FUZZY APPROACH TO SOLVE MULTI-OBJECTIVE CAPACITATED TRANSPORTATION PROBLEM

Lohgaonkar M.H.¹*, Bajaj V.H.²*
¹Department of Statistics, Dr. B. A. M. University, Aurangabad, MS, India.
²Department of Statistics, Dr. B. A. M. University, Aurangabad, MS, India.
* Corresponding Author : vhbajaj@gmail.com

Received : -     Accepted : -     Published : 15-06-2010
Volume : 2     Issue : 1       Pages : 10 - 14
Int J Bioinformatics Res 2.1 (2010):10-14
DOI : http://dx.doi.org/10.9735/0975-3087.2.1.10-14

Keywords : Multi-criteria Decision Making, Capacitated Transportation Problem, Linear Membership Function, Non-linear Membership Function
Conflict of Interest : None declared

The linear multi-objective capacitated transportation problem in which the supply and demand constraints are equality type, capacity restriction on each route are specified and the objectives are non commensurable and conflict in nature. The fuzzy programing technique (Linear, Hyperbolic and Exponential) is used to find optimal compromise solution of a multi-objective capacitated transportation problem has been presented in this paper. An example is illustrate the methodology. Also comparision is taken out, using same example.

[1] Bit A. K. (2004) OPSEARCH 41, 106-120.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[2] Bit A.K., Biswal M.P. and Alam S. S. (1993) Fuzzy sets and systems 50, 135-141  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[3] Charnes A. and Cooper W. W. (1954) Management science 1, 49-59  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[4] Dantzig G. B. (1951) Application of the simplex method to a transportation problems, Chapter XXII in Activity Analysis of Production and allocation (T. C. Koopmans, Ed.), Wiley, New York.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[5] Diaz J. A. (1978) Ekonomickomatematicky Obzor 14, 267-274.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[6] Diaz J. A. (1979) Ekonomickomatematicky Obzor 15, 62-73  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[7] Dhingra A.K. and Moskowitz H. (1991) European journal of Operational Research 55, 348-361  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[8] Hitchcock F. L. (1941) Journal Of Mathematics and Physics 20, 224 - 230  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[9] Isermann H. (1979) Naval Research Logistics Quarterly 26, 123-139  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[10] Leberling H. (1981) Fuzzy sets and systems 6, 105-118.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[11] Ringuest J. L. and Rinks D. B. (1987) European Journal Of operational Research 32, 96-106.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[12] Verma Rakesh, Biswal M.P. and Biswas A. (1997) Fuzzy sets and systems 91, 37-43  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[13] Zadeh, L. A. (1965) Information and Control 8, 338-353  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[14] Zimmermann H. J. (1978) Fuzzy sets and system 1, 45-55.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus