Fuzzy Transportation Problems: A General Analysis
Abstract
The transportation problems have a recognized importance. Their range of applications can be enlarged when some fuzziness in its formulation is accepted. This paper is devoted to the study of a resolution method for fuzzy transportation problems. In order that this may be done, in accordance with the decomposition theorem for fuzzy sets, a formulation as the transshipment problems cut by cut is done. Feasibility or un-feasibility of the former fuzzy problem is analyzed on these cuts by means of four functions. These are straightforwardly defined from the membership functions of the fuzzy parameters involved in the starting formulation. In order to find a fuzzy solution using an auxiliary problem, a parametric type algorithm is proposed. This one is shown to be more efficient than others existing in the current literature because of the lower dimensionality of the mentioned auxiliary problem.
Keywords
fuzzy transportation problem transportation problem fuzzy mathematical programmingPreview
Unable to display preview. Download preview PDF.
References
- Chanas, S., W. Koiodziejczyk, and A. Machaj (1984). A fuzzy approach to the transportation problem. Fuzzy Sets and Syst. 13, 211–221.MATHCrossRefGoogle Scholar
- Delgado, M., and J.L. Verdegay (1984). Resolution of a fuzzy transportation problem with generalized triangular membership functions (in Spanish). Actas del XIV Congreso Nacional de Estadistica, Investigation Operativa e Informatica, Granada (Spain), 748–758.Google Scholar
- Dubois, D., and H. Prade (1980). Fuzzy Sets and Systems. Theory and Applications. Academic Press, New York.MATHGoogle Scholar
- Gal, T. (1979). Postoptimal Analysis, Parametric Programming and Related Topics. Mc Graw Hill, New York.Google Scholar
- Hamacher, H., H. Leberling and H.J. Zimmermann (1978). Sensitivity analysis in fuzzy linear programming. Fuzzy Sets and Syst. 1, 269–281.MathSciNetMATHCrossRefGoogle Scholar
- Negoita, C.V., and D. Ralescu (1975). Applications of Fuzzy Sets to Systems Analysis. Birkhauser Verlag, Basel.MATHGoogle Scholar
- Oheigeartaigh, M. (1982). A fuzzy transportation algorithm. Fuzzy Sets and Syst. 8, 235–243.MathSciNetMATHCrossRefGoogle Scholar
- Prade, H. (1980). Operations research with fuzzy data. In P.P. Wang and S.K. Chang (eds.), Fuzzy Sets. Theory and Applications to Policy Analysis and Information Systems. Plenum Press, New York, 155–170.Google Scholar
- Simonnard, M. (1973). Linear Programming, vol. 2. Extensions. Dunod, Paris.Google Scholar
- Verdegay, J.L. (1983). Transportation problem with fuzzy parameters (in Spanish). Revista de la Real Academia de Ciencias Matematicas, Fisico Quimicas y Naturales de Granada, II, 47–56.Google Scholar
- Verdegay, J.L. (1982). Fuzzy mathematical programming. In M.M. Gupta and E. Sanchez (eds.), Fuzzy Information and Decision Processes. North-Holland, Amsterdam, 231–237.Google Scholar
- Zimmermann, H.-J. (1976). Description and optimization of fuzzy systems, Int. J. Gen. Syst. 2, 209–215.MATHCrossRefGoogle Scholar