Optimal control of customer dynamics using machine learning method with polynomial kernel

In this research, a model of optimal control for customer dynamics based on marketing policies is investigated as a non-automatic system of differential equations. The main purpose of the model is to track and analyze the simultaneous changes in the behavior of regular, referral and potential customers of the company from the time of its inception to now. Implementing an effective marketing policy to optimize these changes and increase the number of customers is of particular importance. In line with this goal, a new supervised machine learning algorithm is presented for the numerical simulation of the problem. The proposed algorithm uses polynomial kernels. Polynomial kernels make it possible to simulate a complex function of data in a way that helps to better understand customer dynamics. Support Vector Least Squares regression provides a simple optimization method for marketing strategies, with this approach, marketing strategies can be optimized without dealing with the details of each customer and instead focusing on the overall effect of this strategy. placed on the set of customers. This research shows how machine learning techniques can help in solving complex management and marketing problems. Over time, the number of regular customers increases and the number of potential customers decreases. However, the number of referral customers shows a rapid growth at the beginning of the time period and a fluctuating increasing pattern over time.