This paper discusses the online optimization and control of a heat-exchanger network (HEN) through a two-level control structure. The low level is a constrained model predictive control (MPC) and the high level is a supervisory online optimiser. Since MPC is a multivariable control technique capable of handling control-input constraints, it is neither necessary to define a variable-pairing approach nor to include individual loop-protections to avoid close-loop saturations. The proposed MPC algorithm uses an approximate linear model of the system to perform the output predictions and to account for the constraints. On the other hand, the supervisory program, based on a rigorous model, computes desired values to key manipulated variables of MPC, leading to minimum utility consumption. The coordination between the supervisory program and MPC is achieved through the definition of an extended cost-function that enables the controller to drive the system to the optimal operating condition. The proposed method was successfully tested by rigorous simulation of a typical HEN of the process industry. (c) 2006 Elsevier B.V. All rights reserved.