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A Bender’s Algorithm of Decomposition Used for the Parallel Machine Problem of Robotic Cell

Author

Listed:
  • Mohammad Reza Komari Alaei

    (Department of Business Administration, Hacettepe University, 06800 Beytepe, Ankara, Turkey)

  • Mehmet Soysal

    (Department of Business Administration, Hacettepe University, 06800 Beytepe, Ankara, Turkey)

  • Atabak Elmi

    (School of Information Technology, Deakin University, Geelong, VIC 3220, Australia)

  • Audrius Banaitis

    (Department of Construction Management and Real Estate, Vilnius Gediminas Technical University, 10223 Vilnius, Lithuania)

  • Nerija Banaitiene

    (Department of Construction Management and Real Estate, Vilnius Gediminas Technical University, 10223 Vilnius, Lithuania)

  • Reza Rostamzadeh

    (Department of Management, Urmia Branch, Islamic Azad University, Urmia, Iran)

  • Shima Javanmard

    (Department of Industrial Engineering, Eqbal Lahoori Institute of Higher Education, Mashhad, Iran)

Abstract

The present research addresses the single transportation robot used to alleviate problems of robotic cell scheduling of the machines. For the purpose of minimizing the make-span, a model of mixed-integer linear programming (MILP) has been suggested. Since the inefficiency exists in NP-hard, a decomposition algorithm posed by Bender was utilized to alleviate the problem in real life situations. The proposed algorithm can be regarded as an efficient attempt to apply optimality Bender’s cuts regarding the problem of parallel machine robotic cell scheduling in order to reach precise resolutions for medium and big sized examples. The numerical analyses have demonstrated the efficiency of the proposed solving approach.

Suggested Citation

  • Mohammad Reza Komari Alaei & Mehmet Soysal & Atabak Elmi & Audrius Banaitis & Nerija Banaitiene & Reza Rostamzadeh & Shima Javanmard, 2021. "A Bender’s Algorithm of Decomposition Used for the Parallel Machine Problem of Robotic Cell," Mathematics, MDPI, vol. 9(15), pages 1-15, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:15:p:1730-:d:599384
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    References listed on IDEAS

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    1. Ümit Bilge & Gündüz Ulusoy, 1995. "A Time Window Approach to Simultaneous Scheduling of Machines and Material Handling System in an FMS," Operations Research, INFORMS, vol. 43(6), pages 1058-1070, December.
    2. Mohammad M. Fazel-Zarandi & J. Christopher Beck, 2012. "Using Logic-Based Benders Decomposition to Solve the Capacity- and Distance-Constrained Plant Location Problem," INFORMS Journal on Computing, INFORMS, vol. 24(3), pages 387-398, August.
    3. Hall, Nicholas G. & Kamoun, Hichem & Sriskandarajah, Chelliah, 1998. "Scheduling in robotic cells: Complexity and steady state analysis," European Journal of Operational Research, Elsevier, vol. 109(1), pages 43-65, August.
    4. Daniel Tonke & Martin Grunow, 2018. "Maintenance, shutdown and production scheduling in semiconductor robotic cells," International Journal of Production Research, Taylor & Francis Journals, vol. 56(9), pages 3306-3325, May.
    5. Chelliah Sriskandarajah & Nicholas Hall & Hichem Kamoun, 1998. "Scheduling large robotic cells without buffers," Annals of Operations Research, Springer, vol. 76(0), pages 287-321, January.
    6. Carlier, Jacques & Haouari, Mohamed & Kharbeche, Mohamed & Moukrim, Aziz, 2010. "An optimization-based heuristic for the robotic cell problem," European Journal of Operational Research, Elsevier, vol. 202(3), pages 636-645, May.
    7. Soukhal, A. & Oulamara, A. & Martineau, P., 2005. "Complexity of flow shop scheduling problems with transportation constraints," European Journal of Operational Research, Elsevier, vol. 161(1), pages 32-41, February.
    8. J. N. Hooker, 2007. "Planning and Scheduling by Logic-Based Benders Decomposition," Operations Research, INFORMS, vol. 55(3), pages 588-602, June.
    9. Milind Dawande & Michael Pinedo & Chelliah Sriskandarajah, 2009. "Multiple Part-Type Production in Robotic Cells: Equivalence of Two Real-World Models," Manufacturing & Service Operations Management, INFORMS, vol. 11(2), pages 210-228, February.
    10. Soukhal, A. & Martineau, P., 2005. "Resolution of a scheduling problem in a flowshop robotic cell," European Journal of Operational Research, Elsevier, vol. 161(1), pages 62-72, February.
    11. Daria Terekhov & J. Christopher Beck & Kenneth N. Brown, 2009. "A Constraint Programming Approach for Solving a Queueing Design and Control Problem," INFORMS Journal on Computing, INFORMS, vol. 21(4), pages 549-561, November.
    12. Canto, Salvador Perez, 2008. "Application of Benders' decomposition to power plant preventive maintenance scheduling," European Journal of Operational Research, Elsevier, vol. 184(2), pages 759-777, January.
    13. Batur, G. Didem & Karasan, Oya Ekin & Akturk, M. Selim, 2012. "Multiple part-type scheduling in flexible robotic cells," International Journal of Production Economics, Elsevier, vol. 135(2), pages 726-740.
    14. Agnetis, A., 2000. "Scheduling no-wait robotic cells with two and three machines," European Journal of Operational Research, Elsevier, vol. 123(2), pages 303-314, June.
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