Online Parallel-Batch Scheduling of Learning Effect Jobs with Incompatible Job Families for Prefabricated Components

In the production scheduling of prefabricated components, we study an online m parallel-batch machines scheduling model considering learning effect jobs with f incompatible job families to minimize the makespan in this paper, where the capacity of batch is unbounded. Job families indicate that a job must belong to some job family and jobs of distinct job families are incapable to be executed in the same batch. The information of each job including its basic processing time b(j) and release time r(j) is unknown in advance and is revealed at the instant of its arrival. Moreover, the actual processing time of job J(j) with learning effect is p(j) = b(j)(a - bt), where a and b are non-negative parameters and t denotes the starting time of prefabricated job J(j), respectively. When m = f, we propose an online algorithm with a competitive ratio of 2 - bbmin. Furthermore, the performance of the online algorithm is demonstrated by numerical experiments.