Abstract
Transportation problems (TPs) play important roles in today’s highly competitive world. To maximize profits, organizations are always aiming for more revenue. In this chapter, we present the selecting fuzzy-zero method (SFZM), which can help us to find the optimal solution for minimizing transportation costs while maximizing profit. We present this SFZM to solve a fuzzy transportation problem (FTP), in which demand, supply, and transportation costs (TCs) are trapezoidal fuzzy numbers (TFNs). By using the existing solution methods, we convert these TFNs to fixed values and thus solve the FTP. We also compare the methods of (Hamdy AT. Operations research: an introduction, 8th edn. Pearson Prentice Hall, Upper Saddle River, 2007; Pandian P, Natarajan G. A. Appl Math Sci 4:79–90, 2010; Reinfeld NV, Vogel WR. Mathematical programming. Englewood Cliffs, Prentice-Hall, 1958; Souhail Dhouib. Int J Oper Res Inf Syst 12:1-16, 2022.) with our SFZM. We illustrate how the SFZM works by laying out numerical examples with a working procedure.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Akpana, T., Ugbeb, J.U., Ajahd, O.: A modified Vogel approximation method for solving balanced transportation problems. Am. Sci. Res. J. Eng. Technol. Sci. 14, 289–302 (2015)
Ashale, T.R.: Newly Proposed Matrix Reduction Technique under Mean Ranking Method for Solving Trapezoidal Fuzzy Transportation Problems Under Fuzzy Environment (2021). https://doi.org/10.20944/preprints202106.0573
Charnes, A., Cooper, W.W., Henderson, A.: An Introduction to Linear Programming. Wiley, New York (1953)
Deshmukh, N.M.: An innovative method for solving transportation problem. Int. J. Phys. Math. Sci. 2, 86–91 (2012)
Ekanayake, E.M.U.S.B., Perera, S.P.C., Daundasekara, W.B., Juman, Z.A.M.S.: A modified ant colony optimization algorithm for solving a transportation problem. J. Adv. Math. Comput. Sci. 35, 83–101 (2020)
Fegade, M.R., Jadhav, V.A., Muley, A.A.: Solving Fuzzy transportation problem using zero suffix and robust ranking methodology. IOSR J. Eng. 2, 36–39 (2012)
Allung, F.M., Blegur, N.K.F., Dethan.: Modified Hungarian method for solving balanced fuzzy transportation problems. J. Varian. 5, 161–170 (2022)
Goyal, S.K.: Improving VAM for unbalanced transportation problems. J. Oper. Res. Soc. 35, 1113–1114 (1984)
Hitchcock, F.L.: The distribution of a product from several sources to numerous localities. J. Phys. Sci. 20, 224–230 (1941)
Hamdy, A.T.: Operations Research: An Introduction, 8th edn, p. 2007. Pearson Prentice Hall, Upper Saddle River (2007)
Karthy, T., Ganesan, K.: Revised improved zero point method for the trapezoidal fuzzy transportation problems. AIP Conference Proceedings. (2019)
Pandian, P., Natarajan, G.: A new algorithm for finding a fuzzy optimal solution for fuzzy transportation problems. Appl. Math. Sci. 4, 79–90 (2010)
Reinfeld, N.V., Vogel, W.R.: Mathematical Programming. Prentice-Hall, Englewood Cliffs, NJ (1958)
Dhouib, S.: Solving the trapezoidal fuzzy transportation problems via new heuristic: The Dhouib-Matrix-TP1. Int. J. Oper. Res. Inf. Syst. 12, 1–16 (2022)
Soomro, A.S., Junaid, M., Tularam, G.A.: Modified Vogel’s approximation method for solving transportation problems. Math. Theory Model. 5 (2015)
Ngastiti, P.T.B., Bayu Surarso, S.: Zero point and zero suffix methods with robust ranking for solving fully fuzzy transportation problems. IOP Conference Series: Journal of Physics: Conference Series. (2018)
Ngastiti, P.T.B., Surarso, B., Sutimin.: Comparison between zero point and zero suffix methods in fuzzy transportation problems. J. Mat. Mantik. 6, 38–46 (2020)
Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 1, 3–28 (1978)
Zimmermann, H.J.: Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst. 1, 45–55 (1978)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Boobalan, J., Raja, P. (2024). Optimal Solution for Transportation Problems Using Trapezoidal Fuzzy Numbers. In: Kamalov, F., Sivaraj, R., Leung, HH. (eds) Advances in Mathematical Modeling and Scientific Computing. ICRDM 2022. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-41420-6_51
Download citation
DOI: https://doi.org/10.1007/978-3-031-41420-6_51
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-031-41419-0
Online ISBN: 978-3-031-41420-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)