A heuristic for the critical chain scheduling problem based on left shifts of activities

The critical chain method (CCM) is a promising project management and scheduling method. Inserting feeding buffers into the baseline schedule is a crucial step in generating the critical chain schedule. However, it will lead to new resource conflicts due to resource constraints. At present, there is a scarcity of study on this subject, and the methods used in the existing literature tend to be oversimplified. This work presents a new solution for critical chain scheduling based on left shifts of activities in the theoretical framework of the CCM. The hypotheses for resolving the precedence and resource conflicts arising from inserting feeding buffers are comprehensively investigated. Under the hypothesis that the sizes of feeding buffers are not permitted to be justified, we insert feeding buffers based on the left shifts of activities and the recursion technique. The priority rule-based method is used in the left shifts to resolve precedence and resource conflicts, and thus, a heuristic for critical chain scheduling is proposed. Finally, we conduct computational experiments to test the performance of 11 priority rules and 121 priority rule pairs in the heuristics. The experimental results will help to choose priority rules when applying the presented heuristic to real-world project management.