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Bounds for Row-Aggregation in Linear Programming

Author

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  • Paul H. Zipkin

    (Columbia University, New York, New York)

Abstract

Most applied linear programs reflect a certain degree of aggregation—either explicit or implicit—of some larger, more detailed problem. This paper develops methods for assessing the loss in accuracy resulting from aggregation. We showed previously that, when columns only are aggregated, a feasible solution to the larger problem can be recovered. This may not be the case under row-aggregation. Several reasonable measures of “accuracy loss” for this case are defined, and the bounds on these quantities derived. These results enable the modeler to compare and evaluate alternative approximate models of the same problem.

Suggested Citation

  • Paul H. Zipkin, 1980. "Bounds for Row-Aggregation in Linear Programming," Operations Research, INFORMS, vol. 28(4), pages 903-916, August.
    • Handle: RePEc:inm:oropre:v:28:y:1980:i:4:p:903-916
    DOI: 10.1287/opre.28.4.903
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    Cited by:

    1. Bjørndal, Endre & Jörnsten, Kurt, 2009. "Lower and upper bounds for linear production games," European Journal of Operational Research, Elsevier, vol. 196(2), pages 476-486, July.
    2. Fu Lin & Sven Leyffer & Todd Munson, 2016. "A two-level approach to large mixed-integer programs with application to cogeneration in energy-efficient buildings," Computational Optimization and Applications, Springer, vol. 65(1), pages 1-46, September.
    3. Merrick, James H. & Weyant, John P., 2019. "On choosing the resolution of normative models," European Journal of Operational Research, Elsevier, vol. 279(2), pages 511-523.
    4. Merrick, James H., 2016. "On representation of temporal variability in electricity capacity planning models," Energy Economics, Elsevier, vol. 59(C), pages 261-274.
    5. Oded Berman & Dmitry Krass, 2005. "An Improved IP Formulation for the Uncapacitated Facility Location Problem: Capitalizing on Objective Function Structure," Annals of Operations Research, Springer, vol. 136(1), pages 21-34, April.
    6. M S Sodhi & C S Tang, 2011. "Determining supply requirement in the sales-and-operations-planning (S&OP) process under demand uncertainty: a stochastic programming formulation and a spreadsheet implementation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(3), pages 526-536, March.
    7. John Turner, 2012. "The Planning of Guaranteed Targeted Display Advertising," Operations Research, INFORMS, vol. 60(1), pages 18-33, February.
    8. Gonzato, Sebastian & Bruninx, Kenneth & Delarue, Erik, 2021. "Long term storage in generation expansion planning models with a reduced temporal scope," Applied Energy, Elsevier, vol. 298(C).
    9. James H. Merrick & John E. T. Bistline & Geoffrey J. Blanford, 2021. "On representation of energy storage in electricity planning models," Papers 2105.03707, arXiv.org, revised May 2021.
    10. Knolmayer, Gerhard, 1981. "A simulation study of simplification strategies in the development of optimization models," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 96, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    11. Murwan Siddig & Yongjia Song, 2022. "Adaptive partition-based SDDP algorithms for multistage stochastic linear programming with fixed recourse," Computational Optimization and Applications, Springer, vol. 81(1), pages 201-250, January.
    12. Teichgraeber, Holger & Brandt, Adam R., 2022. "Time-series aggregation for the optimization of energy systems: Goals, challenges, approaches, and opportunities," Renewable and Sustainable Energy Reviews, Elsevier, vol. 157(C).
    13. Ali Fattahi & Sriram Dasu & Reza Ahmadi, 2023. "Peak-Load Energy Management by Direct Load Control Contracts," Management Science, INFORMS, vol. 69(5), pages 2788-2813, May.
    14. Beltran-Royo, C., 2017. "Two-stage stochastic mixed-integer linear programming: The conditional scenario approach," Omega, Elsevier, vol. 70(C), pages 31-42.
    15. Sodhi, ManMohan S. & Tang, Christopher S., 2009. "Modeling supply-chain planning under demand uncertainty using stochastic programming: A survey motivated by asset-liability management," International Journal of Production Economics, Elsevier, vol. 121(2), pages 728-738, October.
    16. David P. Morton & R. Kevin Wood, 1999. "Restricted-Recourse Bounds for Stochastic Linear Programming," Operations Research, INFORMS, vol. 47(6), pages 943-956, December.
    17. Julia Higle & Suvrajeet Sen, 2006. "Multistage stochastic convex programs: Duality and its implications," Annals of Operations Research, Springer, vol. 142(1), pages 129-146, February.
    18. Alexander H. Gose & Brian T. Denton, 2016. "Sequential Bounding Methods for Two-Stage Stochastic Programs," INFORMS Journal on Computing, INFORMS, vol. 28(2), pages 351-369, May.
    19. ManMohan S. Sodhi, 2005. "LP Modeling for Asset-Liability Management: A Survey of Choices and Simplifications," Operations Research, INFORMS, vol. 53(2), pages 181-196, April.
    20. Yankai Cao & Carl D. Laird & Victor M. Zavala, 2016. "Clustering-based preconditioning for stochastic programs," Computational Optimization and Applications, Springer, vol. 64(2), pages 379-406, June.
    21. Srinivasa, Anand V. & Wilhelm, Wilbert E., 1997. "A procedure for optimizing tactical response in oil spill clean up operations," European Journal of Operational Research, Elsevier, vol. 102(3), pages 554-574, November.

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