Article Sidebar

Download
PDF
Statistic
Read Counter : 952 Download : 698

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Main Article Content

Abstract

The linear fractional transportation problem (LFTP) is widely encountered as a particular type of transportation problem (TP) in real-life. In this paper, a novel algorithm, based on the traditional definition of continuity, is presented to solve the LFTP. An iterative constraint is constructed by combining the objective function of the LFTP and the supply-demand condition since the fractional objective function is continuous at every point of the feasible region. By this constraint obtained, LFTP is converted into an iterative linear programming (LP) problem to reach the optimum solution. In this study, the case of asymptotic solution for LFTP is discussed for the first time in the literature. The numerical examples are performed for the linear and asymptotic cases to illustrate the method, and the approach proposed is compared with the other existing methods to demonstrate the efficiency of the algorithm. Also, an application had environmentalist objective is solved by proposed mathematical method using the software general algebraic modeling system (GAMS) with data set of the real case. Finally, some computational results from tests performed on randomly generated large-scale transportation problems are provided.

Keywords

Linear fractional programming Fractional transportation problem Iterative method Mixed constraints Optimization

Article Details

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Authors who publish with this journal agree to the following License

CC BY: This license allows reusers to distribute, remix, adapt, and build upon the material in any medium or format, so long as attribution is given to the creator. The license allows for commercial use.

 

How to Cite
Akin Bas, S., Gonce Kocken, H., & Ahlatcioglu Ozkok, B. (2022). A novel iterative method to solve a linear fractional transportation problem. Pakistan Journal of Statistics and Operation Research, 18(1), 151-166. https://doi.org/10.18187/pjsor.v18i1.3889
Crossref
Scopus
Google Scholar
Europe PMC

References

  1. Anukokila, P., Radhakrishnan, B., & Anju, A. (2019). Goal programming approach for solving multi-objective fractional transportation problem with fuzzy parameters. RAIRO-Operations Research, 53(1), 157-178.
  2. Bajalinov, E. B. (2003). Linear-fractional programming theory, methods, applications and software (Vol. 84). Springer Science & Business Media.
  3. Bitran, G. R., & Novaes, A. G. (1973). Linear programming with a fractional objective function. Operations Research, 21(1), 22-29.
  4. Cetin, N., & Tiryaki, F. (2014). A fuzzy approach using generalized dinkelbach's algorithm for multiobjective linear fractional transportation problem. Mathematical Problems in Engineering, 2014.
  5. Charnes, A., & Cooper, W. W. (1962). Programming with linear fractional functionals. Naval Research logistics quarterly, 9(3â€4), 181-186.
  6. Gupta, A., Khanna, S., & Puri, M. C. (1993). A paradox in linear fractional transportation problems with mixed constraints. Optimization, 27(4), 375-387.
  7. Gupta, K., & Arora, R. (2017). Solving the problem of industry by finding paradox in fractional plus fractional capacitated transportation problem. Advanced Modeling and Optimization, 19(2).
  8. Gupta, S., Ali, I., & Ahmed, A. (2018). Multi-choice multi-objective capacitated transportation problem—a case study of uncertain demand and supply. Journal of Statistics and Management Systems, 21(3), 467-491.
  9. Güzel, N., Emiroglu, Y., Tapci, F., Guler, C., & Syvry, M. (2012). A solution proposal to the interval fractional transportation problem.
  10. Javaid, S., Jalil, S. A., & Asim, Z. (2017). A model for uncertain multi-objective transportation problem with fractional objectives. Int J Oper Res, 14(1), 11-25.
  11. Liu, S. T. (2016). Fractional transportation problem with fuzzy parameters. Soft computing, 20(9), 3629-3636.
  12. Moanta, D. (2007). Some aspects on solving a linear fractional transportation problem. Journal of Applied Quantitative Methods, 2(3), 343-348.
  13. Ozkok, B. A. (2020). An iterative algorithm to solve a linear fractional programming problem. Computers & Industrial Engineering, 140, 106234.
  14. Pradhan A., Biswal, M. P. (2015, December) Computational methodology for linear fractional transportation problem. In 2015 Winter Simulation Conference (WSC), 3158-3159 IEEE.
  15. Raina, A. A., Gupta, S., & Kour, K. (2018). Fractional Transportation Problem with non-linear discount cost. Sri Lankan Journal of Applied Statistics, 18, 3.
  16. Sadia, S., Gupta, N., & Ali, Q. M. (2016). Multiobjective capacitated fractional transportation problem with mixed constraints. Math Sci Lett, 5(3), 235-242.
  17. Safi, M. R., & Ghasemi, S. M. (2017). Uncertainty in linear fractional transportation problem. International Journal of Nonlinear Analysis and Applications, 8(1), 81-93.
  18. Schaible, S. (1981). Fractional programming: applications and algorithms. European Journal of Operational Research, 7(2), 111-120.
  19. Sheikhi, A., Karbassi, S. M., & Bidabadi, N. (2018). A New Method for Solving Bi-Objective Fractional Transportation Problems.
  20. Sivri, M., Emiroglu, I., Guler, C., & Tasci, F. (2011, April). A solution proposal to the transportation problem with the linear fractional objective function. In 2011 Fourth International Conference on Modeling, Simulation and Applied Optimization (pp. 1-9). IEEE.
  21. Swarup, K. (1966). Transportation technique in linear fractional functional programming. Journal of royal naval scientific service, 21(5), 256-260.
  22. Tantawy, S. F. (2008). A new procedure for solving linear fractional programming problems. Mathematical and Computer Modelling, 48(5-6), 969-973.