The fuel consumption in the fired heaters of atmospheric distillation columns for petroleum refining increases during the refinery operation. This effect is a consequence of fouling in the heat exchangers of the crude preheat train. The application of a cleaning schedule to the crude preheat train can reduce fouling costs. However, the management of the cleanings for the entire set of interconnected heat exchangers is a complex problem. Aiming to contribute to the solution of this problem, this paper presents an optimization approach based on the resolution of a sequence of mixed-integer linear programming problems. Each problem indicates the set of heat exchangers that must be cleaned in a certain time instant. The structure of the crude preheat train is described using an incidence matrix, encompassing supply and demand nodes, heat exchangers, mixers, splitters, and desalters. The sequence of problems is associated to a sliding horizon, where the concatenation of the solutions composes the complete heat exchanger cleaning schedule. Although the present approach cannot guarantee the global optimality of the solution, the linear structure avoids nonconvergence problems. The performance of the proposed approach is illustrated through its application in an example of a crude preheat train from a Brazilian refinery.