Application of the Optimal Control Problem in New Product Launching Process

The optimal control modeling of the economic problems of new product launching has the advantage of giving interpretation the best results and their use in finding the most appropriate choices of four constants that appear in the equations of state. The equations of state have been used and proposed by other researchers in the field, but they have avoided the optimal control theory, considering it too laborious and addressing the issue of the release of a new product on the other mathematical ways. The aim of the study is to propose an optimal control problem specifically to the product launch process which can be used in product promotion process. We suppose that the company has three objectives: the first is to maximize the product image (the goodwill) at launching time T for minimize the advertising cost. The second objective is to actuate the launch – the launching time T, and the third objective is to plan the launch and the advertising campaign on the [0,T] interval.