IDEAS home Printed from https://ideas.repec.org/a/eee/oprepe/v9y2022ics2214716022000203.html
   My bibliography  Save this article

A review on history, trends and perspectives of fuzzy linear programming

Author

Listed:
  • Figueroa–García, Juan Carlos
  • Hernández, Germán
  • Franco, Carlos

Abstract

This paper presents a literature review and analysis of fuzzy linear programming models and methods. This review traces back to the linear programming with fuzzy linear constraints models proposed by Hans Jürgen Zimmermann during 1974–76 which have become the seminal works for scholars and practitioners in this field due to its ease to implement and understand. To do so, we analyze the timeline of publication of the most important works in the field, evaluate the influence of relevant papers using a time-weighted index based on the amount of citations in order to provide a perspective about the future directions in fuzzy linear programming and to recommend selected books, journals and some recent contributions to readers.

Suggested Citation

  • Figueroa–García, Juan Carlos & Hernández, Germán & Franco, Carlos, 2022. "A review on history, trends and perspectives of fuzzy linear programming," Operations Research Perspectives, Elsevier, vol. 9(C).
    • Handle: RePEc:eee:oprepe:v:9:y:2022:i:c:s2214716022000203
    DOI: 10.1016/j.orp.2022.100247
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S2214716022000203
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.orp.2022.100247?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. R. E. Bellman & L. A. Zadeh, 1970. "Decision-Making in a Fuzzy Environment," Management Science, INFORMS, vol. 17(4), pages 141-164, December.
    2. Zeng, Xieting & Kang, Shaozhong & Li, Fusheng & Zhang, Lu & Guo, Ping, 2010. "Fuzzy multi-objective linear programming applying to crop area planning," Agricultural Water Management, Elsevier, vol. 98(1), pages 134-142, December.
    3. Malihe Niksirat, 2022. "Intuitionistic Fuzzy Hub Location Problems: Model and Solution Approach," Fuzzy Information and Engineering, Taylor & Francis Journals, vol. 14(1), pages 74-83, January.
    4. Boris Pérez-Cañedo & José Luis Verdegay & Eduardo René Concepción-Morales & Alejandro Rosete, 2020. "Lexicographic Methods for Fuzzy Linear Programming," Mathematics, MDPI, vol. 8(9), pages 1-21, September.
    5. A. Charnes & Frieda Granot & F. Phillips, 1977. "An Algorithm for Solving Interval Linear Programming Problems," Operations Research, INFORMS, vol. 25(4), pages 688-695, August.
    6. Stojiljković, Mirko M., 2017. "Bi-level multi-objective fuzzy design optimization of energy supply systems aided by problem-specific heuristics," Energy, Elsevier, vol. 137(C), pages 1231-1251.
    7. Sakawa, Masatoshi & Kubota, Ryo, 2000. "Fuzzy programming for multiobjective job shop scheduling with fuzzy processing time and fuzzy duedate through genetic algorithms," European Journal of Operational Research, Elsevier, vol. 120(2), pages 393-407, January.
    8. 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.
    9. Muhammad Athar Mehmood & Muhammad Akram & Majed G. Alharbi & Shahida Bashir, 2021. "Solution of Fully Bipolar Fuzzy Linear Programming Models," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-31, April.
    10. Huang, G. H. & Baetz, B. W. & Patry, G. G., 1995. "Grey fuzzy integer programming: An application to regional waste management planning under uncertainty," Socio-Economic Planning Sciences, Elsevier, vol. 29(1), pages 17-38, March.
    11. Herrera, F. & Verdegay, J. L., 1995. "Three models of fuzzy integer linear programming," European Journal of Operational Research, Elsevier, vol. 83(3), pages 581-593, June.
    12. Rommelfanger, Heinrich, 1989. "Interactive decision making in fuzzy linear optimization problems," European Journal of Operational Research, Elsevier, vol. 41(2), pages 210-217, July.
    13. Hsien-Chung Wu, 2019. "Solving Fuzzy Linear Programming Problems with Fuzzy Decision Variables," Mathematics, MDPI, vol. 7(7), pages 1-105, June.
    14. Roy, T.K. & Maiti, M., 1997. "A fuzzy EOQ model with demand-dependent unit cost under limited storage capacity," European Journal of Operational Research, Elsevier, vol. 99(2), pages 425-432, June.
    15. Elif Garajová & Milan Hladík & Miroslav Rada, 2019. "Interval linear programming under transformations: optimal solutions and optimal value range," 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. 27(3), pages 601-614, September.
    16. Dorota Kuchta, 2005. "Fuzzy solution of the linear programming problem with interval coefficients in the constraints," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 15(3-4), pages 35-42.
    17. Gen, Mitsuo & Yun, YoungSu, 2006. "Soft computing approach for reliability optimization: State-of-the-art survey," Reliability Engineering and System Safety, Elsevier, vol. 91(9), pages 1008-1026.
    18. Wang, Reay-Chen & Liang, Tien-Fu, 2005. "Applying possibilistic linear programming to aggregate production planning," International Journal of Production Economics, Elsevier, vol. 98(3), pages 328-341, December.
    19. Huang, Guo H. & Baetz, Brian W. & Patry, Gilles G., 1995. "Grey integer programming: An application to waste management planning under uncertainty," European Journal of Operational Research, Elsevier, vol. 83(3), pages 594-620, June.
    20. J W Chinneck & K Ramadan, 2000. "Linear programming with interval coefficients," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 51(2), pages 209-220, February.
    21. L Mikhailov, 2000. "A fuzzy programming method for deriving priorities in the analytic hierarchy process," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 51(3), pages 341-349, March.
    22. Rommelfanger, Heinrich, 1996. "Fuzzy linear programming and applications," European Journal of Operational Research, Elsevier, vol. 92(3), pages 512-527, August.
    23. Kumar, Manoj & Vrat, Prem & Shankar, Ravi, 2006. "A fuzzy programming approach for vendor selection problem in a supply chain," International Journal of Production Economics, Elsevier, vol. 101(2), pages 273-285, June.
    24. Ajit Singh & S. Ghosh & Pankaj Sharma, 2007. "Water quality management of a stretch of river Yamuna: An interactive fuzzy multi-objective approach," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 21(2), pages 515-532, February.
    25. Selim, Hasan & Araz, Ceyhun & Ozkarahan, Irem, 2008. "Collaborative production-distribution planning in supply chain: A fuzzy goal programming approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 44(3), pages 396-419, May.
    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. 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.
    2. Zhou, Feng & Huang, Gordon H. & Chen, Guo-Xian & Guo, Huai-Cheng, 2009. "Enhanced-interval linear programming," European Journal of Operational Research, Elsevier, vol. 199(2), pages 323-333, December.
    3. Piao, M.J. & Li, Y.P. & Huang, G.H. & Nie, S., 2015. "Risk analysis for Shanghai's electric power system under multiple uncertainties," Energy, Elsevier, vol. 87(C), pages 104-119.
    4. Mikhailov, L., 2004. "A fuzzy approach to deriving priorities from interval pairwise comparison judgements," European Journal of Operational Research, Elsevier, vol. 159(3), pages 687-704, December.
    5. Yong Zeng & Yanpeng Cai & Guohe Huang & Jing Dai, 2011. "A Review on Optimization Modeling of Energy Systems Planning and GHG Emission Mitigation under Uncertainty," Energies, MDPI, vol. 4(10), pages 1-33, October.
    6. Hu, Qing & Huang, Guohe & Cai, Yanpeng & Huang, Ying, 2011. "Feasibility-based inexact fuzzy programming for electric power generation systems planning under dual uncertainties," Applied Energy, Elsevier, vol. 88(12), pages 4642-4654.
    7. Gaiqiang Yang & Ping Guo & Mo Li & Shiqi Fang & Liudong Zhang, 2016. "An Improved Solving Approach for Interval-Parameter Programming and Application to an Optimal Allocation of Irrigation Water Problem," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(2), pages 701-729, January.
    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. Zhou, Y. & Li, Y.P. & Huang, G.H., 2015. "Planning sustainable electric-power system with carbon emission abatement through CDM under uncertainty," Applied Energy, Elsevier, vol. 140(C), pages 350-364.
    10. Gaiqiang Yang & Ping Guo & Mo Li & Shiqi Fang & Liudong Zhang, 2016. "An Improved Solving Approach for Interval-Parameter Programming and Application to an Optimal Allocation of Irrigation Water Problem," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(2), pages 701-729, January.
    11. Li, Zhong & Huang, Gordon & Zhang, Yimei & Li, Yongping, 2013. "Inexact two-stage stochastic credibility constrained programming for water quality management," Resources, Conservation & Recycling, Elsevier, vol. 73(C), pages 122-132.
    12. Zhang, Y.M. & Lu, H.W. & Nie, X.H. & He, L. & Du, P., 2014. "An interactive inexact fuzzy bounded programming approach for agricultural water quality management," Agricultural Water Management, Elsevier, vol. 133(C), pages 104-111.
    13. H. Zhu & G. Huang & P. Guo & X. Qin, 2009. "A Fuzzy Robust Nonlinear Programming Model for Stream Water Quality Management," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 23(14), pages 2913-2940, November.
    14. Sandra González-Gallardo & Ana B. Ruiz & Mariano Luque, 2021. "Analysis of the Well-Being Levels of Students in Spain and Finland through Interval Multiobjective Linear Programming," Mathematics, MDPI, vol. 9(14), pages 1-27, July.
    15. H. Mishmast Nehi & H. A. Ashayerinasab & M. Allahdadi, 2020. "Solving methods for interval linear programming problem: a review and an improved method," Operational Research, Springer, vol. 20(3), pages 1205-1229, September.
    16. Mula, Josefa & Peidro, David & Poler, Raul, 2010. "The effectiveness of a fuzzy mathematical programming approach for supply chain production planning with fuzzy demand," International Journal of Production Economics, Elsevier, vol. 128(1), pages 136-143, November.
    17. Vasant, Pandian M. & Barsoum, Nader N. & Bhattacharya, Arijit, 2008. "Possibilistic optimization in planning decision of construction industry," International Journal of Production Economics, Elsevier, vol. 111(2), pages 664-675, February.
    18. Jyotiba Gurav & D. Regulwar, 2012. "Multi Objective Sustainable Irrigation Planning with Decision Parameters and Decision Variables Fuzzy in Nature," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(10), pages 3005-3021, August.
    19. Berna Tektaş & Hasan Hüseyin Turan & Nihat Kasap & Ferhan Çebi & Dursun Delen, 2022. "A Fuzzy Prescriptive Analytics Approach to Power Generation Capacity Planning," Energies, MDPI, vol. 15(9), pages 1-26, April.
    20. Li, Y.P. & Huang, G.H. & Chen, X., 2011. "An interval-valued minimax-regret analysis approach for the identification of optimal greenhouse-gas abatement strategies under uncertainty," Energy Policy, Elsevier, vol. 39(7), pages 4313-4324, July.

    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:eee:oprepe:v:9:y:2022:i:c:s2214716022000203. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/operations-research-perspectives .

    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.