International Journal of Fuzzy Logic and Intelligent Systems

Korean Institute of Intelligent Systems (한국지능시스템학회)
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Interval Valued Solution of Multiobjective Problem with Interval Cost, Source and Destination Parameters

  • Published : 2009.03.01
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Abstract

Das et al. [EJOR 117(1999) 100-112] discussed the real valued solution procedure of the multiobjective transportation problem(MOTP) where the cost coefficients of the objective functions, and the source and destination parameters have been expressed as interval values by the decision maker. In this note, we consider the interval valued solution procedure of the same problem. This problem has been transformed into a classical multiobjective transportation problem where the constraints with interval source and destination parameters have been converted into deterministic ones. Numerical examples have been provided to illustrate the solution procedure for this case.

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References

  1. H. Isermann, "The enumeration of all efficient solution for a linear multi-objective transportation problem," Fuzzy Sets and Systems, vol. 18, 15-30, 1986 https://doi.org/10.1016/0165-0114(86)90025-4
  2. J. L. Ringuest, D.B. Rinks, "Interactive solutions for the linear multiobjective transportation problem，" European Journal of Operational Research, vol. 32, pp. 96-106, 1987 https://doi.org/10.1016/0377-2217(87)90274-8
  3. A. K. Bit, M. P. Biswal, S. S. Alam, "Fuzzy programming approach to multicriteria decision making transportation problem," Fuzzy Sets and System, vol. 50, pp. 135-142, 1992 https://doi.org/10.1016/0165-0114(92)90212-M
  4. A. L. Soyster, "Convex programming with setinclusive constraints and applications to inexact linear programming," Operations Research, vol. 21, pp. 1154-1157, 1973 https://doi.org/10.1287/opre.21.5.1154
  5. K. Asi, H. Tanaka, "Fuzzy linear programming with fuzzy numbers," Fuzzy Sets and System, vol. l3, pp. 1-10, 1984 https://doi.org/10.1016/0165-0114(84)90022-8
  6. S. Chanas, D. Kuchta, "Multiobjεctive programming in optimization of interval objective functions a generalized approach," European Journal of Operational Research, vol. 94, pp. 594-598, 1996 https://doi.org/10.1016/0377-2217(95)00055-0
  7. G. Alefeld, J. Herzberger, lntroduction to lnterval computation, Academic Press, New York, 1983
  8. G. R. Bitran, "Linear multiobjectivε problems with interval co-efficient," Management Science, vol. 26, pp. 694-706, 1980 https://doi.org/10.1287/mnsc.26.7.694
  9. D. Dubois, Linear programming with fuzzy data, in:J. C. Benreek (Ed.), Analysis of Fuzzy Information, vol. III, Application in Engineering and Science, CRC Press, Boca Raton, 1987, pp. 241-263
  10. M. Inuiguchi, Y, Kume, "Goal programming problem with interval co-efficient and target intervals," European Journal of Operational Research, vol. 52, pp. 345-360, 1991 https://doi.org/10.1016/0377-2217(91)90169-V
  11. R. E. Moore, Method and applications of interval analysis, SLAM, Philadelphia, PA. 1979
  12. S. Chanas, D. Kuchta, "A concept of solution of the transportation problem with fuzzy cost co-efficient," Fuzzy Sets and Systems, vol. 82, pp. 299-305, 1996 https://doi.org/10.1016/0165-0114(95)00278-2
  13. R. E. Steuer "AIgorithm for linear programming problems with interval objective function co-efficient," Mathematics of Operations Research, vol.6, pp. 333-348, 1981 https://doi.org/10.1287/moor.6.3.333
  14. S. Tong, "Interval number and fuzzy number linear programming," Fuzzy Sets and Systems vol. 66 pp. 301-306, 1994 https://doi.org/10.1016/0165-0114(94)90097-3
  15. H. Ishibuchi, H. Tanaks, "Multiobjective programming in optimization of the interval objective function," European Journal of Operational Research, vol. 48, pp. 219-225, 1990 https://doi.org/10.1016/0377-2217(90)90375-L
  16. M. Inuiguchi, Y, Kume, "Efficient solutions verses non-dominated solution in linear programming with multiple interval objective functions," Bulletin of university of Osaka Preference Series A: Engineering and Natural Science, vol. 40, pp. 293-298, 1991
  17. S. K. Das, A. Goswami, S. S. Alam, Multiobjective transportation problem with interval cost, source and destmation parameters ，" European Journal of Operational Research, vol. 117, pp. 100-112, 1999 https://doi.org/10.1016/S0377-2217(98)00044-7