Groupe d’études et de recherche en analyse des décisions

G-2021-26

Maintenance of a collection of machines under partial observability: Indexability and computation of Whittle index

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We consider the problem of scheduling maintenance for a collection of machines under partial observations when the state of each machine deteriorates stochastically in a Markovian manner. We consider two observational models: first, the state of each machine is not observable at all, and second, the state of each machine is observable only if a service-person visits them. The agent takes a maintenance action, e.g., machine replacement, if he is chosen for the task. We model both problems as restless multi-armed bandit problem and propose the Whittle index policy for scheduling the visits. We show that both models are indexable. For the first model, we derive a closed-form expression for the Whittle index. For the second model, we propose an efficient algorithm to compute the Whittle index by exploiting the qualitative properties of the optimal policy. We present detailed numerical experiments which show that for multiple instances of the model, the Whittle index policy outperforms myopic policy and can be close-to-optimal in different setups.

, 29 pages