Condition-based maintenance in the cyclic patrolling repairman problem

We consider the cyclic patrolling repairman problem combined with condition-based preventive maintenance. In the traditional cyclic patrolling repairman problem, one repairman inspects and repairs a set of machines in a fixed sequence. We introduce the possibility of performing preventive maintenance on the machines based on condition information. In order to determine optimal policies, we provide a Markov decision process formulation of the problem. Furthermore, this Markov decision process is used to analyze the performance of a control-limit policy, which is a commonly used heuristic for condition-based maintenance problems. The control-limit policy significantly outperforms the traditional policy for the patrolling repairman problem with only corrective maintenance. The optimal policy uses a higher maintenance threshold for a machine if the repairman expects to be back at that machine quite fast, or if failure of another machine is imminent. The benefit of the optimal policy compared to the control-limit policy is largest for sufficiently detailed condition information, for relatively stable deterioration processes, and for medium corrective maintenance costs.