Optimal reconstruction periods for stochastically deteriorating infrastructures

In this article we address the problem of identifying the optimal period between reconstructions, also called reconstruction periods, for an infrastructure system whose performance deteriorates stochastically over time. Performance may refer to the physical condition, such as pavement or bridge condition. We first demonstrate that for any stochastic deterioration process and reconstruction period, the long-term cost-effectiveness, defined as the ratio of the total non-monetary benefit to the total monetary cost across several reconstruction periods, is simply the ratio of the expected benefit to the expected cost up to the first reconstruction, assuming that reconstructions bring the facility back to the new state. We then select four popular mathematical forms of facility performance and present methods to determine the optimal reconstruction periods. The reconstruction cost is assumed to satisfy a certain specified structure.