Scheduling with limited machine availability

Most literature in scheduling assumes that machines are available simultaneously at all times. However, this availability may not be true in real industry settings. In this paper, we assume that the machine may not always be available. This happens often in the industry due to a machine breakdown (stochastic) or preventive maintenance (deterministic) during the scheduling period. We study the scheduling problem under this general situation and for the deterministic case.

Machine Scheduling with An Availability Constraint

A survey of scheduling with deterministic machine availability constraints

We address the problem of rescheduling production systems in the face of dynamic job arrivals. Using simple single-and parallel-machine models to gain insight, we provide worst-case and computational analyses of periodic and event-driven rescheduling policies. Our results indicate that event-driven policies can obtain high-quality schedules with less rescheduling than continuous rescheduling policies. We also show that if structure in the job arrival process is exploited very effective periodic rescheduling policies can be designed.

Analysis of periodic and event-driven rescheduling policies in dynamic shops

We will give a survey on results related to scheduling problems where machines are not continuously available for processing. We will deal with single and multi machine problems and analyze their complexity. We survey NP-hardness results, polynomial optimization and approximation algorithms. We also distinguish between on-line and off-line formulations of the problems. Results are concerned with criteria on completion times and due dates.

Machine scheduling with availability constraints

We consider the problem of scheduling tasks on a single machine to minimize the flowtime. The machine is subject to breakdowns during the processing of the tasks. The breakdowns occur at a random times and the machine is unavailable until it is repaired. The times for repair are random and independent of each other and of the breakdown process. A task that is preempted due to a breakdown must be restarted and otherwise preemptions are not allowed. We show in the case of a single breakdown that if the distribution function of the time to breakdown is concave then Shortest Processing Time (SPT) first scheduling stochastically minimizes the flowtime. For the case of multiple breakdowns we show that SPT minimizes the expected flowtime when the times to breakdown are exponentially distributed. If the time for a single breakdown is known before scheduling begins, and the processing times of the tasks are also known, then we show that the problem of deciding whether there is a schedule with flowtime less than or equal to a given value is NP-complete. Finally, we bound the performance of SPT scheduling in the deterministic case when there is a single breakdown.

R. A. H. G. Kan

Papers

Single machine flow-time scheduling with a single breakdown