Media Planning - Maximizing Gross OTS

The problem of generating a cinema schedule for advertisement to maximize gross OTS ( Opportunities-To-See ) attracted the attention of media plan researchers. The development of a cinema schedule so that desired Reach is achieved in each town and the total cost of advertisement does not exceed a given budget was formulated as a mathematical programming problem. The problem has a linear objective function with nonlinear constraints and integer variables. A heuristic procedure was developed by researchers in the past to solve the problem. In this paper a nested dynamic programming formulation is given to obtain an optimal solution to the problem. The structure of the optimal solution and solution procedure for a special case is also discussed.