Abstract
The Multi-index transportation problems are of immense use in present scenario. This paper provides a survey of the work done in the area of such problems from 1955 till date. The purpose of this survey is to provide the reader an up to date account of such problems and their current variants, many of which consider the fuzziness in objective function, constraints and/or coefficients. The survey also studies current approaches to solve such problems.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Anu, A., Arora, S.R.: Multi-Index fixed charge bicriterion transportation problem. Indian J. Pure Appl. Math. 32(5), 739–746 (2001)
Alves, I.C., Yamakami, A., Gomide, F.: An approach for fuzzy linear multicommodity transportation problems and its application. In: Proceedings of 1995 International Joint Conference of the Fourth IEEE International Conference on Fuzzy Systems and The Second International Fuzzy Engineering Symposium, Fuzzy Systems, vol. 2, pp. 773–780 (1995)
Bodkhe, S.G., Bajaj, V.H., Dhaigude, D.B.: Fuzzy programming technique to solve multi-objective solid transportation problem with some non-linear membership functions. Advances in Computational Research 2(1), 15–20 (2010)
Aysun, B.S., Hamza, B.: An axial four-index transportation problem and its algebraic characterizations. International Journal of Computer Mathematics 81(6), 765–773 (2004)
Cadenas, J.M., Jiménez, F.: A genetic algorithm for the multiobjective solid transportation problem: a fuzzy approach. In: International Symposium on Automotive Technology and Automation, Proceedings for the Dedicated Conferences on Mechatronics and Supercomputing Applications in the Transportation Industries, Aachen, Germany, pp. 327–334 (1994)
Chanas, S., Delgado, M., Verdegay, J.L., Vila, M.A.: Interval and fuzzy extensions of classical transportation problems. Transportation Planning and Technology 17, 203–218 (1993)
Galler, B., Dwyer, P.S.: Translating the method of reduced matrices to machines. Naval Res. Logistics Q 4, 55–71 (1957)
Gen, M., Ida, K., Li, Y.: Solving bicriteria solid transportation problem by genetic algorithm, Humans, Information and Technology. Systems, Man and Cybernetics 2, 1200–1207 (1994)
Haley, K.B.: The Solid transportation problem. Op. Res. 10, 448–463 (1962)
Haley, K.B.: The multi-index problem. Op. Res. 11, 368–379 (1963)
Hammer, P.L.: Time minimization transportation problem. Naval Research Logistics Quarterly 16, 345–357 (1969)
Jimenez, F., Verdegay, J.L.: Interval multiobjective solid transportation problem via genetic algorithm. In: Proc. of the Sixth International Conference on Information Processing and Management of Uncertainty in Knowledge Based Systems, vol. 2, pp. 787–792 (1996)
Jimenez, F., Verdegay, J.L.: Obtaining fuzzy solutions to the fuzzy solid transportation problem with genetic algorithms. In: Proceedings of the Sixth IEEE International Conference on Fuzzy Systems, vol. 3, pp. 1657–1663 (1997)
Korsnikov, A.D.: Planar three index transportation problems with dominating index. Mathematical Methods of Operations Research 32(1), 29–33 (1988)
Li, Y., Ida, K., Gen, M.: Evolution Program for multicriteria solid transportation problem with fuzzy numbers. Proc. of IEEE International Conference on Systems, Man and Cybernetics 3, 1960–1965 (1995)
Li, Y., Ida, K., Gen, M., Kobuchi, R.: Neural Network approach for multicriteria solid transportation problem. Computers & Industrial Engineering 33(3-4), 465–468 (1997)
Liu, L., Lin, L.: Fuzzy fixed charge solid transportation problem and its algorithm. In: Fourth International Conference on Fuzzy Systems and Knowledge Discovery, vol. 3, pp. 585–589 (2007)
Schell, E.D.: Distribution of a product of several properties. In: Proc. 2nd Simposium in Linear Programming, pp. 615–642. DCS/ controller, H.Q. U.S. Air Force Washington, D.C (1955)
Tzeng, G.H., Teodorovic, D., Hwang, M.J.: Fuzzy bicriteria multi-index transportation problems for coal allocation planning of Taipower. European Journal of Operational Research 95, 62–72 (1996)
Vignaux, G.A., Michalewicz, Z.: A genetic algorithm for the linear transportation problem. Systems, Man and Cybernetics 21(2), 445–452 (1991)
Zitouni, R., Keraghel, A.: Resolution of a capacitated transportation problem with four subscripts. Kybernetes 32(9/10), 1450–1463 (2003)
Zitouni, R., Keraghel, A., Benterki, D.: Elaboration and Implantation of an Algorithm Solving a Capacitated Four-Index Transportation Problem. Applied Mathematical Sciences 53(1), 2643–2657 (2007)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer India Pvt. Ltd.
About this paper
Cite this paper
Kumar, A., Yadav, S.P. (2012). A Survey of Multi-index Transportation Problems and Its Variants with Crisp and Fuzzy Parameters. In: Deep, K., Nagar, A., Pant, M., Bansal, J. (eds) Proceedings of the International Conference on Soft Computing for Problem Solving (SocProS 2011) December 20-22, 2011. Advances in Intelligent and Soft Computing, vol 130. Springer, India. https://doi.org/10.1007/978-81-322-0487-9_86
Download citation
DOI: https://doi.org/10.1007/978-81-322-0487-9_86
Published:
Publisher Name: Springer, India
Print ISBN: 978-81-322-0486-2
Online ISBN: 978-81-322-0487-9
eBook Packages: EngineeringEngineering (R0)