Minimize the Sum of Total Completion Time and Total Rejection Penalties on a Single Parallel Batching Machine

In this paper, we consider the problem of unbounded single machine parallel batch scheduling with rejection. Jobs can either be scheduled on an unbounded parallel batch processor or be rejected. Jobs processed in the same batch have the same starting time and completion time. For each rejected job, there is a corresponding rejection penalty. Our objective is to minimize the sum of total completion time and total rejection penalties. We present a polynomial time algorithm in time O(n³ log n) by using dynamic programming. This is the first result concerning this objective function for batch scheduling with rejection.