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A Class of Fractional Programming Problems

Author

Listed:
  • Y. Almogy

    (Technion—Israel Institute of Technology, Haifa, Israel)

  • O. Levin

    (Technion—Israel Institute of Technology, Haifa, Israel)

Abstract

The paper deals with problems of maximizing a sum of linear or concave-convex fractional functions on closed and bounded polyhedral sets. It shows that, under certain assumptions, problems of this type can be transformed into equivalent ones of maximizing multiparameter linear or concave functions subject to additional feasibility constraints. The problems are transformed into those finding roots of monotone-decreasing convex functions. Where the objective function is separable, such a root is unique, and any local optimum is a global one, i.e., the objective function is quasi-concave. In problems involving separable linear fractional functions, under some additional assumptions, the parametric presentation results in a combinational property. Where the number of terms in the objective function is equal or less than three, this property leads to an efficient algorithm.

Suggested Citation

  • Y. Almogy & O. Levin, 1971. "A Class of Fractional Programming Problems," Operations Research, INFORMS, vol. 19(1), pages 57-67, February.
    • Handle: RePEc:inm:oropre:v:19:y:1971:i:1:p:57-67
    DOI: 10.1287/opre.19.1.57
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    Cited by:

    1. Suvasis Nayak & Akshay Kumar Ojha, 2019. "Solution approach to multi-objective linear fractional programming problem using parametric functions," OPSEARCH, Springer;Operational Research Society of India, vol. 56(1), pages 174-190, March.
    2. S. Morteza Mirdehghan & Hassan Rostamzadeh, 2016. "Finding the Efficiency Status and Efficient Projection in Multiobjective Linear Fractional Programming: A Linear Programming Technique," Journal of Optimization, Hindawi, vol. 2016, pages 1-8, September.
    3. Vandana Goyal & Namrata Rani & Deepak Gupta, 2022. "Rouben Ranking Function and parametric approach to quadratically constrained multiobjective quadratic fractional programming with trapezoidal fuzzy number coefficients," 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. 13(2), pages 923-932, April.
    4. Vandana Goyal & Namrata Rani & Deepak Gupta, 2022. "An algorithm for quadratically constrained multi-objective quadratic fractional programming with pentagonal fuzzy numbers," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 32(1), pages 49-71.
    5. H. J. Chen & S. Schaible & R. L. Sheu, 2009. "Generic Algorithm for Generalized Fractional Programming," Journal of Optimization Theory and Applications, Springer, vol. 141(1), pages 93-105, April.
    6. Ruan, N. & Gao, D.Y., 2015. "Global solutions to fractional programming problem with ratio of nonconvex functions," Applied Mathematics and Computation, Elsevier, vol. 255(C), pages 66-72.
    7. Li, Yifu & Qi, Xiangtong, 2022. "A geometric branch-and-bound algorithm for the service bundle design problem," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1044-1056.
    8. Vandana Goyal & Namrata Rani & Deepak Gupta, 2021. "Parametric approach to quadratically constrained multi-level multi-objective quadratic fractional programming," OPSEARCH, Springer;Operational Research Society of India, vol. 58(3), pages 557-574, September.
    9. J.-Y. Lin & S. Schaible & R.-L. Sheu, 2010. "Minimization of Isotonic Functions Composed of Fractions," Journal of Optimization Theory and Applications, Springer, vol. 146(3), pages 581-601, September.
    10. Hosseinalifam, M. & Marcotte, P. & Savard, G., 2016. "A new bid price approach to dynamic resource allocation in network revenue management," European Journal of Operational Research, Elsevier, vol. 255(1), pages 142-150.
    11. Juan S. Borrero & Colin Gillen & Oleg A. Prokopyev, 2017. "Fractional 0–1 programming: applications and algorithms," Journal of Global Optimization, Springer, vol. 69(1), pages 255-282, September.
    12. Mojtaba Borza & Azmin Sham Rambely, 2021. "A Linearization to the Sum of Linear Ratios Programming Problem," Mathematics, MDPI, vol. 9(9), pages 1-10, April.

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