Optimizing the marketing budget allocation problem using Lagrangean based techniques

In this Master Thesis project we present a Lagrangean relaxation optimization approach to the marketing budget allocation problem. This approach is aiming to allocate the marketing budget among the various channels such that the effect to the consumers will be maximized. Taking under consideration the cost parameters, the problem is formulated as a Mixed Integer Non‐Linear Programming problem. The Upper Bound solution values are obtained by relaxing the problem using the traditional Lagrangean relaxation technique as well as a series of Lagrangean. The Lower Bound for the problem is obtained through a heuristic algorithm which is based on the Lagrangean method solutions and its values are compared to the solution values produced by a random algorithm. The optimization approach has been implemented for 34 marketing channels. The Upper Bound values derived by the Lagrangean heuristic method has shown to be improved compared to the traditional method, approaching the corresponding Lowe Bound values. Although the Upper Bound values were lowering their minimum values while the constraints of the problem were being modified, they maintained a considerable distance from the Lower Bound values. The optimal solution though has not been met, despite the improved results,. To obtain the optimal solution value of the marketing budget allocation problem, further research recommendations are presented in the end of the paper.