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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.