Some Properties of Schedules for Large Projects with Limited Resources

The Critical Path Method, PERT, and related techniques that make use of arrow diagrams for scheduling large projects implicitly assume that unlimited resources are available for assignment to project activities. When resources are limited, however, the usual concepts of “critical path” and “job slack” basic to these methods lose their normal meaning. Jobs may be delayed by the unavailability of resources as well as by technological orderings. A scheme for analyzing project schedules in the limited resource case is developed in this paper, with the intent of preserving for the project scheduler the operational utility of the slack concept. A new procedure for calculating slack values leads to the identification of a “critical sequence” of jobs in a certain class of project schedules—a notion analogous to that of a critical path in the unlimited resource case. Some properties of project schedules when resources are limited are explored and suggestions are made for utilizing the revised concept of slack in scheduling large projects.