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On the Integer Solutions of the Generalized Transportation Problem Under Fuzzy Environment

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Abstract

It is shown that a fuzzy generalized transportation problem can be converted into a nonfuzzy one which can be changed to an equivalent form for which there is an immediate basic solution by making use of a particular basic solution to the dual problem. The computation involved is minimal. For problems with integer coefficients, an all integer algorithm due to Greenberg can be initialized immediately to the equivalent problem to obtain the optimal integer solution to the original problem in a finite number of steps. The method appears to be efficient.

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References

  1. Balachandran, V., and Thompson, G.L. (1975) An operator theory of parametric programming for the generalized transportation problem: 1 Basic theory, Nav. Res. Log. Quart., 22, pp. 79–100.

    Article  Google Scholar 

  2. Balas, E., and Ivanescu, P.L. (1964) On the generalized transportation problem, Mgmt. Sci., 11, pp. 188–202.

    Article  Google Scholar 

  3. Balas, E. (1966) The dual method for the generalized transportation problem, Mgmt. Sci., 12, pp. 555–568.

    Article  Google Scholar 

  4. Charnes, A., and Cooper, W.W. (1961) Management models and industrial applications of linear programming, Vol. I and II, Wiley, New York.

    Google Scholar 

  5. Dantzig, G.B. (1963) Linear programming and extensions, Princeton University Press.

  6. Dubois, D., and Prade, H. (1980) Fuzzy sets and systems, Theory and applications, Academic Press, New York.

    Google Scholar 

  7. Eisemann, K. (1964) The generalized stepping stone method for the machine loading problem, Mgmt. Sci., 11, pp. 154–176.

    Article  Google Scholar 

  8. Ferguson, A.R., and Dantzig, G.B. (1956) The allocation of aircraft to routes — An example of linear programming under uncertain demand, Mgmt Sci, 3, pp. 45–73.

    Article  Google Scholar 

  9. Garvin, W.W. (1960) Introduction to linear programming, McGraw-Hill, New York.

    Google Scholar 

  10. Greenberg, H. (1971) Integer programming, Academic Press, New York.

    Google Scholar 

  11. Hadley, G. (1962) Linear programming, Addison-Wesley, Reading, Mass.

    Google Scholar 

  12. Hughes, J.B. (1989) Integer solutions of the generalized transportation problem, Unpublished report, University College of North Wales, Bangor, Gwynedd, UK.

    Google Scholar 

  13. Lourie, J.R. (1964) Topology and computation of the generalized transportation problem, Mgmt. Sci., 11, pp. 177–187.

    Article  Google Scholar 

  14. Zadeh, L., and Bellman, R. (1970) Decision- making in a fuzzy environment, Mgmt. Sci., 17, pp. 141–164.

    Article  Google Scholar 

Download references

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  1. Department of Mathematics & Physics, College of Arts & Sciences, University of Qatar, P.O. Box 2713, Doha, Qatar

    Omar M. Saad

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  1. Omar M. Saad
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Saad, O.M. On the Integer Solutions of the Generalized Transportation Problem Under Fuzzy Environment. OPSEARCH 42, 238–251 (2005). https://doi.org/10.1007/BF03398733

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