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Block Angular Structures and the Loading Problem in Flexible Manufacturing Systems

Author

Listed:
  • Panagiotis Kouvelis

    (The University of Texas at Austin, Austin, Texas)

  • Hau L. Lee

    (Stanford University, Stanford, California)

Abstract

Loading problems of Flexible Manufacturing Systems (FMSs) have usually been formulated as an integer program with nonlinear constraints for tool magazine capacities. The nonlinearity and integer nature of the problem results in the loading problem being difficult to solve. Conventional branch-and-bound methods have been proposed, but again the solution time can easily be excessive for moderate sized problems. In this paper, we present an alternative formulation of the FMS loading problem. Such a formulation defines more decision variables, but is able to avoid nonlinearity of the constraints. It also includes the time availabilities of the machines as additional constraints. The main feature of the formulation is that it exhibits a block angular structure. By exploiting this special structure, an efficient branch-and-bound algorithm can be developed. This algorithm has the attractive feature that the bounds of the branches can be computed through simple procedures based on the solution of linear knapsack problems. Some computational results of the algorithm are also presented.

Suggested Citation

  • Panagiotis Kouvelis & Hau L. Lee, 1991. "Block Angular Structures and the Loading Problem in Flexible Manufacturing Systems," Operations Research, INFORMS, vol. 39(4), pages 666-676, August.
    • Handle: RePEc:inm:oropre:v:39:y:1991:i:4:p:666-676
    DOI: 10.1287/opre.39.4.666
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    Citations

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    Cited by:

    1. 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.
    2. Mark S. Hillier & Margaret L. Brandeau, 1998. "Optimal Component Assignment and Board Grouping in Printed Circuit Board Manufacturing," Operations Research, INFORMS, vol. 46(5), pages 675-689, October.
    3. Meltem Denizel & S. Selcuk Erenguc & Hanif D. Sherali, 1996. "Convex envelope results and strong formulations for a class of mixed‐integer programs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(4), pages 503-518, June.
    4. Mohamed, Zubair M., 1995. "Ramifications of tool magazine size on the makespan and routing flexibility of flexible manufacturing systems," European Journal of Operational Research, Elsevier, vol. 87(2), pages 289-298, December.
    5. Mohamed, Zubair M. & Bernardo, John J., 1997. "Tool planning models for flexible manufacturing systems," European Journal of Operational Research, Elsevier, vol. 103(3), pages 497-514, December.
    6. 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.
    7. Mohamed, Zubair M., 1996. "A flexible approach to (re)configure Flexible Manufacturing Cells," European Journal of Operational Research, Elsevier, vol. 95(3), pages 566-576, December.

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