IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v28y1980i2p403-418.html
   My bibliography  Save this article

Bounds on the Effect of Aggregating Variables in Linear Programs

Author

Listed:
  • Paul H. Zipkin

    (Columbia University, New York, New York)

Abstract

This paper explores the effects of aggregating variables in large linear programs. We define a reasonable criterion for the resulting loss in accuracy, and derive bounds on this quantity. A posteriori bounds may be calculated after solving the aggregated problem, and a priori bounds before. Also, we show that standard iterative methods can be used to improve the accuracy of a given aggregated problem. A numerical example illustrates the results.

Suggested Citation

  • Paul H. Zipkin, 1980. "Bounds on the Effect of Aggregating Variables in Linear Programs," Operations Research, INFORMS, vol. 28(2), pages 403-418, April.
    • Handle: RePEc:inm:oropre:v:28:y:1980:i:2:p:403-418
    DOI: 10.1287/opre.28.2.403
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.28.2.403
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.28.2.403?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Fleischmann, Moritz & Kloos, Konstantin & Nouri, Maryam & Pibernik, Richard, 2020. "Single-period stochastic demand fulfillment in customer hierarchies," European Journal of Operational Research, Elsevier, vol. 286(1), pages 250-266.
    2. 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.
    3. Haugen, Kjetil K., 1996. "A Stochastic Dynamic Programming model for scheduling of offshore petroleum fields with resource uncertainty," European Journal of Operational Research, Elsevier, vol. 88(1), pages 88-100, January.
    4. Alonso-Ayuso, Antonio & Carvallo, Felipe & Escudero, Laureano F. & Guignard, Monique & Pi, Jiaxing & Puranmalka, Raghav & Weintraub, Andrés, 2014. "Medium range optimization of copper extraction planning under uncertainty in future copper prices," European Journal of Operational Research, Elsevier, vol. 233(3), pages 711-726.
    5. 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.
    6. John Turner, 2012. "The Planning of Guaranteed Targeted Display Advertising," Operations Research, INFORMS, vol. 60(1), pages 18-33, February.
    7. Klaassen, Pieter, 1997. "Solving stochastic programming models for asset/liability management using iterative disaggregation," Serie Research Memoranda 0010, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    8. 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.
    9. 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).
    10. 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.
    11. Merrick, James H., 2016. "On representation of temporal variability in electricity capacity planning models," Energy Economics, Elsevier, vol. 59(C), pages 261-274.
    12. Merrick, James H. & Bistline, John E.T. & Blanford, Geoffrey J., 2024. "On representation of energy storage in electricity planning models," Energy Economics, Elsevier, vol. 136(C).
    13. 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.
    14. Jornsten, Kurt & Leisten, Rainer, 1995. "Decomposition and iterative aggregation in hierarchical and decentralised planning structures," European Journal of Operational Research, Elsevier, vol. 86(1), pages 120-141, October.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. Kremer, Mirko & Schneeweiss, Christoph & Zimmermann, Michael, 2006. "On the validity of aggregate models in designing supply chain contracts," International Journal of Production Economics, Elsevier, vol. 103(2), pages 656-666, October.
    20. 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.
    21. Beltran-Royo, C., 2017. "Two-stage stochastic mixed-integer linear programming: The conditional scenario approach," Omega, Elsevier, vol. 70(C), pages 31-42.
    22. 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.
    23. 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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:28:y:1980:i:2:p:403-418. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.