Real-time optimization (RTO) is widely used in industry to improve the steady-state performance of a process using the available measurements, reacting to changing prices and demands scenarios and respecting operating, contractual, and environmental constraints. Traditionally, RTO has used nonlinear continuous formulations to model the process. Mixed-integer formulations have not been used in RTO, because of the need of a fast solution (on the order of seconds or a few minutes), and because many discrete decisions, such as startups or shutdowns, are taken with less frequency in a scheduling layer. This work proposes the use of disjunctions in RTO models, listing a series of examples of discrete decisions (different to startups or shutdowns) that can be addressed by RTO. Two model adaptation approaches (the two-step approach and the modifier adaptation strategy) are revised and modified to make them suitable for RTO with discrete decisions. Some common techniques used in RTO (such as filtering the optimal ...