Inventory control of a class of logistic networks

Abstract This paper focuses on a prediction-based control for a class of convolution systems subject to constant input delays, also known as the reduction approach. We propose here a characterization of the D -invariance property of polytope sets for continuous-time systems. Our motivations come from production management, where a general model for a production network is considered. The system is subject to product losses and multiple delays, with bounded demand. This model is transformed into an equivalent free-delay system using Artstein reduction. The question of regulating the inventory levels of the nodes of this production network is then reduced to a pair of sub-problems, that are the regulation of the equivalent system without delay, and the relationship between the output of the system and that of the reduced system. A pair of conditions is therefore obtained, for the verification that a large class of control solutions allow to satisfy the external demand, while meeting the constraints that are imposed to the system. At the end, explicit conditions are found for an example of a supply chain with two nodes.