Optimal Inspection Policies for Deteriorating Markov Processes.
Abstract
A model is presented of a Markov process whose state is unknown except when an inspection is performed. The evolution of the process is governed by fixed transition probability matrices P and Q under non-inspection and inspection, respectively. The costs of inspection and non-inspection depend on the current state. The objective is to characterize inspection policies which minimize expected total discounted cost. The following specific models are presented. Model I is a process which starts in state 0 and is terminated when, on inspection, the state is found to exceed some fixed value M. In Model II the process is repaired (reverts to state 0) when the state at inspection exceeds M. Simple conditions are given which imply that the optimal inspection interval is a non-increasing function of the last observed state. Model III is an inventory process with uncertain supply as well as demand. Given order size n, the number received is Binomial (n;p). Costs of ordering, storage, and shortage are incorporated. In the single period case, conditions are given which imply that the optimal order size is non-increasing in current inventory. This result extends to the undiscounted multiperiod case provided the holding cost is zero. A counterexample is given for a two period case with linear, non-zero holding, shortage, and ordering costs. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1977
- Accession Number
- ADA041318
Entities
People
- Robert D. Levin
Organizations
- University of California, Berkeley