Many heat exchanger networks in continuous processes are subject to fouling, which causes significant losses in efficiency over time. This paper addresses the problem posed in scheduling cleaning operations in order to maintain optimal operation in such networks. A mixed integer nonlinear programming model is presented and is solved using the Outer Approximation/Extended Relaxation algorithm. The methodology is demonstrated via case studies using fouling rates obtained from plant data studies. Both linear and asymptotic fouling behaviors are considered. The challenges posed by the nonconvexity of the problem in finding a global optimum are discussed.