IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v322y2023i2d10.1007_s10479-022-05114-3.html
   My bibliography  Save this article

Allocation of limited resources under quadratic constraints

Author

Listed:
  • Richárd Kicsiny

    (Hungarian University of Agriculture and Life Sciences)

  • Levente Hufnagel

    (Hungarian University of Agriculture and Life Sciences)

  • Zoltán Varga

    (Research Institute of Multidisciplinary Ecotheology, John Wesley Theological College)

Abstract

The proper allocation/distribution of limited resources is a traditional problem with various applications. The mathematical formulation of such problems usually includes constraints describing the set of feasible solutions (feasible set), from which the (nearly) optimal or equilibrium solution should be selected. Often the feasible set is more difficult to determine than to find the optimal or equilibrium solution. Alternatively, the already known feasible set often makes it easier to select the optimal or equilibrium solution. In some other cases, any feasible solutions are the same satisfactory, additional optimization is needless. Accordingly, the main or only task in many cases is to determine the feasible set itself. In the paper, a new theorem is proved for the explicit expression of properly assigned (dependent) variables by means of the other (independent) variables in a system of inequality and quadratic equality constraints. The sum of the (nonnegative) variables can be either prefixed or not. The constraints may describe the feasible set in various resource allocation tasks (possibly in optimization or game-theoretical contexts) or in other problems. Two new lemmas are proved for supporting the proof of the above mentioned theorem, nevertheless, they can also be considered independent results, which may help future mathematical derivations. Supported by a further new lemma, a practical algorithm is derived for assigning in a feasible way the independent variables, to which (possibly limited) arbitrary nonnegative values can be prescribed. Various practical examples are provided to facilitate utilizing the results.

Suggested Citation

  • Richárd Kicsiny & Levente Hufnagel & Zoltán Varga, 2023. "Allocation of limited resources under quadratic constraints," Annals of Operations Research, Springer, vol. 322(2), pages 793-817, March.
    • Handle: RePEc:spr:annopr:v:322:y:2023:i:2:d:10.1007_s10479-022-05114-3
    DOI: 10.1007/s10479-022-05114-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-022-05114-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10479-022-05114-3?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Sana Bouajaja & Najoua Dridi, 2017. "A survey on human resource allocation problem and its applications," Operational Research, Springer, vol. 17(2), pages 339-369, July.
    2. Richárd Kicsiny, 2017. "Solution for a class of closed-loop leader-follower games with convexity conditions on the payoffs," Annals of Operations Research, Springer, vol. 253(1), pages 405-429, June.
    3. Kranich, Laurence, 2020. "Resource-envy-free and efficient allocations: A new solution for production economies with dedicated factors," Journal of Mathematical Economics, Elsevier, vol. 89(C), pages 1-7.
    4. Patriksson, Michael, 2008. "A survey on the continuous nonlinear resource allocation problem," European Journal of Operational Research, Elsevier, vol. 185(1), pages 1-46, February.
    Full references (including those not matched with items on IDEAS)

    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. Thijs Klauw & Marco E. T. Gerards & Johann L. Hurink, 2017. "Resource allocation problems in decentralized energy management," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(3), pages 749-773, July.
    2. Alireza Pooya & Morteza Pakdaman, 2021. "A new continuous time optimal control model for manpower planning with promotion from inside the system," Operational Research, Springer, vol. 21(1), pages 349-364, March.
    3. Jungho Park & Hadi El-Amine & Nevin Mutlu, 2021. "An Exact Algorithm for Large-Scale Continuous Nonlinear Resource Allocation Problems with Minimax Regret Objectives," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 1213-1228, July.
    4. Kenneth David Strang, 2012. "Man versus math: Behaviorist exploration of post-crisis non-banking asset management," Journal of Asset Management, Palgrave Macmillan, vol. 13(5), pages 348-367, October.
    5. Richárd Kicsiny & Zoltán Varga, 2023. "New algorithm for checking Pareto optimality in bimatrix games," Annals of Operations Research, Springer, vol. 320(1), pages 235-259, January.
    6. Lee, Zu-Hsu & Deng, Shiming & Lin, Beixin & Yang, James G.S., 2010. "Decision model and analysis for investment interest expense deduction and allocation," European Journal of Operational Research, Elsevier, vol. 200(1), pages 268-280, January.
    7. Christopher Dance & Alexei Gaivoronski, 2012. "Stochastic optimization for real time service capacity allocation under random service demand," Annals of Operations Research, Springer, vol. 193(1), pages 221-253, March.
    8. Jacobovic, Royi & Kella, Offer, 2020. "Minimizing a stochastic convex function subject to stochastic constraints and some applications," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 7004-7018.
    9. Seyed Hamid Reza Pasandideh & Seyed Taghi Akhavan Niaki & Reza Abdollahi, 2020. "Modeling and solving a bi-objective joint replenishment-location problem under incremental discount: MOHSA and NSGA-II," Operational Research, Springer, vol. 20(4), pages 2365-2396, December.
    10. Sathaye, Nakul & Madanat, Samer, 2012. "A bottom-up optimal pavement resurfacing solution approach for large-scale networks," Transportation Research Part B: Methodological, Elsevier, vol. 46(4), pages 520-528.
    11. Sathaye, Nakul & Madanat, Samer, 2011. "A bottom-up solution for the multi-facility optimal pavement resurfacing problem," Transportation Research Part B: Methodological, Elsevier, vol. 45(7), pages 1004-1017, August.
    12. Hadi El-Amine & Ebru K. Bish & Douglas R. Bish, 2018. "Robust Postdonation Blood Screening Under Prevalence Rate Uncertainty," Operations Research, INFORMS, vol. 66(1), pages 1-17, 1-2.
    13. Martijn H. H. Schoot Uiterkamp & Marco E. T. Gerards & Johann L. Hurink, 2022. "On a Reduction for a Class of Resource Allocation Problems," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1387-1402, May.
    14. Yuichi Takano & Nobuaki Ishii & Masaaki Muraki, 2017. "Multi-period resource allocation for estimating project costs in competitive bidding," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 25(2), pages 303-323, June.
    15. Strang, Kenneth David, 2012. "Importance of verifying queue model assumptions before planning with simulation software," European Journal of Operational Research, Elsevier, vol. 218(2), pages 493-504.
    16. Itay Gurvich & Ward Whitt, 2009. "Scheduling Flexible Servers with Convex Delay Costs in Many-Server Service Systems," Manufacturing & Service Operations Management, INFORMS, vol. 11(2), pages 237-253, June.
    17. Julia de Frutos Cachorro & Guiomar Martín-Herrán & Mabel Tidball, 2022. "Stackelberg competition in groundwater resources with multiple uses," UB School of Economics Working Papers 2022/431, University of Barcelona School of Economics.
    18. Akiyoshi Shioura & Natalia V. Shakhlevich & Vitaly A. Strusevich & Bernhard Primas, 2018. "Models and algorithms for energy-efficient scheduling with immediate start of jobs," Journal of Scheduling, Springer, vol. 21(5), pages 505-516, October.
    19. Kicsiny, R., 2019. "Differential game model with discretized solution for distributing heat produced by solar heating systems," Renewable Energy, Elsevier, vol. 140(C), pages 330-340.
    20. Friedrich, Ulf & Münnich, Ralf & de Vries, Sven & Wagner, Matthias, 2015. "Fast integer-valued algorithms for optimal allocations under constraints in stratified sampling," Computational Statistics & Data Analysis, Elsevier, vol. 92(C), pages 1-12.

    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:annopr:v:322:y:2023:i:2:d:10.1007_s10479-022-05114-3. 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.