The purpose of this article is to introduce mathematical models for two budget problems. The first problem, which deals to the construction of a particular budget, is solved based on an algorithm for the maximum flow problem in bipartite network. The method constructs an efficient budget by repeating a maximum flow computation. The second problem is the budget exercise and studies how the budget can be modeled in time. A mathematical model based on the maximal dynamic flow is proposed and an algorithm to solve it is outlined.