A single resource scheduling problem with job-selection flexibility, tardiness costs and controllable processing times

We consider single-resource scheduling when candidate jobs may be accepted (producing job-specific profit) or rejected. Our solution approaches seek to maximize the profitability of the resulting schedule under job-specific tardiness costs and reducible processing times (at a cost). We present an algorithm that maximizes schedule profit for a given sequence of jobs, along with two heuristic approaches for generating good job sequences. A set of computational tests on randomly generated problem instances demonstrates the relative effectiveness of our proposed heuristic approaches.