Fouling of heat exchangers causes reduced heat transfer and other penalties. Regular cleaning represents one widely used fouling mitigation strategy, where the schedule of cleaning actions can be optimised to minimise the cost of fouling. This paper investigates, for the first time, the situation where there are two cleaning methods available so that the mode of cleaning has to be selected as well as the cleaning interval. Ageing is assumed to convert the initial deposit, labelled 'gel', into a harder and more conductive form, labelled 'coke', which cannot be removed by one of the cleaning methods. The second method can remove both the gel layer and the coke layer, but costs more and requires the unit to be off-line longer for cleaning. Experimental data demonstrating the effects of ageing are presented. The industrial application is the comparison of cleaning-in-place methods with off-line mechanical cleaning. A process model is constructed for an isolated counter-current heat exchanger subject to fouling, where ageing is described by a simple two-layer model. Solutions generated by an NLP-based approach prove to be superior to a simpler heuristic. A series of case studies demonstrate that combinations of chemical and mechanical cleaning can be superior to mechanical cleaning alone for certain combinations of parameters. (C) 2011 Elsevier Ltd. All rights reserved.