Maintenance and production scheduling on a single machine with stochastic failures

In this paper we study the problem of determining a production schedule for an order of n jobs on a single machine which is subject to stochastic machine failures. To avoid long downtime of the machine caused by unexpected failures, preventive maintenance should be planned as well. If a failure cannot be averted, a corrective maintenance activity is performed. Both maintenance activities are assumed to restore the machine to become `as good as new'. Furthermore it is assumed that jobs, interrupted by a machine failure, have to get restarted after the corrective maintenance is finished (non-resumable case). The aim is to minimise the average cost, composed of cost through order tardiness, when exceeding a due date, and cost for preventive as well as corrective maintenance activities. In order to regard practical relevance we compare simple production and maintenance scheduling rules for a huge number of jobs. In the course of a simulation study we first illustrate that in general an adjusted First Fit Decreasing algorithm generates the best results compared to other common used scheduling rules. We secondly show that the optimal length of the preventive maintenance interval can be estimated by using an extended decomposition approach which regards the non-resumable case, even if the processing times of the jobs are very long.