Parallel-batch scheduling with rejection: Structural properties and approximation algorithms - Ou, Jinwen; Lu, Lingfa; Zhong, Xueling (European journal of operational research, 2023)
•Parallel-batch scheduling with dynamic job arrivals and rejection.•Important structural properties are developed and skillfully applied.•A (3−1/b)-approximation algorithm with a complexity of O(nlogn).•An efficient PTAS with a complexity of O(nlogn+Cn). In this paper, we consider a parallel-batch machine scheduling (PBMS) model that unifies several existing scheduling models in the extant literature. In our scheduling model, a given set of jobs with different release dates are scheduled onto a machine that can process multiple jobs simultaneously in a batch. However, the number of jobs in a batch is limited. Each job can be rejected subject to a job-dependent penalty cost, but the total penalty cost of the jobs rejected is required to be no greater than a given bound. The objective is to minimize the weighted sum of the makespan of accepted jobs and the total rejection penalty of rejected jobs. We provide some important structural properties and develop fast approximation algorithms. We also present an efficient polynomial time approximation scheme (EPTAS) with near-linear-time complexity. Our results significantly improve both the time complexities and performance bounds of several existing algorithms and approximation schemes.