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Using error bounds to compare aggregated generalized transportation models

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  • Igor Litvinchev
  • Socorro Rangel

Abstract

A comparative study of aggregation error bounds for the generalized transportation problem is presented. A priori and a posteriori error bounds were derived and a computational study was performed to (a) test the correlation between the a priori, the a posteriori, and the actual error and (b) quantify the difference of the error bounds from the actual error. Based on the results we conclude that calculating the a priori error bound can be considered as a useful strategy to select the appropriate aggregation level. The a posteriori error bound provides a good quantitative measure of the actual error. Copyright Springer Science+Business Media, LLC 2006

Suggested Citation

  • Igor Litvinchev & Socorro Rangel, 2006. "Using error bounds to compare aggregated generalized transportation models," Annals of Operations Research, Springer, vol. 146(1), pages 119-134, September.
    • Handle: RePEc:spr:annopr:v:146:y:2006:i:1:p:119-134:10.1007/s10479-006-0051-6
    DOI: 10.1007/s10479-006-0051-6
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    References listed on IDEAS

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    1. Hallefjord, Asa & Jornsten, Kurt O. & Varbrand, Peter, 1993. "Solving large scale generalized assignment problems -- An aggregation / disaggregation approach," European Journal of Operational Research, Elsevier, vol. 64(1), pages 103-114, January.
    2. David F. Rogers & Robert D. Plante & Richard T. Wong & James R. Evans, 1991. "Aggregation and Disaggregation Techniques and Methodology in Optimization," Operations Research, INFORMS, vol. 39(4), pages 553-582, August.
    3. Paul H. Zipkin, 1980. "Bounds on the Effect of Aggregating Variables in Linear Programs," Operations Research, INFORMS, vol. 28(2), pages 403-418, April.
    4. D. Klingman & A. Napier & J. Stutz, 1974. "NETGEN: A Program for Generating Large Scale Capacitated Assignment, Transportation, and Minimum Cost Flow Network Problems," Management Science, INFORMS, vol. 20(5), pages 814-821, January.
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    Cited by:

    1. John Turner, 2012. "The Planning of Guaranteed Targeted Display Advertising," Operations Research, INFORMS, vol. 60(1), pages 18-33, February.

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