In real life situations the parameters of Transportation problems are not certain. Either the parameters are fuzzy numbers or multiple choices are available. In this paper we consider a Transportation problem where the parameters like costs of transportation are multi choice in nature and other parameters like demands and supplies in the constrain are trapezoidal fuzzy numbers. We use binary variable approach to make a choice out of the available cost coefficients and ranking function is used to deal with trapezoidal fuzzy numbers. The problem was solved with existing methods and softwares like LINGO. A numerical example illustrate the purpose method.
The Travelling Salesman problem is one of the most common problem in O.R. But in real life situation the problem is often not useful due to its crisp nature. Use of fuzzy can make the problem more useful in day to day life. We consider a Travelling Salesman Problem with costs of travelling as trapezoidal fuzzy numbers. Fuzzy ranking function is used to handel trapezoidal fuzzy numbers. Hungering Algorithm is used to solve the problem. An example illustrates the use of the proposed method.
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