Application of optimal control theory in marketing: What is the optimal number of choices on a shopping website?

Abstract

There have been some recent interests in making websites responsive to the dynamic behaviour of users. We present a method for applying the steps of optimal control theory to internet shopping platforms. The information rate is a state variable to maximise and the rate of change in number of options available to the consumer is our control variable to minimise. We apply optimal control theory to identify the optimal number of options. We specify and solve the necessary and sufficient conditions for the optimal control for a class of objective functions, which gives a nonlinear two-point boundary value problem.