The transportation problems are framed with multi-goals which are evaluated in various scales and in the meantime in conflict. The many-sided quality of the social and monetary atmosphere require express thought of criteria other than cost around then certifiable issues like delivering an item from a few supply origin to a few interest destination can be formulated as multi-objective transportation models. Grey situation decision making is alluding to the procedure of better choice and shortcoming disposal in which different countermeasure should be preferred according to the different events. This paper applied the grey situation decision making theory for the solution of multi-objective transportation problem.

In transportation problem, for transporting a product from supply origins to demand destinations, a company declared the tender, once a company gain total transportation cost. Numbers of Transportation Company are interested in this tender. Out of them, some companies are not able to fulfill the requirements of the tender so such companies are combining to gather and jointly apply in tendering to get the assignment. All the companies which are jointly applying, having different power. So it is necessary for all companies to decide some strategies according to their cost, profit and units of supply before applying in such tendering procedure so that all companies will get maximum benefit. In this paper, we developed the model and solve such type of transportation problems with proper illustration by using LINGO package and Nash Bargaining model based approach when more than two companies are jointly applied in the tendering process and from that we find non integer and integer solutions respectively.