Business process modelling is the description of business process chains and their associated aspects such as resources, information, organization and so on. Business process instantiation is the operational process-centred performance configuration through project-oriented task decomposition, resource assignment and activity arrangement. The present paper elucidates the links between business process modelling and project-oriented business process instantiation, and proposes the optimization model and algorithm of resource assignment of business processes in multi-project environment. Based on the extended AON (activity on node) graph, the trade-off analytical model between time and cost is developed considering resources, cost and time constraints as well as decision nodes such as OR and XOR (exclusively OR) besides AND junction in IDEF3 process models for multi-project resource assignment. The proposed algorithm employs genetic algorithm to deal with resource assignment and stack technique and unified time window to tackle resource constraints and decision nodes. The validity of the model and the effectiveness of the algorithm are revealed. The proposed methodology, model and algorithm of project-oriented resource assignment from business process modelling to business process instantiation are a useful support for the establishment of truly integrated enterprise modelling and analysis environment.