The Bounded Batch Scheduling with Common Due Window and Non-identical Size Jobs.

The common due window scheduling problem with batching on a single machine is dealt with to minimize the total penalty of weighted earliness and tardiness. In this paper it is assumed that a job incurs no penalty as long as it is completed within the common due window. The problem is extended to the environment of non-identical job sizes. Then several optimal properties are given to schedule batches effectively. And by introducing the concept of PRN, it is proven that the PRN of each batch should be made as small as possible in order to minimize the objective. Based on these properties, an algorithm F-PRN for batch forming is proposed for the problem.