On Optimizing Production Nodes in Supply Chain Systems

Summary. In this chapter a supply chain system is considered, focusing in particular on a single production node. For the single node we propose a hybrid model that combines a continuous-time dynamics, associated with the production process, with a discrete-event dynamics, related to arrivals of raw materials and departures of finite products. The system state variables are given by the inventory levels of raw materials and finite products, while the decisions to be taken concern the arrival process (in terms of number of orders, quantities and ordering time instants), the production process (definition of the production function) and the departure process (determination of the delivery time instants). The resulting optimization problem is nonlinear and functional and it is decomposed into two subproblems that are studied separately (the former is related to the production and the delivery process, the latter concerns the replenishment policy). Some properties of the optimal solution of these subproblems are shown and, in some cases, the optimal control strategies are found. In the final part of the chapter, the proposed optimization approach is extended to consider the case of multi-site schemes, by introducing two simple cases of cooperative and competitive structures.