This work focuses on the application of distributed model predictive control to find the optimal decision variables to maximize profit in supply chains. A reduced version of the MIT beer game made of only two elements is taken as an application example. Three controllers, i.e., a standard centralized model predictive controller, an distributed non-cooperative model predictive controller and a recently proposed distributed scheme based on a cooperative game are applied to maximize profit. The properties of these controllers are compared extensively under different simulation scenarios.