Optimal control of manufacturing processes in Hybrid Inventory-Production systems

In this paper, the proposed Hybrid Inventory-Production model represents a manufacturing center with two inventories (the input one for raw parts and the output one for processed parts) and a production resource which moves parts from the input to the output inventory, at a certain rate. In the considered modelling framework, time-driven and event-driven dynamics coexist, yielding to a hybrid system. An optimization problem is defined where decisions concern the production process (piece-wise constant function changing its value at asynchronous time instants) and the arrival process. Then, an optimal control problem is stated in order to find the closed-loop solutions as functions of the system state. In particular, a multi-stage optimal control problem is defined and it is solved by applying dynamic programming techniques.