Rescheduling for machine disruption to minimize makespan and maximum lateness

We consider a scheduling problem where a set of jobs has already been scheduled to minimize some cost objective on a single machine when the machine becomes unavailable for a period of time. The decision-maker needs to reschedule the jobs without excessively disrupting the original schedule. The disruption is measured as the maximum time deviation, for any given job, between the original and new schedules. We examine a general model where the maximum time disruption appears both as a constraint and as part of the cost objective. For a scheduling cost modeled as the makespan or maximum lateness, we provide a pseudopolynomial time optimal algorithm, a constant factor approximation algorithm, and a fully polynomial time approximation scheme. The approximation algorithm has an asymptotically achievable worst-case performance ratio of 2 and has average performance close to optimal. Managerial insights are given on how scheduling costs are affected by machine disruption and the approximation algorithm.