The ability of online optimization to improve the dynamic performance of complex systems, particularly in production scheduling and process control applications, has led to a significant interest in, and adoption of, online optimization algorithms and techniques for a range of industries. However, these algorithms' abilities to account for subtle features in complex systems may cause nonintuitive and rapid alterations to the optimal trajectory for the human operators often observing, evaluating, and particularly in scheduling applications, executing the tasks prescribed by the optimization algorithm. In practice, these alterations are often restricted in some manner by the scheduling algorithm to alleviate operators' concerns and improve overall facility operation. Although numerous rescheduling penalties and constraints for production scheduling algorithms have been proposed, theoretical properties concerning the dynamics of these modified systems have been largely ignored. In this paper, we provide a general modification to a common online optimization technique known as economic model predictive control (MPC) that allows trajectory alterations, or rescheduling, to be penalized in both process control and production scheduling applications. We then demonstrate that the modified problem is actually a type of suboptimal MPC algorithm. Furthermore, we prove that the economic MPC problem with a rescheduling penalty retains the same nominal feasibility and performance guarantees of the original economic MPC problem. Specific mathematical forms of this penalty relevant to production rescheduling environments are presented, and two simple production scheduling case studies illustrate the effect of this rescheduling penalty.