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Capacity and tool allocation problem in flexible manufacturing systems

Author

Listed:
  • S Bilgin

    (Middle East Technical University)

  • M Azizoǧlu

    (Middle East Technical University)

Abstract

This study addresses an allocation problem that arises in the semiconductor industry and flexible manufacturing systems where the tools should be loaded on computer numerical controlled (CNC) machines to process a number of operations. The time and tool magazine capacities of the CNC machines and the number of available tools of each type are limited. The objective is to maximize the total weight of operation assignments. We present a mixed integer programming formulation of the problem and show that the problem is NP-hard in the strong sense. We show that the linear programming relaxation upper bound dominates the best possible Lagrangean relaxation upper bound. We develop several lower bounding procedures and a lower bounding procedure using Lagrangean relaxation approach. Our computational results show that the upper and lower bounding procedures produce near-optimal solutions in reasonable times.

Suggested Citation

  • 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.
    • Handle: RePEc:pal:jorsoc:v:57:y:2006:i:6:d:10.1057_palgrave.jors.2602039
    DOI: 10.1057/palgrave.jors.2602039
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    References listed on IDEAS

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    1. Marshall L. Fisher, 1981. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 27(1), pages 1-18, January.
    2. 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.
    3. Marshall L. Fisher, 1985. "An Applications Oriented Guide to Lagrangian Relaxation," Interfaces, INFORMS, vol. 15(2), pages 10-21, April.
    4. Toktay, L. Beril & Uzsoy, Reha, 1998. "A capacity allocation problem with integer side constraints," European Journal of Operational Research, Elsevier, vol. 109(1), pages 170-182, August.
    5. D'Alfonso, Thomas H. & Ventura, Jose A., 1995. "Assignment of tools to machines in a flexible manufacturing system," European Journal of Operational Research, Elsevier, vol. 81(1), pages 115-133, February.
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    Cited by:

    1. S Özpeynirci & M Azizoğlu, 2010. "A Lagrangean relaxation based approach for the capacity allocation problem in flexible manufacturing systems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(5), pages 872-877, May.

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