Dynamic optimal control policy in advertising price and quality

This study presents an algorithm for deriving the long-term policies of quality level, price and advertisement for a product. The diffusion models and cost functions are combined to formulate profit functions capable of determining future profit trends. The algorithm first implements the optimal control theory to derive the optimal conditions of the profit function. Then the genetic algorithm is employed to search for the approximate solutions of quality level, price and advertising expenditure at each period on the planning horizon (life cycle). Examples of different scenarios of the model parameters are presented to describe the results obtained herein. Sensitivity analysis for the major parameters is performed to specify their effects on profits. Results in this study allow us, firstly, to obtain explicit solutions simultaneously with respect to quality, price and advertising policies, secondly, to propose an appropriate algorithm for solving the different scenarios of the dynamic profit function, which consists of the diffusion function and cost function, and thirdly, to enhance the long-term profit performance via the policies proposed herein, that is the approximation of the best solution.