Unrelated Parallel-Machine Scheduling with Controllable Processing Time

This paper explores an unrelated parallel-machine resource allocation scheduling problem with controllable processing time. The objective is to minimize the cost function containing the weighted of total load, total completion time, total absolute deviation of completion time, and total compression cost. We show that the proposed problem is polynomial time solvable. We also discuss a special case of the problem and show that it can be optimally solved by lower order algorithm.