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Generalized Assignment with Nonlinear Capacity Interaction

Author

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  • Joseph B. Mazzola

    (Fuqua School of Business, Duke University, Durham, North Carolina 27706)

Abstract

The utility of the generalized assignment problem (GAP) is well known in regard to resource allocation problems arising in the areas of production planning, scheduling, and facility location. This paper introduces an important generalization of the GAP, which is called the 0-1 generalized assignment problem with nonlinear capacity constraints (NLGAP) and which allows for capacity interaction among tasks assigned to the same agent. For example, NLGAP can be used to model the hierarchical production planning problem involving the assignment of product families to production facilities in the case where process changeover gives rise to nonlinear capacity interaction among product families assigned to be produced at the same facility. Other applications of NLGAP occur readily throughout the areas of production planning and scheduling. We define a branch-and-bound algorithm for the NLGAP. This algorithm draws upon the underlying structure of the problem by combining in a novel manner recent advances in both nonlinear 0-1 programming and bounding techniques for the GAP. A heuristic for obtaining approximate solutions to NLGAP is also defined. We discuss computational experience with both the exact algorithm and the heuristic. The computational results demonstrate that the heuristic is extremely effective in obtaining near-optimal solutions and that the branch-and-bound algorithm can solve to optimality NLGAPs with 5 agents, 20 tasks, and over 1000 nonlinear terms per constraint.

Suggested Citation

  • Joseph B. Mazzola, 1989. "Generalized Assignment with Nonlinear Capacity Interaction," Management Science, INFORMS, vol. 35(8), pages 923-941, August.
  • Handle: RePEc:inm:ormnsc:v:35:y:1989:i:8:p:923-941
    DOI: 10.1287/mnsc.35.8.923
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    File URL: http://dx.doi.org/10.1287/mnsc.35.8.923
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    Citations

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    Cited by:

    1. Cattrysse, D. G. & van Wassenhove, L. N., 1990. "A Survey Of Algorithms For The Generalized Assignment Problem," Econometric Institute Archives 272389, Erasmus University Rotterdam.
    2. 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.
    3. Joseph B. Mazzola & Alan W. Neebe, 2012. "A generalized assignment model for dynamic supply chain capacity planning," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(6), pages 470-485, September.
    4. Mazzola, Joseph B. & Neebe, Alan W. & Rump, Christopher M., 1998. "Multiproduct production planning in the presence of work-force learning," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 336-356, April.
    5. Haddadi, Salim & Ouzia, Hacene, 2004. "Effective algorithm and heuristic for the generalized assignment problem," European Journal of Operational Research, Elsevier, vol. 153(1), pages 184-190, February.
    6. Joseph B. Mazzola & Steven P. Wilcox, 2001. "Heuristics for the multi‐resource generalized assignment problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(6), pages 468-483, September.
    7. Joseph B. Mazzola & Robert H. Schantz, 1997. "Multiple‐facility loading under capacity‐based economies of scope," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(3), pages 229-256, April.

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