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An Integer Programming Procedure for Assembly System Design Problems

Author

Listed:
  • Stephen C. Graves

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

  • Bruce W. Lamar

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

Abstract

Recent advances in robot technology have revolutionized the concept of manufacturing and assembly systems. These advances have created the need for new mathematical models to reflect the capabilities of the new technologies. In this paper, we focus on the system design problem by defining a work station selection and task assignment problem for automated assembly systems. We formulate this problem as a zero-one integer program and describe a procedure for seeking lower and upper bounds to the optimal value of the integer program. The upper bound provides a feasible solution to the integer formulation and the lower bound is tighter than the standard linear programming relaxation of the integer formulation. Computational results indicate that the proposed bounds are extremely tight. In fact, in each of the 42 test problems evaluated, the lower and upper bound coincided, indicating that the optimal solution to the integer program had been obtained.

Suggested Citation

  • Stephen C. Graves & Bruce W. Lamar, 1983. "An Integer Programming Procedure for Assembly System Design Problems," Operations Research, INFORMS, vol. 31(3), pages 522-545, June.
    • Handle: RePEc:inm:oropre:v:31:y:1983:i:3:p:522-545
    DOI: 10.1287/opre.31.3.522
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    Citations

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    Cited by:

    1. Christoph Müller & Martin Grunewald & Thomas S. Spengler, 2017. "Redundant configuration of automated flow lines based on “Industry 4.0”-technologies," Journal of Business Economics, Springer, vol. 87(7), pages 877-898, October.
    2. Miralles, Cristobal & Garcia-Sabater, Jose Pedro & Andres, Carlos & Cardos, Manuel, 2007. "Advantages of assembly lines in Sheltered Work Centres for Disabled. A case study," International Journal of Production Economics, Elsevier, vol. 110(1-2), pages 187-197, October.
    3. Anulark Pinnoi & Wilbert E. Wilhelm, 1998. "Assembly System Design: A Branch and Cut Approach," Management Science, INFORMS, vol. 44(1), pages 103-118, January.
    4. Jonathan Oesterle & Lionel Amodeo & Farouk Yalaoui, 2019. "A comparative study of Multi-Objective Algorithms for the Assembly Line Balancing and Equipment Selection Problem under consideration of Product Design Alternatives," Journal of Intelligent Manufacturing, Springer, vol. 30(3), pages 1021-1046, March.
    5. Becker, Christian & Scholl, Armin, 2006. "A survey on problems and methods in generalized assembly line balancing," European Journal of Operational Research, Elsevier, vol. 168(3), pages 694-715, February.
    6. Agpak, Kursad & Gokcen, Hadi, 2005. "Assembly line balancing: Two resource constrained cases," International Journal of Production Economics, Elsevier, vol. 96(1), pages 129-140, April.
    7. Boysen, Nils & Fliedner, Malte, 2008. "A versatile algorithm for assembly line balancing," European Journal of Operational Research, Elsevier, vol. 184(1), pages 39-56, January.
    8. Boysen, Nils & Schulze, Philipp & Scholl, Armin, 2022. "Assembly line balancing: What happened in the last fifteen years?," European Journal of Operational Research, Elsevier, vol. 301(3), pages 797-814.
    9. Boysen, Nils & Fliedner, Malte & Scholl, Armin, 2008. "Assembly line balancing: Which model to use when," International Journal of Production Economics, Elsevier, vol. 111(2), pages 509-528, February.
    10. Wilbert E. Wilhelm & Radu Gadidov, 2004. "A Branch-and-Cut Approach for a Generic Multiple-Product, Assembly-System Design Problem," INFORMS Journal on Computing, INFORMS, vol. 16(1), pages 39-55, February.
    11. Pinnoi, Anulark & Wilhelm, Wilbert E., 2000. "Valid inequalities for a class of assembly system problems," European Journal of Operational Research, Elsevier, vol. 126(1), pages 31-50, October.
    12. Wilbert E. Wilhelm, 1987. "Complexity of sequencing tasks in assembly cells attended by one or two robots," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(5), pages 721-738, October.

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