Machine Maintenance with Workload Considerations

Mark E. Lewis
School of Operations Research and Industrial Engineering
226 Rhodes Hall
, New York 14853

David L. Kaufman
University of Michigan
Department of Industrial and Operations Engineering
1205 Beal Avenue, Ann Arbor, MI 48109-2117

Machine maintenance is modeled in the setting of a single-server queue. Machine deterioration corresponds to slower service rates and failure.  This leads to higher congestion and an increase in customer holding costs. The decision-maker decides when to perform maintenance, which may be done preemptively; before catastrophic failures. Similar to classic maintenance control models, the information available to  the decision-maker includes the state of the server. Unlike classic models, the information also includes the number of customers in queue. Considered are both a repair model, with random repair times, and a replacement model, with fixed costs but instantaneous repairs. It is shown in general that the optimal maintenance policies have switching curve structure that is monotone in the server state. However, the switching curve policies for the repair model are not always monotone in the number of customers in the queue. Numerical examples and two heuristics are also presented.