Parallel-Machine Rescheduling with Job Rejection in the Presence of Job Unavailability

Abstract

This chapter focuses on a scheduling problem on identical parallel machines to minimize the total completion time under the assumption that all the jobs are available at time zero. However, before processing begins, some jobs are delayed and become unavailable at time zero, so all the jobs need to be rescheduled with a view to not causing excessive schedule disruption with respect to the planned schedule. To reduce the negative impact of job unavailability and achieve an acceptable service level, one option in rescheduling the jobs is to reject a subset of the jobs at a cost (the rejection cost). Three criteria are thus involved: the total completion time of the accepted jobs in the adjusted schedule, the degree of disruption measured by the maximum completion time disruption to any accepted job between the planned and adjusted schedules, and the total rejection cost. The overall objective is to minimize the former criterion, while keeping the objective values of the latter two criteria to no greater than the given limits.