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The power of linear programming: some surprising and unexpected LPs

Author

Listed:
  • Bruce Golden

    (University of Maryland)

  • Linus Schrage

    (The University of Chicago)

  • Douglas Shier

    (Clemson University)

  • Lida Anna Apergi

    (University of Maryland)

Abstract

Linear programming has had a tremendous impact in the modeling and solution of a great diversity of applied problems, especially in the efficient allocation of resources. As a result, this methodology forms the backbone of introductory courses in operations research. What students, and others, may not appreciate is that linear programming transcends its linear nomenclature and can be applied to an even wider range of important practical problems. The objective of this article is to present a selection, and just a selection, from this range of problems that at first blush do not seem amenable to linear programming formulation. The exposition focuses on the most basic models in these selected applications, with pointers to more elaborate formulations and extensions. Thus, our intent is to expand the modeling awareness of those first encountering linear programming. In addition, we hope this article will be of interest to those who teach linear programming and to seasoned academics and practitioners, alike.

Suggested Citation

  • Bruce Golden & Linus Schrage & Douglas Shier & Lida Anna Apergi, 2021. "The power of linear programming: some surprising and unexpected LPs," 4OR, Springer, vol. 19(1), pages 15-40, March.
    • Handle: RePEc:spr:aqjoor:v:19:y:2021:i:1:d:10.1007_s10288-020-00441-2
    DOI: 10.1007/s10288-020-00441-2
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    References listed on IDEAS

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    1. Flavell, RB, 1976. "A new goal programming formulation," Omega, Elsevier, vol. 4(6), pages 731-732.
    2. Emrouznejad, Ali & Yang, Guo-liang, 2018. "A survey and analysis of the first 40 years of scholarly literature in DEA: 1978–2016," Socio-Economic Planning Sciences, Elsevier, vol. 61(C), pages 4-8.
    3. G. Dantzig & R. Fulkerson & S. Johnson, 1954. "Solution of a Large-Scale Traveling-Salesman Problem," Operations Research, INFORMS, vol. 2(4), pages 393-410, November.
    4. Todd Retchless & Bruce Golden & Edward Wasil, 2007. "Ranking US Army Generals of the 20th Century: A Group Decision-Making Application of the Analytic Hierarchy Process," Interfaces, INFORMS, vol. 37(2), pages 163-175, April.
    5. G Appa, 2002. "On the uniqueness of solutions to linear programs," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(10), pages 1127-1132, October.
    6. A. Charnes & W. W. Cooper, 1962. "Programming with linear fractional functionals," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 9(3‐4), pages 181-186, September.
    7. Ali Emrouznejad & Marianna Marra, 2017. "The state of the art development of AHP (1979–2017): a literature review with a social network analysis," International Journal of Production Research, Taylor & Francis Journals, vol. 55(22), pages 6653-6675, November.
    8. A. Charnes & C. E. Lemke, 1954. "Minimization of non‐linear separable convex functionals," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 1(4), pages 301-312, December.
    9. Freed, Ned & Glover, Fred, 1981. "Simple but powerful goal programming models for discriminant problems," European Journal of Operational Research, Elsevier, vol. 7(1), pages 44-60, May.
    10. Yoram Wind & Thomas L. Saaty, 1980. "Marketing Applications of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 26(7), pages 641-658, July.
    11. Willy Gochet & Antonie Stam & V. Srinivasan & Shaoxiang Chen, 1997. "Multigroup Discriminant Analysis Using Linear Programming," Operations Research, INFORMS, vol. 45(2), pages 213-225, April.
    12. Dylan Jones & Mehrdad Tamiz, 2010. "Practical Goal Programming," International Series in Operations Research and Management Science, Springer, edition 1, number 978-1-4419-5771-9, December.
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    Cited by:

    1. Yves Crama & Michel Grabisch & Silvano Martello, 2024. "21 volumes for the 21st century," 4OR, Springer, vol. 22(1), pages 1-16, March.
    2. Bruce Golden & Linus Schrage & Douglas Shier & Lida Anna Apergi, 2024. "The unexpected power of linear programming: an updated collection of surprising applications," Annals of Operations Research, Springer, vol. 343(2), pages 573-605, December.
    3. Yves Crama & Michel Grabisch & Silvano Martello, 2024. "Still more surveys in operations research…," Annals of Operations Research, Springer, vol. 343(2), pages 559-571, December.

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