Abstract. It is well-known that Linear Programming Problem (L PP) is one of the most potential mathematical tools for efficient allocati on of operational resources. Many problems in real situation can be formulated as LPP . When a situation can be entirely modeled as a network, very efficient algorithms exi st for the solution of the optimization problem which is many times more efficient than the solution methods of LPP. Transportation problems (TP), as is known, are a ba sic network problem which can be formulated as a LPP. The main objective of TP is to minimize the transportation cost of distributing a product from a number of sources (e. g. factories) to a number of destinations (e.g. ware houses). It is to be mentio ned that Balanced TP and Unbalanced TP are the types of TP. If the sum of the supplies of all the sources is equal to the sum of the demands of all the destinations, the problem is termed as a balanced transportation problem. Again, if the sum of the supplies of all t he sources is not equal to the sum of the demand of all the destinations, the problem is term ed as unbalanced transportation problem. Here we have developed a new method of fi nding an Initial Basic Feasible Solution (IBFS) for both the Balanced TP and Unbala nced TP.