IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v22y1974i4p802-807.html
   My bibliography  Save this article

Application of Programs with Maximin Objective Functions to Problems of Optimal Resource Allocation

Author

Listed:
  • Seymour Kaplan

    (New York University, New York, New York)

Abstract

A mathematical program with a maximin objective function is defined as an optimization problem of the following type: Maxz = min i c i x i , subject to AX = b, X ≧ 0. Although the c i can be in the interval (− ∞, ∞), the paper discusses the more common practical case where all c i ≧ 0. It shows that problems of this type arise in a variety of applications where it is required to maximize a production function of the “fixed proportion” type subject to a set of linear constraints. Although it is well known that the solution to this type of problem can be found by linear programming, this paper shows that, if the existence of a certain condition can be demonstrated, then a simplified method can be used to determine the optimum solution. Many problems of practical interest can be solved by this simplified method; an example involving the readiness of a ship is presented.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:22:y:1974:i:4:p:802-807
    DOI: 10.1287/opre.22.4.802
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.22.4.802
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.22.4.802?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. 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.
    2. 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.
    3. 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.
    4. Hanan Luss, 1999. "On Equitable Resource Allocation Problems: A Lexicographic Minimax Approach," Operations Research, INFORMS, vol. 47(3), pages 361-378, June.
    5. M Kumral, 2011. "Incorporating geo-metallurgical information into mine production scheduling," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(1), pages 60-68, January.
    6. Buchanan, John & Gardiner, Lorraine, 2003. "A comparison of two reference point methods in multiple objective mathematical programming," European Journal of Operational Research, Elsevier, vol. 149(1), pages 17-34, August.
    7. 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.
    8. Takahito Kuno & Kouji Mori & Hiroshi Konno, 1989. "A mofified gub algorithm for solving linear minimax problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(3), pages 311-320, June.
    9. Aparna Jayaram & R. K. Amit & Amit Agarwal & Xiaodong Luo, 2024. "Elasticity-integrated pricing and allocation heuristic for airline revenue management," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 23(4), pages 305-317, August.
    10. 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.
    11. 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.
    12. K. Mathur & M. Puri & S. Bansal, 1995. "On ranking of feasible solutions of a 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. 3(2), pages 265-283, December.

    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:22:y:1974:i:4:p:802-807. 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.