Abstract
We consider a multi-project scheduling problem with time constraints on resources, which appear in the planning of new projects that need to use the same resources as other projects under execution. We seek the optimal sequence of activities and the shortest completion time for all projects taken together. We propose a solution procedure using a branch and bound method for small size problems, where the bounding operations are established by a lower bound as well as an equivalence relation between the sequences of activities. An approximate solution by heuristics is required because of the high computational complexity. The approximate solutions obtained by eight heuristic rules are compared with the shortest completion times by using randomly generated simulating problems. We conclude that an earliest finishing time order rule provides effective heuristic rules for multi-project planning with time constraints on resources; however, a latest finishing time order rule is effective for a large-scale project.
