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International journal of fuzzy logic and intelligent systems

In conventional transportation problem (TP), all the parameters are always certain.But, many of the real life situations in industry or organization, the parameters (supply, demand and cost) of the TP are not precise which are imprecise in nature in different factors like the market condition, variations in rates of diesel, traffic jams, weather in hilly areas, capacity of men and machine, long power cut, labourer's over time work, unexpected failures in machine, seasonal changes and many more.To counter these problems, depending on the nature of the parameters, the TP is classified into two categories namely type-2 and type-4 fuzzy transportation problems (FTPs) under uncertain environment and formulates the problem and utilizes the trapezoidal fuzzy number (TrFN) to solve the TP.The existing ranking procedure of Liou and Wang (1992) is used to transform the type-2 and type-4 FTPs into a crisp one so that the conventional method may be applied to solve the TP.Moreover, the solution procedure differs from TP to type-2 and type-4 FTPs in allocation step only.Therefore a simple and efficient method denoted by PSK (P.Senthil Kumar) method is proposed to obtain an optimal solution in terms of TrFNs.From this fuzzy solution, the decision maker (DM) can decide the level of acceptance for the transportation cost or profit.Thus, the major applications of fuzzy set theory are widely used in areas such as inventory control, communication network, aggregate planning, employment scheduling, and personnel assignment and so on.

A Simple Method for Solving Type-2 and Type-4 Fuzzy Transportation Problems