The media planning problem deals with the optimal allocation of a given budget over a predefined set of advertising vehicles. This problem can be formulated as a nonlinear integer program and solved by means of dynamic programming. A number of other exact and approximate solution methods are proposed, including a branch and bound algorithm, a fully polynomial approximation scheme and a greedy heuristic. It is shown that this greedy heuristic has (1) time and space complexity linear in the number of vehicle options and (2) a nonzero performance lower bound. The proposed decision support system overcomes some of the shortcomings of existing media planning models, including lack of transparency, low levels of interactivity, inability to handle S-shaped advertising response and utilization of exposure distribution models with weak empirical support. It is demonstrated by means of simulation that the proposed procedure yields solutions that are close to optimal even under extreme conditions and that it is sufficiently fast for online use. In the conclusions chapter, applications other than media planning are discussed for the heuristic developed here. Finally, a Pascal implementation of the decision support system is included.