IDEAS home Printed from https://ideas.repec.org/a/wut/journl/v2y2019p77-88id1421.html
   My bibliography  Save this article

Generating a set of compromise solutions of a multi objective linear programming problem through game theory

Author

Listed:
  • Mustafa Sivri
  • Hale Gonce Kocken
  • Inci Albayrak
  • Sema Akin

Abstract

Most of real-life problems, including design, optimization, scheduling and control, etc., are inherently characterized by multiple conflicting objectives, and thus multi-objective linear programming (MOLP) problems are frequently encountered in the literature. One of the biggest difficulties in solving MOLP problems lies in the trade-off among objectives. Since the optimal solution of one objective may lead other objective(s) to bad results, all objectives must be optimized simultaneously. Additionally, the obtained solution will not satisfy all the objectives in the same satisfaction degree. Thus, it will be useful to generate a set of compromise solutions in order to present it to the decision maker (DM). With this motivation, after determining a modified payoff matrix for MOLP, all possible ratios are formed between all rows. These ratio matrices are considered a two person zero-sum game and solved by linear programming (LP) approach. Taking into consideration the results of the related game, the original MOLP problem is converted to a single objective LP problem. Since there exist numerous ratio matrices, a set of compromise solutions is obtained for MOLP problem. Numerical examples are used to demonstrate this approach.

Suggested Citation

  • Mustafa Sivri & Hale Gonce Kocken & Inci Albayrak & Sema Akin, 2019. "Generating a set of compromise solutions of a multi objective linear programming problem through game theory," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 29(2), pages 77-88.
    • Handle: RePEc:wut:journl:v:2:y:2019:p:77-88:id:1421
    DOI: 10.37190/ord190205
    as

    Download full text from publisher

    File URL: https://ord.pwr.edu.pl/assets/papers_archive/1421%20-%20published.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.37190/ord190205?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
    ---><---

    References listed on IDEAS

    as
    1. Carlos Romero & Francisco Amador & Antonio Barco, 1987. "Multiple Objectives in Agricultural Planning: A Compromise Programming Application," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 69(1), pages 78-86.
    2. Lahdelma, Risto & Miettinen, Kaisa & Salminen, Pekka, 2005. "Reference point approach for multiple decision makers," European Journal of Operational Research, Elsevier, vol. 164(3), pages 785-791, August.
    3. Cococcioni, Marco & Pappalardo, Massimo & Sergeyev, Yaroslav D., 2018. "Lexicographic multi-objective linear programming using grossone methodology: Theory and algorithm," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 298-311.
    4. Sabri, Ehap H. & Beamon, Benita M., 2000. "A multi-objective approach to simultaneous strategic and operational planning in supply chain design," Omega, Elsevier, vol. 28(5), pages 581-598, October.
    5. Das, S. K. & Goswami, A. & Alam, S. S., 1999. "Multiobjective transportation problem with interval cost, source and destination parameters," European Journal of Operational Research, Elsevier, vol. 117(1), pages 100-112, August.
    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. Pokharel, Shaligram, 2008. "A two objective model for decision making in a supply chain," International Journal of Production Economics, Elsevier, vol. 111(2), pages 378-388, February.
    2. Hashem Omrani & Farzane Adabi & Narges Adabi, 2017. "Designing an efficient supply chain network with uncertain data: a robust optimization—data envelopment analysis approach," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(7), pages 816-828, July.
    3. Podinovski, Vladislav V., 2020. "Maximum likelihood solutions for multicriterial choice problems," European Journal of Operational Research, Elsevier, vol. 286(1), pages 299-308.
    4. Al-Husain, Raed & Khorramshahgol, Reza, 2020. "Incorporating analytical hierarchy process and goal programming to design responsive and efficient supply chains," Operations Research Perspectives, Elsevier, vol. 7(C).
    5. Augustine Esogbue & Qiang Song & Donovan Young, 2006. "Non-Euler–Lagrangian Pareto-optimality Conditions for Dynamic Multiple Criterion Decision Problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(3), pages 525-542, July.
    6. Das, Kanchan, 2011. "Integrating effective flexibility measures into a strategic supply chain planning model," European Journal of Operational Research, Elsevier, vol. 211(1), pages 170-183, May.
    7. Pérez-Mesa, Juan Carlos & Galdeano-Gómez, Emilio & Salinas Andújar, Jose A., 2012. "Logistics network and externalities for short sea transport: An analysis of horticultural exports from southeast Spain," Transport Policy, Elsevier, vol. 24(C), pages 188-198.
    8. Lakshminarayan, P. G. & Atwood, J. D. & Johnson, Stanley R. & Sposito, V. A., 1991. "Compromise Solution for Economic-Environmental Decisions in Agriculture," Staff General Research Papers Archive 375, Iowa State University, Department of Economics.
    9. Qian Zhou & Shuxiang Wang, 2021. "Study on the Relations of Supply Chain Digitization, Flexibility and Sustainable Development—A Moderated Multiple Mediation Model," Sustainability, MDPI, vol. 13(18), pages 1-19, September.
    10. Chan, Chi Kin & Lee, Y.C.E. & Campbell, J.F., 2013. "Environmental performance—Impacts of vendor–buyer coordination," International Journal of Production Economics, Elsevier, vol. 145(2), pages 683-695.
    11. R. Pelissari & M. C. Oliveira & S. Ben Amor & A. Kandakoglu & A. L. Helleno, 2020. "SMAA methods and their applications: a literature review and future research directions," Annals of Operations Research, Springer, vol. 293(2), pages 433-493, October.
    12. Rezapour, Shabnam & Allen, Janet K. & Mistree, Farrokh, 2015. "Uncertainty propagation in a supply chain or supply network," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 73(C), pages 185-206.
    13. Zuo-Jun Max Shen & Mark S. Daskin, 2005. "Trade-offs Between Customer Service and Cost in Integrated Supply Chain Design," Manufacturing & Service Operations Management, INFORMS, vol. 7(3), pages 188-207, September.
    14. Sujeet Kumar Singh & Shiv Prasad Yadav, 2018. "Intuitionistic fuzzy multi-objective linear programming problem with various membership functions," Annals of Operations Research, Springer, vol. 269(1), pages 693-707, October.
    15. Saraiva, Joao Paulo & Pinheiro, Antonio Cipriano, 2007. "A Multi-Criteria Approach for Irrigation Water Management," Agricultural Economics Review, Greek Association of Agricultural Economists, vol. 8(1), pages 1-13, January.
    16. Farahani, Reza Zanjirani & Rezapour, Shabnam & Drezner, Tammy & Fallah, Samira, 2014. "Competitive supply chain network design: An overview of classifications, models, solution techniques and applications," Omega, Elsevier, vol. 45(C), pages 92-118.
    17. Stokes, Jeffrey R. & Tozer, Peter R., 2002. "Sire selection with multiple objectives," Agricultural Systems, Elsevier, vol. 73(2), pages 147-164, August.
    18. Irfan Ali & Srikant Gupta & Aquil Ahmed, 2019. "Multi-objective linear fractional inventory problem under intuitionistic fuzzy environment," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 10(2), pages 173-189, April.
    19. Luis Diaz-Balteiro & Carlos Iglesias-Merchan & Carlos Romero & Silvestre García de Jalón, 2020. "The Sustainable Management of Land and Fisheries Resources Using Multicriteria Techniques: A Meta-Analysis," Land, MDPI, vol. 9(10), pages 1-18, October.
    20. Ahmad Rezaee & Farzad Dehghanian & Behnam Fahimnia & Benita Beamon, 2017. "Green supply chain network design with stochastic demand and carbon price," Annals of Operations Research, Springer, vol. 250(2), pages 463-485, March.

    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:wut:journl:v:2:y:2019:p:77-88:id:1421. 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: Adam Kasperski (email available below). General contact details of provider: https://edirc.repec.org/data/iopwrpl.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.