Batch scheduling with common due date to minimizing the total (weighted) tardiness

Batch scheduling is a new type of scheduling problem, in which a processor can process multiple jobs at the same time. This paper studies single processor batch scheduling with jobs coming from different job families and all the jobs having the same due date. We prove that minimizing the sum of tardiness of all jobs is NP-hard based on id-encoding. We also develop pseudo-polynomial time algorithms to minimize the sum of tardiness and the sum of weighted tardiness of all the jobs, respectively. To minimize the sum of tardiness and the sum of weighted tardiness can help to improve the custom satisfaction with the production system.