A mathematical framework for the planning and control of complex systems

A two-level framework is proposed in this paper for a class of complex systems in order to optimize, at a tactical planning level, the activities over a medium-term horizon, and to control, at an operational level, the system resource functioning over a short-term horizon or in real time. At the tactical planning level, an aggregate model of the system is defined and an optimization problem is stated and solved; the optimal solution of such a problem provides a reference plan to be tracked. At the operational level, both optimal control strategies are employed to face perturbations that may affect the system, and a detailed discrete-event or hybrid model is defined to verify some properties and performance indexes of the system. The application of the proposed framework to a logistic intermodal node is illustrated.