Optimization of inventory levels and production effort in Hybrid Inventory-Production (HIP) systems

A production node within a network of interconnected production centers (as in supply chains) is considered in this paper, with the aim of optimizing inventory levels and production effort. The proposed Hybrid Inventory-Production model consists of two inventories (the input one for raw parts and the output one for processed parts) and a production resource which transforms parts and moves them from the input to the output inventory, at a certain rate. The production node interacts with other nodes in the network by the arrival process (raw parts entering the node) and the departure process (processed parts leaving the node). In HIP systems, arrival and departure processes, as well as the production process, are supposed to be piece-wise constant functions that change their values at asynchronous time instants. Based on this model and considering different cost terms, a mixed-integer nonlinear optimization problem has been defined. Then, some assumptions have been considered and the optimization problem has been simplified until obtaining a linear statement.