IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v98y1998i1d10.1023_a1022601301102.html
   My bibliography  Save this article

Min-Max Optimization of Several Classical Discrete Optimization Problems

Author

Listed:
  • G. Yu

    (University of Texas at Austin)

Abstract

In this paper, we study discrete optimization problems with min-max objective functions. This type of problems has direct applications in the recent development of robust optimization. The following well-known classes of problems are discussed: minimum spanning tree problem, resource allocation problem with separable cost functions, and production control problem. Computational complexities of the corresponding min-max version of the above-mentioned problems are analyzed. Pseudopolynomial algorithms for these problems are provided under certain conditions.

Suggested Citation

  • G. Yu, 1998. "Min-Max Optimization of Several Classical Discrete Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 98(1), pages 221-242, July.
    • Handle: RePEc:spr:joptap:v:98:y:1998:i:1:d:10.1023_a:1022601301102
    DOI: 10.1023/A:1022601301102
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1022601301102
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1022601301102?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
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Stephen Jacobsen, 1971. "On Marginal Allocation in Single Constraint Min-Max Problems," Management Science, INFORMS, vol. 17(11), pages 780-783, July.
    2. Bazaraa, Mokhtar S. & Goode, Jamie J., 1982. "An algorithm for solving linearly constrained minimax problems," European Journal of Operational Research, Elsevier, vol. 11(2), pages 158-166, October.
    3. Pang, Jong-Shi & Chang-Sung, Yu, 1989. "A min-max resource allocation problem with substitutions," European Journal of Operational Research, Elsevier, vol. 41(2), pages 218-223, July.
    4. Czuchra, Waldemar, 1986. "A graphical method to solve a maximin allocation problem," European Journal of Operational Research, Elsevier, vol. 26(2), pages 259-261, August.
    5. Seymour Kaplan, 1974. "Application of Programs with Maximin Objective Functions to Problems of Optimal Resource Allocation," Operations Research, INFORMS, vol. 22(4), pages 802-807, August.
    6. Gang Yu, 1996. "On the Max-Min 0-1 Knapsack Problem with Robust Optimization Applications," Operations Research, INFORMS, vol. 44(2), pages 407-415, April.
    7. Rachelle S. Klein & Hanan Luss & Uriel G. Rothblum, 1993. "Minimax Resource Allocation Problems with Resource-Substitutions Represented by Graphs," Operations Research, INFORMS, vol. 41(5), pages 959-971, October.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. V. Jeyakumar & J. Vicente-Pérez, 2014. "Dual Semidefinite Programs Without Duality Gaps for a Class of Convex Minimax Programs," Journal of Optimization Theory and Applications, Springer, vol. 162(3), pages 735-753, September.
    2. Eduardo Conde, 2014. "A Minmax Regret Linear Regression Model Under Uncertainty in the Dependent Variable," Journal of Optimization Theory and Applications, Springer, vol. 160(2), pages 573-596, February.
    3. Uhan, Nelson A., 2015. "Stochastic linear programming games with concave preferences," European Journal of Operational Research, Elsevier, vol. 243(2), pages 637-646.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hanan Luss, 1999. "On Equitable Resource Allocation Problems: A Lexicographic Minimax Approach," Operations Research, INFORMS, vol. 47(3), pages 361-378, June.
    2. Hanan Luss & Donald R. Smith, 1988. "Multiperiod allocation of limited resources: A minimax approach," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(4), pages 493-501, August.
    3. Sbihi, Abdelkader, 2010. "A cooperative local search-based algorithm for the Multiple-Scenario Max-Min Knapsack Problem," European Journal of Operational Research, Elsevier, vol. 202(2), pages 339-346, April.
    4. Klein, Rachelle S. & Luss, Hanan & Rothblum, Uriel G., 1995. "Multiperiod allocation of substitutable resources," European Journal of Operational Research, Elsevier, vol. 85(3), pages 488-503, September.
    5. Yamada, Takeo & Futakawa, Mayumi & Kataoka, Seiji, 1998. "Some exact algorithms for the knapsack sharing problem," European Journal of Operational Research, Elsevier, vol. 106(1), pages 177-183, April.
    6. Fujimoto, Masako & Yamada, Takeo, 2006. "An exact algorithm for the knapsack sharing problem with common items," European Journal of Operational Research, Elsevier, vol. 171(2), pages 693-707, June.
    7. Alexandre Belloni & Mitchell J. Lovett & William Boulding & Richard Staelin, 2012. "Optimal Admission and Scholarship Decisions: Choosing Customized Marketing Offers to Attract a Desirable Mix of Customers," Marketing Science, INFORMS, vol. 31(4), pages 621-636, July.
    8. Jinfa Chen & David D. Yao & Shaohui Zheng, 2001. "Optimal Replenishment and Rework with Multiple Unreliable Supply Sources," Operations Research, INFORMS, vol. 49(3), pages 430-443, June.
    9. Alireza Amirteimoori & Simin Masrouri, 2021. "DEA-based competition strategy in the presence of undesirable products: An application to paper mills," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 31(2), pages 5-21.
    10. Stephen A. Smith & Narendra Agrawal, 2000. "Management of Multi-Item Retail Inventory Systems with Demand Substitution," Operations Research, INFORMS, vol. 48(1), pages 50-64, February.
    11. Muralidharan S. Kodialam & Hanan Luss, 1998. "Algorithms for Separable Nonlinear Resource Allocation Problems," Operations Research, INFORMS, vol. 46(2), pages 272-284, April.
    12. I. Stancu-Minasian & R. Caballero & E. Cerdá & M. Muñoz, 1999. "The stochastic bottleneck linear programming problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(1), pages 123-143, June.
    13. Christian Schmitt & Bismark Singh, 2024. "Quadratic Optimization Models for Balancing Preferential Access and Fairness: Formulations and Optimality Conditions," INFORMS Journal on Computing, INFORMS, vol. 36(5), pages 1150-1167, September.
    14. J.L. Zhang & X.S. Zhang, 2003. "Sequential Penalty Algorithm for Nonlinear Constrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 118(3), pages 635-655, September.
    15. Kasin Ransikarbum & Scott J. Mason, 2016. "Multiple-objective analysis of integrated relief supply and network restoration in humanitarian logistics operations," International Journal of Production Research, Taylor & Francis Journals, vol. 54(1), pages 49-68, January.
    16. Fabrice Talla Nobibon & Roel Leus, 2014. "Complexity Results and Exact Algorithms for Robust Knapsack Problems," Journal of Optimization Theory and Applications, Springer, vol. 161(2), pages 533-552, May.
    17. Richard Francis & Timothy Lowe, 2014. "Comparative error bound theory for three location models: continuous demand versus discrete demand," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 144-169, April.
    18. Adam Kasperski & Paweł Zieliński, 2009. "A randomized algorithm for the min-max selecting items problem with uncertain weights," Annals of Operations Research, Springer, vol. 172(1), pages 221-230, November.
    19. Ogryczak, Wlodzimierz & Wierzbicki, Adam & Milewski, Marcin, 2008. "A multi-criteria approach to fair and efficient bandwidth allocation," Omega, Elsevier, vol. 36(3), pages 451-463, June.
    20. Shahparvari, Shahrooz & Chhetri, Prem & Abbasi, Babak & Abareshi, Ahmad, 2016. "Enhancing emergency evacuation response of late evacuees: Revisiting the case of Australian Black Saturday bushfire," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 93(C), pages 148-176.

    More about this item

    Keywords

    ;
    ;
    ;

    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:spr:joptap:v:98:y:1998:i:1:d:10.1023_a:1022601301102. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.