Optimization of multi-product nodes in supply chains

In this paper, supply chain nodes are considered, with the aim of optimizing the production of parts belonging to different classes (the case of two classes is here taken into account). The production node is modelled by a discrete-event model, being the system state, consisting of the continuous level of input and output inventories, affected by the asynchronous processes relevant to part arrivals and product departures. Moreover, also the resource capacity of the node is represented by a continuous variable (to be shared among the two classes). In the paper, two optimization problems are proposed: the former is only stated due to its intrinsic complexity, whereas the latter (a simplified version of the former) is stated and solved. In the latter problem, an optimization is performed each time an event occurs, in order to determine which the next event is, when the next event will occur, how many raw parts/products will arrive/depart, and which portions of production capacity are assigned to the two classes.