Dynamic optimal control policy in advertising price and quality

This study presents an algorithm for deriving the long-term polices of qual ity level, price and advertisement for a product. The diffusion models and cost functions are combined to formulate profit functions capable of determ ining future profit trends. The algorithm first implements the optimal cont rol theory to derive the optimal conditions of the profit function. Then th e genetic algorithm is employed to search for the approximate solutions of quality level, price and advertising expenditure at each period on the plan ning horizon (life cycle). Examples of different scenarios of the model par ameters 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 soluti ons simultaneously with respect to quality, price and advertising policies, secondly, to propose an appropriate algorithm for solving the different sc enarios of the dynamic profit function, which consists of the diffusion fun ction and cost function, and thirdly, to enhance the long-term profit perfo rmance via the polices proposed herein, that is the approximation of the be st solution.