Solving the resource-constrained multi-project scheduling problem with an improved critical chain method

In view of the fact that the critical chain method (CCM) is mainly used in single project scheduling, this article improves the method and applies it to multi-project scheduling. Taking into consideration the flow of the drum resource within and among sub-projects, this study proposes methods that can be used to identify the critical chain and buffer settings, based on the concepts of the task chain, sub-project drum resource flow, and multi-project drum resource flow. The improvement of the CCM includes two aspects. First, by analysing the impact of the drum buffer and capacity constrained buffer on the project buffer and feeding buffer, the calculation methods of these buffers are optimised. Second, a risk contribution index is designed for the modification of these buffers, in order to further improve their anti-interference ability. Then, combined with the improved CCM and the different hierarchical scheduling objectives, a critical chain resource-constrained multi-project scheduling model with a hierarchical strategy is proposed as a way of solving multi-project scheduling plans. Eight theoretical test cases with different scales, and a practical example under different risk levels of uncertainty are used to test this model. The results show that the stability of the scheduling plans clearly improved, and the project duration and tardiness costs were significantly reduced, thus proving the effectiveness of the model.