An application of entropy programming for the transportation problem

Consider the classical transportation problem and such an optimization problem is formulated where some constraints are not required to be exactly satisfied. Rather the deviation of the two sides is put into the objective function in such a way that the weighted average of the original objective function and the deviation should be minimal. The generalization of the Kullbach, S. and Leibler, P. information is used as the deviation of a given vector from another given one. So a mixed entropy programming problem is obtained. Then a short outline of the mixed entropy programming problem and its duality problem is given. An efficient algorithm is developed for solving this optimalization problem and its convergence is shown. Finally an example is given which demonstrates the difference between the classical solution and the entropy solution.