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A Branch and Bound Approach for Machine Load Balancing in Flexible Manufacturing Systems

Author

Listed:
  • Mohammed Berrada

    (Département d'Études et de Recherches en Automatique, Centre d'Études et de Recherches de Toulouse, 31055 Toulouse Cedex, France)

  • Kathryn E. Stecke

    (Graduate School of Business Administration, The University of Michigan, Ann Arbor, Michigan 48109-1234)

Abstract

A flexible manufacturing system (FMS) is an integrated system of computer numerically controlled machine tools connected with automated material handling. A set of production planning problems for FMSs has been defined (Stecke [Stecke, Kathryn E. 1983. Formulation and solution of nonlinear integer production planning problems for flexible manufacturing systems. Management Sci. 29 (3, March) 273--288.]), and this paper considers one called the loading problem. This problem involves assigning to the machine tools, operations and associated cutting tools required for part types that have been selected to be produced simultaneously. The part types will be machined during the upcoming production period (say, of one to three weeks duration on average) and according to a prespecified part mix. This assignment is constrained by the capacity of each machine's tool magazine as well as by the production capacities of both the system, and each machine type. There are several loading objectives that are applicable in a flexible manufacturing situation. This paper considers the most commonly applied one, that of balancing the workload on all machines. This paper first discusses a nonlinear integer mathematical programming formulation of the loading problem. The problem is formulated in all detail. Then an efficient solution procedure is proposed and illustrated with an example. Computational results are provided to demonstrate the efficiency of the suggested special-purpose procedures.

Suggested Citation

  • Mohammed Berrada & Kathryn E. Stecke, 1986. "A Branch and Bound Approach for Machine Load Balancing in Flexible Manufacturing Systems," Management Science, INFORMS, vol. 32(10), pages 1316-1335, October.
    • Handle: RePEc:inm:ormnsc:v:32:y:1986:i:10:p:1316-1335
    DOI: 10.1287/mnsc.32.10.1316
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    Citations

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    Cited by:

    1. S Bilgin & M Azizoǧlu, 2006. "Capacity and tool allocation problem in flexible manufacturing systems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(6), pages 670-681, June.
    2. Kumar, Ashok & Jacobson, Sheldon H. & Sewell, Edward C., 2000. "Computational analysis of a flexible assembly system design problem," European Journal of Operational Research, Elsevier, vol. 123(3), pages 453-472, June.
    3. Soares, Leonardo Cabral R. & Carvalho, Marco Antonio M., 2020. "Biased random-key genetic algorithm for scheduling identical parallel machines with tooling constraints," European Journal of Operational Research, Elsevier, vol. 285(3), pages 955-964.
    4. Crama, Yves, 1997. "Combinatorial optimization models for production scheduling in automated manufacturing systems," European Journal of Operational Research, Elsevier, vol. 99(1), pages 136-153, May.
    5. Kumar, Akhilesh & Prakash & Tiwari, M.K. & Shankar, Ravi & Baveja, Alok, 2006. "Solving machine-loading problem of a flexible manufacturing system with constraint-based genetic algorithm," European Journal of Operational Research, Elsevier, vol. 175(2), pages 1043-1069, December.
    6. Beezão, Andreza Cristina & Cordeau, Jean-François & Laporte, Gilbert & Yanasse, Horacio Hideki, 2017. "Scheduling identical parallel machines with tooling constraints," European Journal of Operational Research, Elsevier, vol. 257(3), pages 834-844.
    7. Atan, Tankut S. & Pandit, Ram, 1996. "Auxiliary tool allocation in flexible manufacturing systems," European Journal of Operational Research, Elsevier, vol. 89(3), pages 642-659, March.
    8. Sawik, Tadeusz, 1998. "A lexicographic approach to bi-objective loading of a flexible assembly system," European Journal of Operational Research, Elsevier, vol. 107(3), pages 656-668, June.
    9. Gaalman, G. J. C. & Nawijn, W. M., 1996. "Tool sharing in parallel part production," International Journal of Production Economics, Elsevier, vol. 46(1), pages 521-533, December.
    10. Potts, C. N. & Whitehead, J. D., 2001. "Workload balancing and loop layout in the design of a flexible manufacturing system," European Journal of Operational Research, Elsevier, vol. 129(2), pages 326-336, March.
    11. Dauzère-Pérès, Stéphane & Ding, Junwen & Shen, Liji & Tamssaouet, Karim, 2024. "The flexible job shop scheduling problem: A review," European Journal of Operational Research, Elsevier, vol. 314(2), pages 409-432.
    12. Yumin He & Kathryn E. Stecke & Milton L. Smith, 2016. "Robot and machine scheduling with state-dependent part input sequencing in flexible manufacturing systems," International Journal of Production Research, Taylor & Francis Journals, vol. 54(22), pages 6736-6746, November.

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