Operation Research problems (OR) have been solved by operation research technique efficiently for a long time. Graph theory techniques are competent with OR techniques in some area like transport problem. Identification of a better technique to solve the OR problem is very important. In this paper, the better performance of Big M method on transport network with non -integer edge capacities is reported. The redundant constraints removal in Big M method improve its performance. Graph theory is a very natural and powerful tool in operation research. The areas of OR in which graph theory is used most frequently and profitably are transport networks and theory of games In this paper, network -flow problems is formulated and solved using graph theory technique and operation research technique and the better performance is reported. The redundant constraints removal in OR technique improves its performance.