Model Predictive Control(MPC) is widely used, especially in the chemical process industry. Model Predictive Controllers calculate the optimal control inputs at each time step, based on past information, a plant model, a quadratic objective and given constraints. Typically this involves solving a large linearly constrained quadratic program(LCQP) at each time step. Standard methods turn out to be too slow to calculate the desired inputs in time, i.e. each sampling instant. By exploiting the structure of the LCQP, specific methods for solving the QP’s in MPC were developed recently. We will compare these methods with classical QP solvers and show their necessity when controlling large systems from the example of a high density polyethylene production plant.