Priority-based scheduling of scarce resources

In the priority scheduling problem limited resources must be assigned to prioritized jobs of fixed duration. The optimal solution to an instance of the priority scheduling problem assigns resources to as many top priority jobs as possible. The priority scheduling problem is formalized, and it is proved that it is computationally difficult, or NP-hard. An exponential though efficient algorithm which obtains optimal solutions is also proposed. The algorithm is demonstrated on several vexing problems. Finally, modifications to the algorithm which would allow it to obtain 'near optimal' solutions in polynomial time are suggested.<>