Minimizing Capacity Loss on Single Machine Scheduling Problems subject to Breakdowns and Preventive Maintenance

We analyze a one machine scheduling problem subject to breakdowns and preventive maintenance. The primary objective in this work is to minimize the capacity loss due to rework resulting from breakdowns and potential capacity loss due to unnecessary maintenance. We propose a model where the timeline is split into two alternating regions as risk free and risky regions by assuming that the machine does not breakdown for a fixed amount of time after the last maintenance. We show how to partition and schedule jobs into these regions to minimize the capacity loss. We argue that strategically placed maintenance creates a hedging opportunity for the decision maker between the expected rework loss and the time lost due to the preventive maintenance so that it can eliminate unnecessary processing loss.