Logistic network modeling and optimization: An approach based on (max,+) algebra and coloured Petri nets

Abstract

The present article deals with supply chain management considered as a Discrete Event System (DES). We introduce a new modeling approach based on linear and non-stationary (max, +) equations obtained from a Timed Coloured Petri Nets (TCPN) describing the studied system’s behavior. Our contribution does not lie only on the modeling of the dynamics associated with vehicles and their timetables at different sites (e.g., suppliers, warehouses, customers), but also on the evaluation of loading, unloading, and delivery times of products from suppliers to customers, taking into account their appropriate characteristics (e.g., number, nature, destination). Moreover, a control approach is performed to optimize the number of vehicles to deploy on the network by ensuring product storage times below a given threshold at some specific sites considered strategic (e.g., delivery hubs). The developed models can be used as a decision-making system for logistic companies to result in efficient supply chain management. The developed models are tested and validated on several configurations and scenarios to demonstrate our approach’s applicability.