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A GOLDEN SECTION METHOD FOR THE MULTI-OBJECTIVE FRACTIONAL SOLID TRANSPORTATION PROBLEM USING THE EXPONENTIAL MEMBERSHIP FUNCTION

Year 2022, Volume: 18 Issue: 1, 121 - 141, 01.04.2022

Abstract

The multi-objective Solid Transportation Problem (MSTP) is type of vector minimization (or maximization) problem with three parameters: source, destination, and mode of transport. It may have fractional objective functions in real-life applications to maximize the profitability ratio like profit/cost or profit/time. We refer to such transportation problems as the Multi-objective Fractional Solid Transportation Problem (MFSTP). In this article is presented a fuzzy approach that combines the usage of linear programming and the golden section algorithm with linear and exponential membership functions and a strongly efficient solution is obtained. Finally, a numerical example from the literature is solved to show the solution algorithm and a comparison is presented with the solution found by using a linear membership function.

Supporting Institution

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

References

  • Ammar, E. E., and Khalifa, H. A. (2014). “Study on multi-objective solid transportation problem with fuzzy numbers”. European Journal of Scientific Research, Vol. 125, No. 1, pp. 7-19.
  • Anitha Kumari, T., Venkateswarlu, B., and Akilbasha, A. (2021). “Optimizing a fully rough interval integer solid transportation problems”. Journal of Intelligent and Fuzzy Systems, Vol. 41, Issue 1, pp. 2429–2439.
  • Anuradha, D., Jayalakshmi, M., Deepa, G., and Sujatha, V. (2019). “Solution of multi-objective solid transportation problem in fuzzy approach”. In AIP Conference Proceedings, Vol. 2177, Issue 1.
  • Basu, M., and Acharya, D. P. (2002). “On quadratic fractional generalized solid BI-criterion transportation problem”. Journal of Applied Mathematics and Computing, Vol. 10, Issue 1–2, pp.131–143.
  • Bit, A. K., Biswal, M. P., and Alam, S. S. (1993). “Fuzzy programming approach to multiobjective solid transportation problem”. Fuzzy Sets and Systems, Vol. 57, Issue 2, pp. 183-194.
  • Cadenas J. M., and Jimenez, F. (1994). “A genetic algorithm for the multi-objective solid transportation problem: A fuzzy approach”. In Proceedings for the Dedicated Conferences on Mechatronics and Supercomputing Applications in the Transportation Industries, Aachen, Germany, pp. 327–334.
  • Cui, Q., and Sheng, Y. (2013). “Uncertain Programming Model for Solid Transportation Problem”. International Information Institute, 15, pp. 342-348.
  • Dalman, H. (2016). “A fuzzy approach for interval multiobjective solid transportation problem”. New Trends in Mathematical Sciences, Vol. 4, No. 4, pp. 114-127.
  • Gen, M., Ida, K., Li, Y., and Kubota E. (1995). “Solving bicriteria solid transportation problem with fuzzy numbers by a genetic algorithm”. Computers and Industrial Engineering, Vol. 29, Issue 1-4, pp. 537-541.
  • Ida, K., Gen, M., and Li, Y. (1995). “Solving multicriteria solid transportation problem with fuzzy numbers by genetic algorithms”. In European Congress on Intelligent Techniques and Soft Computing (EUFIT' 95), Aachen, Germany, pp. 434- 441.
  • Jana, S. H., and Jana, B. (2020). “Application of fuzzy programming techniques to solve solid transportation problem with additional constraints”. Operations Research and Decisions, Vol. 30, No. 1, pp. 67-84.
  • Jimenez, F., and Verdegay, J. L. (1998). “Uncertain solid transportation problems”. Fuzzy sets and Systems, Vol. 100, Issues 1-3, pp. 45-57.
  • Jimenez, F., and Verdegay, L. J. (1999). “Solving fuzzy solid transportation problem by an evolutionary algorithm based on parametric approach”. European Journal of Operational Research, Vol. 117, Issue 3, pp. 485- 510.
  • Khalifa, H. A. E. (2019). “Fuzzy Compromise Approach for Solving Interval-Valued Fractional Multi-Objective Multi-Product Solid Transportation Problems”. Journal of System Management, Issue 2, pp. 1–20.
  • Khalifa, H. A., and Al-Shabi, M. (2018). “Utilizing of Fractional Programming for Multi-Objective Multi-Item Solid Transportation Problems in Fuzzy Environment”. International Journal of Current Research, Vol.10, Issue 11, pp. 75024-75035.
  • Khalifa, H. A.W., Kumar P., and Alharbi, M. G. (2021). “On characterizing solution for multi-objective fractional two-stage solid transportation problem under fuzzy environment”. Journal of İntelligent Systems, Vol.30, Issue 1, pp. 620-635.
  • Kumar, G. N., and Dutta, D. (2015). “Solving multi- objective fuzzy solid transportation problem based on expected value and the goal programming approach”. IOSR Journal of Mathematics, Vol. 11, Issue 2, pp. 88- 96.
  • Li, Y., Ida, K., and Gen, M. (1997). “Improved genetic algorithm for solving multiobjective solid transportation problem with fuzzy numbers”. Japan Society for Fuzzy Theory and Systems, Vol. 9, No. 2, pp. 239-250
  • Nagarajan, A., Jeyaraman, K., and Krishna Prabha, S. (2014). “Multi- objective solid transportation problem with interval cost in source and demand parameters”. International Journal of Computer & Organization Trends, Vol. 4, Issue 3, pp. 24-32.
  • Ojha, A., Das, B., Mondal, S., and Maiti, M. (2009). “An entropy based solid transportation problem for general fuzzy costs and time with fuzzy equality”. Mathematical Computation Model, Vol. 50, No. 1-2, pp. 166- 178.
  • Ojha, A., Mondal, S. K., & Maiti, M. (2014). A solid transportation problem with partial nonlinear transportation cost. Journal of Applied and Computational Mathematics, 3(150), 1-6.
  • Pandian, P., and Anuradha, D. (2010). “A new approach for solving solid transportation problems”. Applied Mathematical Sciences, Vol. 4, No. 69-72, pp. 3603-3610.
  • Radhakrishnan, B., and Anukokila, P. (2014). “Fractional Goal Programming for Fuzzy Solid Transportation Problem with Interval Cost”. Fuzzy Information and Engineering, Vol. 6, Issue 3, pp. 359–377.
  • Sakawa M., and Yano, H. (1988). “An interactive fuzzy satisficing method for multiobjective linear fractional programming problems”. Fuzzy Sets and Systems, Vol. 28, Issue 2, pp. 129-144.
  • Sakawa, M., and Yumine, T. (1983). “Interactive fuzzy decision-making for multiobjective linear fractional programming problems”. Large Scale Systems, 5, pp. 105-113.
  • Singh, S., Pradhan, A., and Biswal, M. P. (2019). “Multi-objective solid transportation problem under stochastic environment”. Sadhana - Academy Proceedings in Engineering Sciences, 44(5).
  • Sobana, V. E., and Anuradha, D. (2018). “Solution of Solid Transportation Problem in Fuzzy Approach”. International Journal of Pure and Applied Mathematics, Vol. 119, No. 9, pp. 313–321.
  • Tao, Z., and Xu, J. (2012). “A class of rough multiple objective programming and its application to solid transportation problem”. Information Sciences, Vol. 188, pp. 215–235.

ÇOK AMAÇLI ÜÇ BOYUTLU KESİRLİ TAŞIMA PROBLEMİ İÇİN ÜSTEL ÜYELİK FONKSİYONU KULLANARAK ALTIN ORAN METODU

Year 2022, Volume: 18 Issue: 1, 121 - 141, 01.04.2022

Abstract

Çok amaçlı üç boyutlu taşıma problemi kaynak, varış yeri ve taşıma şekli parametrelerine sahip vektör minimizasyon (veya maksimizasyon) probleminin özel bir tipidir. Amaçları, kârlılık oranının- kâr/maliyet veya kâr/zaman- maksimizasyonu gibi iki lineer fonksiyonun oranı olabilir. Bu tür problemler, Çok Amaçlı Kesirli Üç Boyutlu Taşıma Problemi olarak adlandırılmaktadır. Bu çalışmada, lineer programlama ve altın oran yönteminin lineer ve üstel üyelik fonksiyonları ile kullanıldığı bulanık bir yaklaşım sunulmakta ve pareto-optimal bir çözüm elde edilmektedir. Son olarak, çözüm yöntemini göstermek için literatürden sayısal bir örnek çözülmüş ve doğrusal üyelik fonksiyonu kullanılarak elde edilen çözümle bir karşılaştırma yapılmıştır.

References

  • Ammar, E. E., and Khalifa, H. A. (2014). “Study on multi-objective solid transportation problem with fuzzy numbers”. European Journal of Scientific Research, Vol. 125, No. 1, pp. 7-19.
  • Anitha Kumari, T., Venkateswarlu, B., and Akilbasha, A. (2021). “Optimizing a fully rough interval integer solid transportation problems”. Journal of Intelligent and Fuzzy Systems, Vol. 41, Issue 1, pp. 2429–2439.
  • Anuradha, D., Jayalakshmi, M., Deepa, G., and Sujatha, V. (2019). “Solution of multi-objective solid transportation problem in fuzzy approach”. In AIP Conference Proceedings, Vol. 2177, Issue 1.
  • Basu, M., and Acharya, D. P. (2002). “On quadratic fractional generalized solid BI-criterion transportation problem”. Journal of Applied Mathematics and Computing, Vol. 10, Issue 1–2, pp.131–143.
  • Bit, A. K., Biswal, M. P., and Alam, S. S. (1993). “Fuzzy programming approach to multiobjective solid transportation problem”. Fuzzy Sets and Systems, Vol. 57, Issue 2, pp. 183-194.
  • Cadenas J. M., and Jimenez, F. (1994). “A genetic algorithm for the multi-objective solid transportation problem: A fuzzy approach”. In Proceedings for the Dedicated Conferences on Mechatronics and Supercomputing Applications in the Transportation Industries, Aachen, Germany, pp. 327–334.
  • Cui, Q., and Sheng, Y. (2013). “Uncertain Programming Model for Solid Transportation Problem”. International Information Institute, 15, pp. 342-348.
  • Dalman, H. (2016). “A fuzzy approach for interval multiobjective solid transportation problem”. New Trends in Mathematical Sciences, Vol. 4, No. 4, pp. 114-127.
  • Gen, M., Ida, K., Li, Y., and Kubota E. (1995). “Solving bicriteria solid transportation problem with fuzzy numbers by a genetic algorithm”. Computers and Industrial Engineering, Vol. 29, Issue 1-4, pp. 537-541.
  • Ida, K., Gen, M., and Li, Y. (1995). “Solving multicriteria solid transportation problem with fuzzy numbers by genetic algorithms”. In European Congress on Intelligent Techniques and Soft Computing (EUFIT' 95), Aachen, Germany, pp. 434- 441.
  • Jana, S. H., and Jana, B. (2020). “Application of fuzzy programming techniques to solve solid transportation problem with additional constraints”. Operations Research and Decisions, Vol. 30, No. 1, pp. 67-84.
  • Jimenez, F., and Verdegay, J. L. (1998). “Uncertain solid transportation problems”. Fuzzy sets and Systems, Vol. 100, Issues 1-3, pp. 45-57.
  • Jimenez, F., and Verdegay, L. J. (1999). “Solving fuzzy solid transportation problem by an evolutionary algorithm based on parametric approach”. European Journal of Operational Research, Vol. 117, Issue 3, pp. 485- 510.
  • Khalifa, H. A. E. (2019). “Fuzzy Compromise Approach for Solving Interval-Valued Fractional Multi-Objective Multi-Product Solid Transportation Problems”. Journal of System Management, Issue 2, pp. 1–20.
  • Khalifa, H. A., and Al-Shabi, M. (2018). “Utilizing of Fractional Programming for Multi-Objective Multi-Item Solid Transportation Problems in Fuzzy Environment”. International Journal of Current Research, Vol.10, Issue 11, pp. 75024-75035.
  • Khalifa, H. A.W., Kumar P., and Alharbi, M. G. (2021). “On characterizing solution for multi-objective fractional two-stage solid transportation problem under fuzzy environment”. Journal of İntelligent Systems, Vol.30, Issue 1, pp. 620-635.
  • Kumar, G. N., and Dutta, D. (2015). “Solving multi- objective fuzzy solid transportation problem based on expected value and the goal programming approach”. IOSR Journal of Mathematics, Vol. 11, Issue 2, pp. 88- 96.
  • Li, Y., Ida, K., and Gen, M. (1997). “Improved genetic algorithm for solving multiobjective solid transportation problem with fuzzy numbers”. Japan Society for Fuzzy Theory and Systems, Vol. 9, No. 2, pp. 239-250
  • Nagarajan, A., Jeyaraman, K., and Krishna Prabha, S. (2014). “Multi- objective solid transportation problem with interval cost in source and demand parameters”. International Journal of Computer & Organization Trends, Vol. 4, Issue 3, pp. 24-32.
  • Ojha, A., Das, B., Mondal, S., and Maiti, M. (2009). “An entropy based solid transportation problem for general fuzzy costs and time with fuzzy equality”. Mathematical Computation Model, Vol. 50, No. 1-2, pp. 166- 178.
  • Ojha, A., Mondal, S. K., & Maiti, M. (2014). A solid transportation problem with partial nonlinear transportation cost. Journal of Applied and Computational Mathematics, 3(150), 1-6.
  • Pandian, P., and Anuradha, D. (2010). “A new approach for solving solid transportation problems”. Applied Mathematical Sciences, Vol. 4, No. 69-72, pp. 3603-3610.
  • Radhakrishnan, B., and Anukokila, P. (2014). “Fractional Goal Programming for Fuzzy Solid Transportation Problem with Interval Cost”. Fuzzy Information and Engineering, Vol. 6, Issue 3, pp. 359–377.
  • Sakawa M., and Yano, H. (1988). “An interactive fuzzy satisficing method for multiobjective linear fractional programming problems”. Fuzzy Sets and Systems, Vol. 28, Issue 2, pp. 129-144.
  • Sakawa, M., and Yumine, T. (1983). “Interactive fuzzy decision-making for multiobjective linear fractional programming problems”. Large Scale Systems, 5, pp. 105-113.
  • Singh, S., Pradhan, A., and Biswal, M. P. (2019). “Multi-objective solid transportation problem under stochastic environment”. Sadhana - Academy Proceedings in Engineering Sciences, 44(5).
  • Sobana, V. E., and Anuradha, D. (2018). “Solution of Solid Transportation Problem in Fuzzy Approach”. International Journal of Pure and Applied Mathematics, Vol. 119, No. 9, pp. 313–321.
  • Tao, Z., and Xu, J. (2012). “A class of rough multiple objective programming and its application to solid transportation problem”. Information Sciences, Vol. 188, pp. 215–235.
There are 28 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Nurdan Kara 0000-0001-6195-288X

Hale Köçken 0000-0003-1121-7099

Publication Date April 1, 2022
Published in Issue Year 2022 Volume: 18 Issue: 1

Cite

APA Kara, N., & Köçken, H. (2022). A GOLDEN SECTION METHOD FOR THE MULTI-OBJECTIVE FRACTIONAL SOLID TRANSPORTATION PROBLEM USING THE EXPONENTIAL MEMBERSHIP FUNCTION. Journal of Naval Sciences and Engineering, 18(1), 121-141.