A Mean Variance Approach to the Optimal Machine Maintenance and Replacement Problem

Abstract

This paper considers a simultaneous maintenance and replacement problem under uncertainty. The effects of maintenance and deterioration are assumed to have a probabilistic effect (of the Markovian type) on a machine's salvage value. This leads to the definition of a non-stationary stochastic process of the machine's salvage value whose mean and variance evolutions are found. These evolutions together with an expected discounted profit functional (as that given by Thompson) allows us to apply the tools of optimal control theory to determine a "certainty-equivalent" maintenance program and the optimum replacement date of the machine. A discussion of the uncertain effects of deterioration and maintenance and managers attitudes towards risk is included as well.