On Fuzzy Multi-Objective Multi-Item Solid Transportation Problems

International Journal of Computer & Organization Trends  (IJCOT)          
© 2015 by IJCOT Journal
Volume - 5 Issue - 1
Year of Publication : 2015
Authors : E. E. Ammar , H. A. Khalifa
DOI : 10.14445/22492593/IJCOT-V17P301


E. E. Ammar , H. A. Khalifa "On Fuzzy Multi-Objective Multi-Item Solid Transportation Problems", International Journal of Computer & organization Trends (IJCOT), V5(1):32-50 Jan - Feb 2015, ISSN:2249-2593, www.ijcotjournal.org. Published by Seventh Sense Research Group.


In general. There is no single optimal solution in multi-objective problems, but rather a set of non inferior (pareto optimal) solutions from which the decision maker (DM) must select the most preferred or best compromise solution as the one to implement. In this paper, a multi-objective multi-item solid transportation problem by incorporating fuzzy numbers into the coefficients of the objective functions and / or supply quantities and / or demand quantities and / or conveyance capacities . The concept of -fuzzy efficient solution is introduced in which the ordinary efficient solution is extended based on the -levels of fuzzy numbers. A necessary and sufficient condition for such a solution is established. The existing results concerning the qualitative analysis of the notions (solvability set and stability set of the first kind under the concept of -parametric optimality are studied. A solution procedure for determining the stability set of the first kind corresponding to one of -pareto optimal solution is proposed. An illustrative numerical example is given to clarify the obtained results.


[1] Abd El-Wahed, W. F., and Lee, M. S., (2006). Interactive fuzzy goal programming for multi-objective transportation problems, Omega, (34): 158-166.
[2] Ammar, E. E., and Youness, E. A., (2005). Study on multi-objective transportation problem with fuzzy numbers, Applied Mathematics and Computation, (166) : 241-253.
[3] Ammar, E. E., and Khalifa, H. A., (2014). Study on multi-objective solid transportation problem with fuzzy numbers, European Journal of Scientific Research, (125): 7-19.
[4] Ammar, E. E., and Khalifa, H. A., (2015). Study on possibilistic multi-objective solid transportation problem, International Journal of Current Research, (7): 11942-11953.
[5] Bit, A. K., Biswal, M. P., and Alam, S. A., (1993). Fuzzy programming approach to multi-objective solid transportation problem, Fuzzy Sets and Systems, (57): 183-194.
[6] Chanas, S., Kolodziejck, W., and Machaj, A., (1984). A fuzzy approach to the transportation problem, Fuzzy Sets and Systems, (13): 211-221.
[7] Das, S. K., Goswami, A., and Alam, S. S., (1999). Multi-objective transportation problem with interval cost, source and destination parameters, European Journal of Operational Research, (117): 100-112.
[8] Dubois, D., and Prade, H., (1980). Fuzzy Sets and Systems: Theory and Applications (Academic Press, New York).
[9] Gen, M., Ida, k., and Li, Y., (1995).Solving bicriteria solid transportation problem with fuzzy numbers by genetic algorithms, Proceedings of the 17th International Conference or Computation and Industrial Engineering, Arizona, (3).
[10] Hussein, M. L., (1998). Complete solutions of multiple objective transportation problems with possibilistic coefficients, Fuzzy Sets and Systems, (93): 293-299.
[11] Ida, K., Gen, M., and Li, X., (1995). Solving multicriteria solid transportation problem with fuzzy numbers by genetic algorithm, European Congress on Intelligent Techniques and Soft Computing (EUFIT` 95), Aachen, Germany, 434-441.
[12] Jimenez, F., and Verdsgay, J. L., (1998). Uncertain solid transportation problems, Fuzzy Sets and Systems, 100 (1-3): 45-57.
[13] Kundu, P., Kar, S., and Mait, M., (2013). Multi-objective multi-item solid transportation problem in fuzzy environment, Applied mathematical Modeling, (37): 2028-2038.
[14] Li, Y., Ida, K., Gene, M., and Kobuchi, R., (1997). Neural network approach for multicriteria solid transportation problem with fuzzy numbers, Comput. Ind. Eng., (33): 589-592.
[15] Nagajon, A., and Jeyaraman, K., (2010). Solution of chance constrained programming problem for multi-objective interval solid transportation problem under stochastic environment using fuzzy approach, Int. J. Compt. Appli., (9): 19-29.
[16] Osman, M., (1977). Qualitative analysis of basic notions in parametric convex programming, I (Parameters in the objective function, Appl. Math., (22): 333-348.
[17] Sakawa, M., and Yano, H., (1989). Interactive decision making for multi-objective nonlinear programming problems with fuzzy parameters, Fuzzy Sets and Systems, (29): 315-326.
[18] Shell, E., (1955).Distribution of a product by several properties, Directorate of management analysis, Proceedings of the second Symposium in Linear Programming DCSL Computroller H. Q. U. S. A. F., Washington, D. C., (2): 615-642.
[19] Yang, L., and Liu, L., (2007). Fuzzy fixed charge solid transportation problem and algorithm, Appl. Soft Computing, (7): 879-889.

Multi-objective multi-item solid transportation; fuzzy numbers; ?-fuzzy efficient; ?-optimality; parametric analysis.