Nowadays, the urgent need for sustainable development is imposing radical changes in how to design, produce and distribute the right product, in the right place, at the right time and at the right price. A new paradigm named "Physical internet" has been presented as worldwide open interconnected logistics system to make the current logistical systems more flexible and sustainable. This paper addresses the inventory management in the classical supply chain and the Physical Internet supply chain networks while considering possible perturbations during the delivery of goods between the hubs. We consider a supply chain network configuration from the literature. Two simulation models are proposed to test both the classical supply chain network and the Physical Internet supply chain under perturbations. Three scenarios are considered by varying delivery delays, retailers' demands and the number of trucks for the two simulation models. Several key performance indicators (KPIs) are considered, such as resources usage, transportation cost, storage cost and delivery delays.