The efficiency of equipment units in chemical process plants decreases with time because of fouling, byproduct formation, catalyst deactivation, etc. Therefore, periodic equipment maintenance and/or cleaning are required to restore original operating conditions that allow the desired high productivity rates to be maintained. Maintenance imposes a tradeoff decision between the cost associated with equipment shutdown and the resulting benefit of improvements in productivity. When parallel processing lines are considered in a production facility, the problem becomes more complex because of the presence of material interrelationships. In this work, the solution to this complex maintenance problem is addressed by introducing a simple formulation (NLP) for the planning problem and a procedure for the subsequent implementation of the discrete decisions involved (clean or not, feed assignments) in a real-time environment. This methodology can be considered an extension of the real-time evolution (RTE) approach for continuous processes (Sequeira, S. E.; Graells, M.; Puigjaner, L. Ind. Eng. Chem. Res. 2002, 41 (7), 1815). The main advantage of the proposed methodology is the robustness resulting from the use of on-line information, which reduces the model dependency and, thus, the undesirable effects of variability and plant-model mismatch. The proposed off-line and on-line approaches are tested with benchmark case studies, their performance is evaluated using dynamic simulations, and their long-term behavior is monitored via Monte Carlo simulations.