IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v205y2010i1p42-46.html
   My bibliography  Save this article

Generalized linear fractional programming under interval uncertainty

Author

Listed:
  • Hladík, Milan

Abstract

Data in many real-life engineering and economical problems suffer from inexactness. Herein we assume that we are given some intervals in which the data can simultaneously and independently perturb. We consider a generalized linear fractional programming problem with interval data and present an efficient method for computing the range of optimal values. The method reduces the problem to solving from two to four real-valued generalized linear fractional programs, which can be computed in polynomial time using an appropriate interior point method solver. We consider also the inverse problem: How much can data of a real generalized linear fractional program vary such that the optimal values do not exceed some prescribed bounds. We propose a method for calculating (often the largest possible) ranges of admissible variations; it needs to solve only two real-valued generalized linear fractional programs. We illustrate the approach on a simple von Neumann economic growth model.

Suggested Citation

  • Hladík, Milan, 2010. "Generalized linear fractional programming under interval uncertainty," European Journal of Operational Research, Elsevier, vol. 205(1), pages 42-46, August.
    • Handle: RePEc:eee:ejores:v:205:y:2010:i:1:p:42-46
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(10)00026-3
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Nesterov, Y. & Nemirovskii, A., 1995. "An interior-point method for generalized linear-fractional programming," LIDAM Reprints CORE 1168, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Schaible, Siegfried & Ibaraki, Toshidide, 1983. "Fractional programming," European Journal of Operational Research, Elsevier, vol. 12(4), pages 325-338, April.
    3. Castrodeza, Carmen & Lara, Pablo & Pena, Teresa, 2005. "Multicriteria fractional model for feed formulation: economic, nutritional and environmental criteria," Agricultural Systems, Elsevier, vol. 86(1), pages 76-96, October.
    4. Li, Wu, 2008. "A multi-agent growth model based on the von Neumann-Leontief framework," MPRA Paper 11302, University Library of Munich, Germany.
    5. 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.
    6. J. v. Neumann, 1945. "A Model of General Economic Equilibrium," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 13(1), pages 1-9.
    7. Liu, Shiang-Tai, 2008. "Posynomial geometric programming with interval exponents and coefficients," European Journal of Operational Research, Elsevier, vol. 186(1), pages 17-27, April.
    8. Wu, X.Y. & Huang, G.H. & Liu, L. & Li, J.B., 2006. "An interval nonlinear program for the planning of waste management systems with economies-of-scale effects--A case study for the region of Hamilton, Ontario, Canada," European Journal of Operational Research, Elsevier, vol. 171(2), pages 349-372, June.
    9. Schaible, Siegfried, 1981. "Fractional programming: Applications and algorithms," European Journal of Operational Research, Elsevier, vol. 7(2), pages 111-120, June.
    10. Caballero, Rafael & Hernandez, Monica, 2006. "Restoration of efficiency in a goal programming problem with linear fractional criteria," European Journal of Operational Research, Elsevier, vol. 172(1), pages 31-39, July.
    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. Nie, S. & Huang, Charley Z. & Huang, G.H. & Li, Y.P. & Chen, J.P. & Fan, Y.R. & Cheng, G.H., 2016. "Planning renewable energy in electric power system for sustainable development under uncertainty – A case study of Beijing," Applied Energy, Elsevier, vol. 162(C), pages 772-786.
    2. Jeyakumar, V. & Li, G.Y. & Srisatkunarajah, S., 2013. "Strong duality for robust minimax fractional programming problems," European Journal of Operational Research, Elsevier, vol. 228(2), pages 331-336.
    3. C. Ren & P. Guo & M. Li & J. Gu, 2013. "Optimization of Industrial Structure Considering the Uncertainty of Water Resources," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(11), pages 3885-3898, September.
    4. Li, Mo & Guo, Ping & Singh, Vijay P., 2016. "An efficient irrigation water allocation model under uncertainty," Agricultural Systems, Elsevier, vol. 144(C), pages 46-57.
    5. Zhu, H. & Huang, W.W. & Huang, G.H., 2014. "Planning of regional energy systems: An inexact mixed-integer fractional programming model," Applied Energy, Elsevier, vol. 113(C), pages 500-514.

    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. Milan Hladík, 2011. "Optimal value bounds in nonlinear programming with interval data," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 93-106, July.
    2. Bo Zhang & YueLin Gao & Xia Liu & XiaoLi Huang, 2022. "An Outcome-Space-Based Branch-and-Bound Algorithm for a Class of Sum-of-Fractions Problems," Journal of Optimization Theory and Applications, Springer, vol. 192(3), pages 830-855, March.
    3. Abderrahman Bouhamidi & Mohammed Bellalij & Rentsen Enkhbat & Khalid Jbilou & Marcos Raydan, 2018. "Conditional Gradient Method for Double-Convex Fractional Programming Matrix Problems," Journal of Optimization Theory and Applications, Springer, vol. 176(1), pages 163-177, January.
    4. Illes, Tibor & Szirmai, Akos & Terlaky, Tamas, 1999. "The finite criss-cross method for hyperbolic programming," European Journal of Operational Research, Elsevier, vol. 114(1), pages 198-214, April.
    5. Ching-Feng Wen & Hsien-Chung Wu, 2011. "Using the Dinkelbach-type algorithm to solve the continuous-time linear fractional programming problems," Journal of Global Optimization, Springer, vol. 49(2), pages 237-263, February.
    6. Ching-Feng Wen & Hsien-Chung Wu, 2012. "Using the parametric approach to solve the continuous-time linear fractional max–min problems," Journal of Global Optimization, Springer, vol. 54(1), pages 129-153, September.
    7. Goedhart, Marc H. & Spronk, Jaap, 1995. "Financial planning with fractional goals," European Journal of Operational Research, Elsevier, vol. 82(1), pages 111-124, April.
    8. Tunjo Perić & Josip Matejaš & Zoran Babić, 2023. "Advantages, sensitivity and application efficiency of the new iterative method to solve multi-objective linear fractional programming problem," 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. 31(3), pages 751-767, September.
    9. X. Qin & G. Huang, 2009. "An Inexact Chance-constrained Quadratic 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(4), pages 661-695, March.
    10. Sakawa, Masatoshi & Kato, Kosuke, 1998. "An interactive fuzzy satisficing method for structured multiobjective linear fractional programs with fuzzy numbers," European Journal of Operational Research, Elsevier, vol. 107(3), pages 575-589, June.
    11. Zacharias Bragoudakis & Evangelia Kasimati & Christos Pierros & Nikolaos Rodousakis & George Soklis, 2022. "Measuring Productivities for the 38 OECD Member Countries: An Input-Output Modelling Approach," Mathematics, MDPI, vol. 10(13), pages 1-21, July.
    12. Arthur Brackmann Netto, 2017. "The Double Edge of Case-Studies: A Frame-Based Definition of Economic Models," Working Papers, Department of Economics 2017_21, University of São Paulo (FEA-USP).
    13. Pham, Manh D. & Zelenyuk, Valentin, 2019. "Weak disposability in nonparametric production analysis: A new taxonomy of reference technology sets," European Journal of Operational Research, Elsevier, vol. 274(1), pages 186-198.
    14. Amir, Shmuel, 1995. "Welfare maximization in economic theory: Another viewpoint," Structural Change and Economic Dynamics, Elsevier, vol. 6(3), pages 359-376, August.
    15. Bogliacino, Francesco & Rampa, Giorgio, 2014. "Expectational bottlenecks and the emerging of new organizational forms," Structural Change and Economic Dynamics, Elsevier, vol. 29(C), pages 28-39.
    16. Caspar Sauter, 2014. "How should we measure environmental policy stringency? A new approach," IRENE Working Papers 14-01, IRENE Institute of Economic Research.
    17. Matheus Assaf, 2017. "Coast to Coast: How MIT's students linked the Solow model and optimal growth theory," Working Papers, Department of Economics 2017_20, University of São Paulo (FEA-USP).
    18. Heinz D. Kurz, 2011. "The Contributions of Two Eminent Japanese Scholars to the Development of Economic Theory: Michio Morishima and Takashi Negishi," Chapters, in: Heinz D. Kurz & Tamotsu Nishizawa & Keith Tribe (ed.), The Dissemination of Economic Ideas, chapter 13, Edward Elgar Publishing.
    19. Rashed Khanjani Shiraz & Madjid Tavana & Debora Di Caprio & Hirofumi Fukuyama, 2016. "Solving Geometric Programming Problems with Normal, Linear and Zigzag Uncertainty Distributions," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 1075-1078, September.
    20. Soyster, A.L. & Murphy, F.H., 2013. "A unifying framework for duality and modeling in robust linear programs," Omega, Elsevier, vol. 41(6), pages 984-997.

    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:ejores:v:205:y:2010:i:1:p:42-46. 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.elsevier.com/locate/eor .

    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.