A distributed multi-project scheduling problem is considered, in which several projects share scarce resources, and a planning department (planner) is responsible for allocating the resources among the projects. Information asymmetry and heterogeneous resources are assumed to be due to the geographical distribution of the planner and the projects. The projects compete for the limited global resources to maximize their local benefit, such that they may lie or overstate resource importance to the planner. In this paper, a multi-agent system is developed to address this problem due to the concerns of private information and highly autonomous nature of project agents, which makes a central coordination approach unsuitable. Different from previous work, a project agent may employ the lying strategy to increase its possibility of winning the desired resource, while the planner can adopt an integrity policy to penalize this behaviour. Another main contribution is that a heuristic procedure is designed and combined with an argumentation-based approach for this multi-agent system that can improve computation efficiency. Finally, the proposed combined multi-agent system is compared with a central coordination algorithm to demonstrate its efficacy. Numerical experiments show that the combined multi-agent system is more effective in exploration. It outperforms the central coordination algorithm for problems of a larger scale, especially those with a tighter global resource constraint. Experimental results also reveal that the proper integrity policy could considerably reduce the negative effect of dishonesty of the project agents on the global objective by eliminating the potential to benefit from lying. (C) 2021 Elsevier B.V. All rights reserved.