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A linear relaxation heuristic for the generalized assignment problem

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  • Michael A. Trick

Abstract

We examine the basis structure of the linear relaxation of the generalized assignment problem. The basis gives a surprising amount of information. This leads to a very simple heuristic that uses only generalized network optimization codes. Lower bounds can be generated by cut generation, where the violated inequalities are found directly from the relaxation basis. An improvement heuristic with the same flavor is also presented.

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  • Michael A. Trick, 1992. "A linear relaxation heuristic for the generalized assignment problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(2), pages 137-151, March.
    • Handle: RePEc:wly:navres:v:39:y:1992:i:2:p:137-151
    DOI: 10.1002/1520-6750(199203)39:23.0.CO;2-D
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    References listed on IDEAS

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    1. G. Terry Ross & Richard M. Soland, 1977. "Modeling Facility Location Problems as Generalized Assignment Problems," Management Science, INFORMS, vol. 24(3), pages 345-357, November.
    2. McBride, Richard D., 1985. "Solving embedded generalized network problems," European Journal of Operational Research, Elsevier, vol. 21(1), pages 82-92, July.
    3. Marshall L. Fisher & R. Jaikumar & Luk N. Van Wassenhove, 1986. "A Multiplier Adjustment Method for the Generalized Assignment Problem," Management Science, INFORMS, vol. 32(9), pages 1095-1103, September.
    4. Marshall L. Fisher, 1985. "An Applications Oriented Guide to Lagrangian Relaxation," Interfaces, INFORMS, vol. 15(2), pages 10-21, April.
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    Cited by:

    1. H. Edwin Romeijn & Dolores Romero Morales, 2003. "An asymptotically optimal greedy heuristic for the multiperiod single‐sourcing problem: The cyclic case," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(5), pages 412-437, August.
    2. Mutsunori Yagiura & Toshihide Ibaraki & Fred Glover, 2004. "An Ejection Chain Approach for the Generalized Assignment Problem," INFORMS Journal on Computing, INFORMS, vol. 16(2), pages 133-151, May.
    3. Jayant R. Kalagnanam & Milind W. Dawande & Mark Trumbo & Ho Soo Lee, 2000. "The Surplus Inventory Matching Problem in the Process Industry," Operations Research, INFORMS, vol. 48(4), pages 505-516, August.
    4. Christopher Hojny & Tristan Gally & Oliver Habeck & Hendrik Lüthen & Frederic Matter & Marc E. Pfetsch & Andreas Schmitt, 2020. "Knapsack polytopes: a survey," Annals of Operations Research, Springer, vol. 292(1), pages 469-517, September.
    5. H. Edwin Romeijn & Dolores Romero Morales, 2001. "Generating Experimental Data for the Generalized Assignment Problem," Operations Research, INFORMS, vol. 49(6), pages 866-878, December.
    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. Charles H. Reilly, 2009. "Synthetic Optimization Problem Generation: Show Us the Correlations!," INFORMS Journal on Computing, INFORMS, vol. 21(3), pages 458-467, August.
    8. Hellsten, Erik Orm & Sacramento, David & Pisinger, David, 2020. "An adaptive large neighbourhood search heuristic for routing and scheduling feeder vessels in multi-terminal ports," European Journal of Operational Research, Elsevier, vol. 287(2), pages 682-698.

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