A note: approximation algorithms for batch scheduling on shops with job rejection

The most popular and cited model of batch scheduling was introduced and solved almost four decades ago. This pioneering model assumed a single machine, serial batching of unit-time jobs and batch-independent setup times. In the current note, we extend this setting by (i) allowing job-rejection, and (ii) considering flowshop and openshop. The objective function contains two cost components: sum of job completion times and total rejection cost. We introduce approximation algorithms for these problems, which are based on solving to optimality the relaxed versions (allowing non-integer batches) in the first stage, followed by rounding procedures to create integer batches. The results of our numerical tests verify that these efficient approximation algorithms produce very close-to-optimal schedules.