Process units subject to fouling often require regular cleaning, giving rise to repeated cycles of fouling and cleaning. The initial stages of fouling are strongly influenced by the effectiveness of the most recent cleaning step and, similarly, the effectiveness and rate of cleaning are determined by the extent and nature of the deposit layer present on the surface. The optimal operating cycle will therefore be determined by fouling-cleaning interactions. Deposit aging is an important factor in this, as an aged deposit is usually more difficult to clean. Aging therefore introduces an element of choice into fouling-cleaning operating cycles, between in situ chemical methods and ex situ mechanical methods, with associated differences in effectiveness, time, and cost. This paper reports a reformulation of the cleaning scheduling problem to consider the choice of cleaning method, as well as the timing of cleaning. A case study based on a shell-and-tube heat exchanger processing crude oil is used to illustrate the concepts and scope of application of this approach. A novel and more general formulation of the problem, linking design, fouling, and cost aspects via dimensionless groups, is then presented and illustrated with a second case study based on a simpler exchanger model.