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This eoffprint is for personal use only and shall not be self-archived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com".

In this paper, we investigate transportation problem in which supplies and demands are intuitionistic fuzzy numbers. Intuitionistic fuzzy zero point method is proposed to find the optimal solution in terms of triangular intuitionistic fuzzy numbers. A new relevant numerical example is also included.

In conventional transportation problem (TP), supplies, demands and costs are always certain. In this paper, the author tried to categories the TP under the mixture of certain and uncertain environment and formulates the problem and utilizes the crisp numbers, triangular fuzzy numbers (TFNs) and trapezoidal fuzzy numbers (TrFNs) to solve the TP. The existing ranking procedure of Liou and Wang is used to transform the type-1 and type-3 fuzzy transportation problem (FTP) into a crisp one so that the conventional method may be applied to solve the TP. The solution procedure differs from TP to type-1 and type-3 FTP in allocation step only. Therefore, the new method called PSK method and new multiplication operation on TrFN is proposed to find the mixed optimal solution in terms of crisp numbers, TFNs and TrFNs. The main advantage of this method is computationally very simple, easy to understand and also the optimum objective value obtained by our method is physically meaningful. The effectiveness of the proposed method is illustrated by means of a numerical example.

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.