A moving window decision-making algorithm is proposed for the cleaning schedule optimization of heat exchanger network system subject to fouling in refinery crude preheat train. This algorithm is designed by incorporating the moving window scheme into a conventional multi-period optimal control problem (OCP) framework and has a distinct feature that it can efficiently handle a complex problem where a long-time horizon is considered. When compared with the conventional multi-period OCP method using fixed time horizon, our algorithm always shows an excellent performance regarding the computational time, still finding a compatible optimal solution. In our moving window decision-making algorithm, it is important to determine the optimal moving window size for the given time horizon as it significantly influences the optimization performance.