The paper deals with the entropy programming problem and its duality results. The measure of the divergence between two non-negative vectors is the generalised Kullbach-Leibler information. The author focusses on two applications of this problem, namely, the transportation and gravity model. In the first case some constraints are not required to be exactly satisfied, rather the above divergence of the two sides is put into the objective function such a way that the weighted average of the original and the divergence should be minimal. In the second case the gravity model for trip distribution is considered. Similar to the above case again some constraints are added to the objective. In both cases efficient algorithms are developed possessing good convergence properties.