Parallel batch scheduling with nested processing set restrictions

Abstract

We study the problem of scheduling n jobs on m parallel batching machines with nested processing set restrictions. Each job has a release time before which it cannot be processed, and has a restricted set of batching machines to which it can be assigned, called its processing set. Two distinct processing sets are either nested or disjoint. Each batching machine can process up to B (B<n) jobs simultaneously as a batch, where B is known as the batch capacity. The processing time of a batch is the maximum of the processing times of the jobs belonging to it. The objective is to minimize the makespan (maximum completion time) of the schedule. When all jobs are released at the same time, we present a fast algorithm with approximation ratio 3−1/m. For the case of unequal release times, we develop a fast algorithm with approximation ratio 4−1/m, as well as a polynomial time approximation scheme (PTAS).