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Petri nets have long been used in modeling and simulating project execution because of their great capability to describe concurrent activities and simulate the evolvement of processes. Although a number of extended Petri net models have been proposed to model and simulate resource sharing and activity dependence in projects, none of them has ever included a resource assignment mechanism into their models. Because resource assignments influence how limited resources are allocated among conflicting activities, they may heavily affect the availability of resources and the execution of projects. Therefore, a model without considering resource-sharing and resource assignment strategies may lead to a misunderstanding about project scheduling, resource consumption behaviors, and estimated project time. Accordingly, this paper proposes a new extended Petri net model that can describe how resources are shared and assigned among concurrent activities of multiple projects. The proposed model is named as resource assignment Petri net (RAPN), which extends an object composition Petri net with new places, transitions, attributes, and firing rules to model resource-sharing and resource assignment strategies. Finally, we prove that RAPN can correctly model the resource consumption behaviors of projects and can correctly compute the total elapsed time of projects.