Entropy Approach in Transportation Model

In this paper we apply entropy in transportation model using maximum entropy method introduced by Shannon. A transportation model for trip distribution describes the number of trips between two zones where generalized cost is usually some combination of the travel, the distance traveled and the actual monetary cots. If the transportation model is of the power form and if the total number of origins and destination in each zone are known, then the resulting trip matrix depends solely on parameter, which generally estimated from data. In this paper it is shown that as parameter tends to infinity the trip matrix tends to limit in which the total cost of trips is the least possible allowed by the given origin and destination totals. If the transportation problem has many cost minimizing solutions then it is shown that the limit is one particular solution in which each non zero flow from an origin to a destination is a product of two strictly positive factor, one associated with the origin and other with the destination.