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  1. R. S. Hansmann
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  2. T. Rieger
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  3. U. T. Zimmermann
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Correspondence to T. Rieger.

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Hansmann, R.S., Rieger, T. & Zimmermann, U.T. Flexible job shop scheduling with blockages. Math Meth Oper Res 79, 135–161 (2014). https://doi.org/10.1007/s00186-013-0456-3

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  • DOI: https://doi.org/10.1007/s00186-013-0456-3

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