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State-of-the-art approaches for membrane cleaning scheduling have focused on the Mixed-Integer Nonlinear Programming (MINLP) formulation so far, a strategy leading to a combinatorial problem that does not capture accurately the dynamic behaviour of the system. In this work, the Reverse Osmosis (RO) cleaning scheduling problem is solved using a novel approach based on the Multistage Integer Nonlinear Optimal Control Problem (MSINOCP) formulation. The approach produces an automated solution for the membrane cleaning scheduling, which also obviates the need for any form of combinatorial optimisation. Two different simulations, for 26 and 52 periods of operation (each period with a duration of one week), are carried out to illustrate the application of the proposed framework and the total cost is 1.17 and 2.48 107 €, respectively. The RO network configuration considers 2 stages, each with 3 individual RO modules. The results show evidently that the new proposed solution framework can solve successfully this type of problems, even for large scale configurations, long time horizons and arbitrary realistic complexity of the underlying dynamic model of the RO process considered. • Novel methodology for Reverse Osmosis cleaning scheduling maintenance problems • Multistage Optimal Control Problem formulation • Continuous controls replacing binary variables obviate combinatorial optimisation • Bang-bang control behaviour ensuring integrality of solutions • Successful handling and solution of long-term scheduling in non-greedy way [ABSTRACT FROM AUTHOR]