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Unrelated Parallel Machine Scheduling Problem with Precedence Constraints: Polyhedral Analysis and Branch-and-Cut

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Combinatorial Optimization (ISCO 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9849))

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Abstract

We consider the problem of unrelated parallel machines with precedence constraints (UPMPC), with the aim of minimizing the makespan. Each task has to be assigned to a unique machine and no preemption is allowed. In this paper, we show the relation between the interval graph and the UPMSPC problem. We propose valid inequalities and study the facial structure of their polytope. Facets are presented to strength the associated integer linear program formulation to help in solving the global problem. We develop a Branch and Cut algorithm for solving the problem and present some experimental results.

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References

  1. Agnetis, A., Kellerer, H., Nicosia, G., Pacifici, A.: Parallel dedicated machines scheduling with chain precedence constraints. Eur. J. Oper. Res. 221(2), 296–305 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  2. Schrijver, A.: Combinatorial Optimization: Polyhedra and Efficiency, vol. 24. Springer Science & Business Media, Heidelberg (2003)

    MATH  Google Scholar 

  3. Gacias, B., Artigues, C., Lopez, P.: Parallel machine scheduling with precedence constraints and setup times. Comput. Oper. Res. 37(12), 2141–2151 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  4. Lekkeikerker, C., Boland, J.: Representation of a finite graph by a set of intervals on the real line. Fundam. Math. 51(1), 45–64 (1962)

    MathSciNet  Google Scholar 

  5. Mokotoff, E., Chrétienne, P.: A cutting plane algorithm for the unrelated parallel machine scheduling problem. Eur. J. Oper. Res. 141(3), 515–525 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  6. Hall, N.G., Posner, M.E.: Generating experimental data for computational testing with machine scheduling applications. Oper. Res. 49(7), 854–865 (2011)

    MathSciNet  MATH  Google Scholar 

  7. Aardal, K., Van Hoesel, C.P.M.: Polyhedral techniques in combinatorial optimization II: applications and computations. Stat. Neerl. 53(2), 131–177 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  8. Ghirardi, M., Potts, C.N.: Makespan minimization for scheduling unrelated parallel machines: a recovering beam search approach. Eur. J. Oper. Res. 165(2), 457–467 (2005)

    Article  MATH  Google Scholar 

  9. Hassan, M.-A., Kacem, I., Martin, S., Osman, I.M.: Mathematical formulations for the unrelated parallel machines with precedence constraints. In: Proceedings of the International Conference on Computers & Industrial Engineering, 45th edn. (2015)

    Google Scholar 

  10. Graham, R.L., Lawler, E.L., Lenstra, J.K., RinnooyKan, A.H.G.: Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann. Discrete Math. 5, 287–326 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  11. Martello, S., Soumis, F., Toth, P.: Exact and approximation algorithms for makespan minimization on unrelated parallel machines. Discrete Appl. Math. 75(2), 169–188 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  12. Jiinger, M., Reinelt, G., Thienel, S.: Practical problem solving with cutting plane algorithms in combinatorial optimization. Comb. Optim. Dimacs 20, 111–152 (1995)

    MathSciNet  MATH  Google Scholar 

  13. Coll, P.E., Ribeiro, C.C., de Souza, C.C.: Multiprocessor scheduling under precedence constraints: polyhedral results. Discrete Appl. Math. 154(5), 770–801 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  14. Damodaran, P., Sharma, H.V., Moraga, R.: Scheduling unrelated parallel machines with sequence dependent setup times to minimize makespan. In: Proceedings of the IIE Annual Conference, p. 1. Institute of Industrial Engineers-Publisher (2012)

    Google Scholar 

  15. Kumar, V.A., Marathe, M.V., Parthasarathy, S., Srinivasan, A.: Scheduling on unrelated machines under tree-like precedence constraints. Algorithmica 55(1), 205–226 (2009)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. LCOMS EA 7306, Université de Lorraine, 57000, Metz, France

    Mohammed-Albarra Hassan, Imed Kacem & Sébastien Martin

  2. University of Gezira, Wadmedani, Sudan

    Mohammed-Albarra Hassan

  3. Sudan University of Science and Technology, Khartoum, Sudan

    Izzeldin M. Osman

Authors
  1. Mohammed-Albarra Hassan
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  2. Imed Kacem
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  3. Sébastien Martin
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  4. Izzeldin M. Osman
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Corresponding author

Correspondence to Mohammed-Albarra Hassan .

Editor information

Editors and Affiliations

  1. University of Salerno , Fisciano, Italy

    Raffaele Cerulli

  2. Kyoto University , Kyoto, Japan

    Satoru Fujishige

  3. LAMSADE, Université Paris-Dauphine , Paris , France

    A. Ridha Mahjoub

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Hassan, MA., Kacem, I., Martin, S., Osman, I.M. (2016). Unrelated Parallel Machine Scheduling Problem with Precedence Constraints: Polyhedral Analysis and Branch-and-Cut. In: Cerulli, R., Fujishige, S., Mahjoub, A. (eds) Combinatorial Optimization. ISCO 2016. Lecture Notes in Computer Science(), vol 9849. Springer, Cham. https://doi.org/10.1007/978-3-319-45587-7_27

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  • DOI: https://doi.org/10.1007/978-3-319-45587-7_27

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45586-0

  • Online ISBN: 978-3-319-45587-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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