The performance and operability of heat exchanger networks (HENs) is strongly affected by fouling, which involves the deposition of unwanted material, which reduces the heat-transfer rate and increases the pressure drop, the operational costs, and the environmental impact of the process. Periodical cleaning and control of the flow rate distribution in the HEN are used to mitigate the effects of fouling and restore the performance of the units. The optimal cleaning scheduling has been formulated as a mixed-integer linear programming (MILP) or mixed-integer nonlinear programming (MINLP) problem and is solved using various approaches. The optimal control has been formulated as a nonlinear programming (NLP) problem and is used to define the flow rate distribution of the network. Both problems share the same objective: minimization of the total cost of the operation. In principle, the simultaneous solution of the optimal control problem and the optimal cleaning scheduling problem should provide greater savings than the independent or sequential solution of the two problems, since the interactions of the two mitigation alternatives are considered. However, these two problems have been typically considered separately, because of modeling and solution challenges. Also, it is not quite clear what additional benefit a simultaneous solution may bring. The challenges for solving the integrated problem are the large scale of the associated optimization problem and the different time scales involved in each operational layer. Here, a general and efficient formulation is proposed, using a continuous time discretization scheme for the integrated problem of scheduling and control of HENs subject to fouling. A dynamic model of the heat exchangers is proposed that is sufficiently detailed to represent the physics of interest with novel modifications to address simultaneously their control and scheduling in a network. The problem is formulated as a MINLP and solved using deterministic optimization algorithms. The flexibility of the model and variations of the formulation are demonstrated with two small case studies. The formulation complexity versus scale and advantages are analyzed. The results show that considering the two problems simultaneously has a very strong synergistic effect, with over a 20% decrease in operational cost achieved, in comparison to using either fouling mitigation alternative individually.