Time performance optimization and resource conflict resolution are two important challenges in multiple project management contexts. Compared with traditional project management, multi-project management usually suffers limited and insufficient resources, and a tight and urgent deadline to finish all concurrent projects. In this case, time performance optimization of the global project management is badly needed. To our best knowledge, existing work seldom pays attention to the formal modeling and analyzing of multi-project management in an effort to eliminate resource conflicts and optimizing the project execution time. This work proposes such a method based on PRT-Net, which is a Petri net-based formulism tailored for a kind of project constrained by resource and time. The detailed modeling approaches based on PRT-Net are first presented. Then, resource conflict detection method with corresponding algorithm is proposed. Next, the priority criteria including a key-activity priority strategy and a waiting-short priority strategy are presented to resolve resource conflicts. Finally, we show how to construct a conflict-free PRT-Net by designing resource conflict resolution controllers. By experiments, we prove that our proposed priority strategy can ensure the execution time of global multiple projects much shorter than those without using any strategies.