Machine Maintenance with
Mark E. Lewis
of Operations Research and
New York 14853
David L. Kaufman
Machine maintenance is modeled in the setting of a single-server queue.
Machine deterioration corresponds to slower service rates and
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.
University of Michigan
Department of Industrial and Operations Engineering
1205 Beal Avenue, Ann Arbor, MI 48109-2117