Greedy Priority-Queue Scheduling Problem

Problem: A scheduling-style problem requiring a non-trivial greedy approach using a priority queue (exact statement not preserved by the candidate, but required identifying a greedy strategy verified via exchange-argument reasoning).

Approach: Model each task/job as an element with a cost/deadline/weight, push candidates onto a min/max-heap keyed by the greedy criterion (e.g. earliest deadline, highest penalty-avoided), and repeatedly pop the best candidate while updating remaining capacity/time. The exchange-argument justifies why picking the locally best choice at each step doesn't lose global optimality.