Abstract
Solid transportation problem mainly deals with the situation of optimizing different objective functions related to many industrial problems considering constraints sets and due to the constraints uncertainty is always present in different parameters of solid transportation problems. This chapter intends to present a comprehensive study on the development of a mathematical model for solid transportation problems considering uncertain parameters and the neutrosophic fuzzy numbers are used to define those uncertain parameters. For the developed model, a solution approach is hereby discussed in this chapter. The feasibility conditions are validated with the case of numerical implementation of the model and its solution technique. A conversion process that converts a neutrosophic fuzzy number to an equivalent crisp number is discussed in this chapter, and using this method, only an equivalent form of the fuzzy model is obtained, which is later on solved with the LINGO software. A discussion is made based on the obtained result to validate the proposed methodology and the models of solid transportation problems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Hitchcock, F.L.: The distribution of a product from several sources to numerous localities. J. Math. Phys. 20(1–4), 224–230 (1941)
Shell, E.: Distribution of a product by several properties, directorate of management analysis. In: Proceedings of the Second Symposium in Linear Programming, Vol. 2, pp. 615–642 (1955)
Haley, K.: New methods in mathematical programming-the solid transportation problem. Oper. Res. 10(4), 448–463 (1962)
Sengupta, D., Das, A., Bera, U.K.: A gamma type-2 defuzzification method for solving a solid transportation problem considering carbon emission. Appl. Intelli. 48(11), 3995–4022 (2018)
Das, A., Bera, U.K., Maiti, M.: A solid transportation problem in uncertain environment involving type-2 fuzzy variable. Neural Comput. Appl. 31(9), 4903–4927 (2019)
Kundu, P., Kar, S., Maiti, M.: Multi-objective solid transportation problems with budget constraint in uncertain environment. Int. J. Syst. Sci. 45(8), 1668–1682 (2014)
Sengupta, D., Das, A., Dutta, A., Bera, U.K.: A fixed charge solid transportation problem with possibility and expected value approaches in hybrid uncertain environment. In: International Conference on Information Technology and Applied Mathematics. Springer, Heidelberg, pp. 182–193 (2019)
Pramanik, S., Jana, D.K., Mondal, S.K., Maiti, M.: A fixed-charge transportation problem in two-stage supply chain network in gaussian type-2 fuzzy environments. Inf. Sci. 325, 190–214 (2015)
Ojha, A., Das, B., Mondal, S., Maiti, M.: A solid transportation problem for an item with fixed charge, vechicle cost and price discounted varying charge using genetic algorithm. Appl. Soft Comput. 10(1), 100–110 (2010)
Mondal, A., Roy, S.K., Midya, S.: Intuitionistic fuzzy sustainable multi-objective multi-item multi-choice step fixed-charge solid transportation problem. J. Ambient Intelli. Humanized Comput. 1–25 (2021)
Zadeh, L.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)
Atanassov, K.: Intuitionistic fuzzy sets. Int. J. Bioautomation 20, 1 (2016)
Mendel, J.M.: Type-2 fuzzy sets and systems: an overview. IEEE Comput. Intelli. Mag. 2(1), 20–29 (2007)
Torra, V.: Hesitant fuzzy sets. Int. J. Intelli. Syst. 25(6), 529–539 (2010)
Smarandache, F.: Neutrosophic set-a generalization of the intuitionistic fuzzy set. Int. J. Pure Appl. Math. 24(3), 287 (2005)
Sarma, D., Das, A., Bera, U.K., Hezam, I.M.: Redistribution for cost minimization in disaster management under uncertainty with trapezoidal neutrosophic number. Comput. Ind. 109, 226–238 (2019)
Ghosh, S., Roy, S.K., Verdegay, J.L.: Fixed-Charge Solid Transportation Problem with Budget Constraints Based on Carbon Emission in Neutrosophic Environment (2021)
Singh, A., Das, A., Bera, U.K., Lee, G.M.: Prediction of transportation costs using trapezoidal neutrosophic fuzzy analytic hierarchy process and artificial neural networks. IEEE Access 9, 103497–103512 (2021)
Oepen, S., Flickinger, D., Toutanova, K., Manning, C.D.: Lingo redwoods. Res. Language Comput. 2(4), 575–596 (2004)
Abdel-Basset, M., Gunasekaran, M., Mohamed, M., Smarandache, F.: A novel method for solving the fully neutrosophic linear programming problems. Neural Comput. Appl. 1–11 (2018)
Mohamed, M., Abdel-Basset, M., Zaied, A.N.H., Smarandache, F.: Neutrosophic integer programming problem. In: Infinite Study (2017)
Ganesan, K., Veeramani, P.: Fuzzy linear programs with trapezoidal fuzzy numbers. Ann. Oper. Res. 143(1), 305–315 (2006)
Ebrahimnejad, A., Tavana, M.: A novel method for solving linear programming problems with symmetric trapezoidal fuzzy numbers. Appl. Math. Modelling 38(17–18), 4388–4395 (2014)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Das, A. (2023). A Comprehensive Study on Neutrosophic Fuzzy Solid Transportation Model and Its Solution Technique. In: Sahoo, L., Senapati, T., Yager, R.R. (eds) Real Life Applications of Multiple Criteria Decision Making Techniques in Fuzzy Domain. Studies in Fuzziness and Soft Computing, vol 420. Springer, Singapore. https://doi.org/10.1007/978-981-19-4929-6_24
Download citation
DOI: https://doi.org/10.1007/978-981-19-4929-6_24
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-19-4928-9
Online ISBN: 978-981-19-4929-6
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)