IDEAS home Printed from https://ideas.repec.org/a/spr/fuzodm/v15y2016i4d10.1007_s10700-016-9231-2.html
   My bibliography  Save this article

Bilevel linear programming with ambiguous objective function of the follower

Author

Listed:
  • Masahiro Inuiguchi

    (Osaka University)

  • Puchit Sariddichainunta

    (Osaka University)

Abstract

Bilevel linear optimization problems are the linear optimization problems with two sequential decision steps of the leader and the follower. In this paper, we focus on the ambiguity of coefficients of the follower in his objective function that hinder the leader from exactly calculating the rational response of the follower. Under the assumption that the follower’s possible range of the ambiguous coefficient vector is known as a certain convex polytope, the leader can deduce the possible set of rational responses of the follower. The leader further assumes that the follower’s response is the worst-case scenario to his objective function, and then makes a decision according to the maximin criteria. We thus formulate the bilevel linear optimization problem with ambiguous objective function of the follower as a special kind of three-level programming problem. In our formulation, we show that the optimal solution locates on the extreme point and propose a solution method based on the enumeration of possible rational responses of the follower. A numerical example is used to illustrate our proposed computational method.

Suggested Citation

  • Masahiro Inuiguchi & Puchit Sariddichainunta, 2016. "Bilevel linear programming with ambiguous objective function of the follower," Fuzzy Optimization and Decision Making, Springer, vol. 15(4), pages 415-434, December.
    • Handle: RePEc:spr:fuzodm:v:15:y:2016:i:4:d:10.1007_s10700-016-9231-2
    DOI: 10.1007/s10700-016-9231-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10700-016-9231-2
    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/s10700-016-9231-2?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. Wang, S. & Huang, G.H., 2015. "A multi-level Taguchi-factorial two-stage stochastic programming approach for characterization of parameter uncertainties and their interactions: An application to water resources management," European Journal of Operational Research, Elsevier, vol. 240(2), pages 572-581.
    2. Aihong Ren & Yuping Wang, 2014. "A cutting plane method for bilevel linear programming with interval coefficients," Annals of Operations Research, Springer, vol. 223(1), pages 355-378, December.
    3. Jimenez, Mariano & Arenas, Mar & Bilbao, Amelia & Rodri'guez, M. Victoria, 2007. "Linear programming with fuzzy parameters: An interactive method resolution," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1599-1609, March.
    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. Puchit Sariddichainunta & Masahiro Inuiguchi, 2017. "Global optimality test for maximin solution of bilevel linear programming with ambiguous lower-level objective function," Annals of Operations Research, Springer, vol. 256(2), pages 285-304, September.

    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. Changyu Zhou & Guohe Huang & Jiapei Chen, 2018. "A Multi-Objective Energy and Environmental Systems Planning Model: Management of Uncertainties and Risks for Shanxi Province, China," Energies, MDPI, vol. 11(10), pages 1-21, October.
    2. Zhalechian, M. & Tavakkoli-Moghaddam, R. & Zahiri, B. & Mohammadi, M., 2016. "Sustainable design of a closed-loop location-routing-inventory supply chain network under mixed uncertainty," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 89(C), pages 182-214.
    3. Peidro, David & Mula, Josefa & Jiménez, Mariano & del Mar Botella, Ma, 2010. "A fuzzy linear programming based approach for tactical supply chain planning in an uncertainty environment," European Journal of Operational Research, Elsevier, vol. 205(1), pages 65-80, August.
    4. Azra Ghobadi & Mohammad Fallah & Reza Tavakkoli-Moghaddam & Hamed Kazemipoor, 2022. "A Fuzzy Two-Echelon Model to Optimize Energy Consumption in an Urban Logistics Network with Electric Vehicles," Sustainability, MDPI, vol. 14(21), pages 1-31, October.
    5. Zhengping Liu & Wang Zhang & Hongxian Liu & Guohe Huang & Jiliang Zhen & Xin Qi, 2019. "Characterization of Renewable Energy Utilization Mode for Air-Environmental Quality Improvement through an Inexact Factorial Optimization Approach," Sustainability, MDPI, vol. 11(8), pages 1-19, April.
    6. Mohammed, Ahmed & Wang, Qian, 2017. "The fuzzy multi-objective distribution planner for a green meat supply chain," International Journal of Production Economics, Elsevier, vol. 184(C), pages 47-58.
    7. Olcay Polat & Duygu Topaloğlu, 2019. "Milk Collection Network Design In A Fuzzy Environment," Economy & Business Journal, International Scientific Publications, Bulgaria, vol. 13(1), pages 376-384.
    8. Majdi Argoubi & Haifa Jammeli & Hatem Masri, 2020. "The intellectual structure of the waste management field," Annals of Operations Research, Springer, vol. 294(1), pages 655-676, November.
    9. Javid Ghahremani-Nahr & Hamed Nozari & Maryam Rahmaty & Parvaneh Zeraati Foukolaei & Azita Sherejsharifi, 2023. "Development of a Novel Fuzzy Hierarchical Location-Routing Optimization Model Considering Reliability," Logistics, MDPI, vol. 7(3), pages 1-16, September.
    10. Dattatray Regulwar & Jyotiba Gurav, 2011. "Irrigation Planning Under Uncertainty—A Multi Objective Fuzzy Linear Programming Approach," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 25(5), pages 1387-1416, March.
    11. Niu, G. & Li, Y.P. & Huang, G.H. & Liu, J. & Fan, Y.R., 2016. "Crop planning and water resource allocation for sustainable development of an irrigation region in China under multiple uncertainties," Agricultural Water Management, Elsevier, vol. 166(C), pages 53-69.
    12. Kargar, Bahareh & Pishvaee, Mir Saman & Jahani, Hamed & Sheu, Jiuh-Biing, 2020. "Organ transportation and allocation problem under medical uncertainty: A real case study of liver transplantation," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 134(C).
    13. Mohammad Kanan & Muhammad Salman Habib & Tufail Habib & Sadaf Zahoor & Anas Gulzar & Hamid Raza & Zaher Abusaq, 2022. "A Flexible Robust Possibilistic Programming Approach for Sustainable Second-Generation Biogas Supply Chain Design under Multiple Uncertainties," Sustainability, MDPI, vol. 14(18), pages 1-32, September.
    14. Mohammadi, M. & Torabi, S.A. & Tavakkoli-Moghaddam, R., 2014. "Sustainable hub location under mixed uncertainty," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 62(C), pages 89-115.
    15. Patoghi, Amirhosein & Mousavi, Seyed Meysam, 2021. "A new approach for material ordering and multi-mode resource constraint project scheduling problem in a multi-site context under interval-valued fuzzy uncertainty," Technological Forecasting and Social Change, Elsevier, vol. 173(C).
    16. Sonia Irshad Mari & Young Hae Lee & Muhammad Saad Memon, 2016. "Sustainable and Resilient Garment Supply Chain Network Design with Fuzzy Multi-Objectives under Uncertainty," Sustainability, MDPI, vol. 8(10), pages 1-22, October.
    17. Naoum-Sawaya, Joe & Ghaddar, Bissan & Arandia, Ernesto & Eck, Bradley, 2015. "Simulation-optimization approaches for water pump scheduling and pipe replacement problems," European Journal of Operational Research, Elsevier, vol. 246(1), pages 293-306.
    18. Mohammad Mehdi Nasrabadi & Mohammad Ali Yaghoobi & Mashaallah Mashinchi, 2010. "Solution algorithms for a class of continuous linear programs with fuzzy valued objective functions," Fuzzy Information and Engineering, Springer, vol. 2(1), pages 5-26, March.
    19. Amin Mahmoudi & Saad Ahmed Javed & Abbas Mardani, 2022. "Gresilient supplier selection through Fuzzy Ordinal Priority Approach: decision-making in post-COVID era," Operations Management Research, Springer, vol. 15(1), pages 208-232, June.
    20. Yu, L. & Li, Y.P. & Huang, G.H., 2019. "Planning municipal-scale mixed energy system for stimulating renewable energy under multiple uncertainties - The City of Qingdao in Shandong Province, China," Energy, Elsevier, vol. 166(C), pages 1120-1133.

    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:fuzodm:v:15:y:2016:i:4:d:10.1007_s10700-016-9231-2. 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.