On optimizing replenishment policies in production nodes of supply chain models

A hybrid model for the representation of a generic production center of a supply chain is presented and discussed in this paper. The model is characterized by two inventory levels (defined as continuous variables) and by arrival and departure processes of raw materials and final products modelled as finite and discrete-time sequences which are realized in asynchronous time instants. An optimization problem relevant to the minimization of the inventory cost for raw materials and of order costs is introduced and solved. The decision variables of the problem are relevant to the arrival process (as they correspond to the number of orders, the time instants in which raw materials enter the node and the ordered quantities). Some important properties of the optimal solution are proved in the paper and a solution procedure is provided.