A paradox in a fixed charge transportation problem

This paper discusses a paradox in a Fixed Charge Transportation Problem. A paradox arises when the fixed charge transportation problem admits of a total cost which is lower than the optimum cost, by transporting larger quantities of goods over the same routes. A sufficient condition for the existence of a paradox is established. Paradoxical Range of Flow is obtained for any given flow in which the corresponding objective function value is less than the optimum value of the fixed charge transportation problem. The results are illustrated with the help of an example.