Optimal Highway Maintenance Policies under Uncertainty

We develop an inspection and maintenance policy to minimize the cost of maintaining a given section of road or highway when there is a great deal of uncertainty in the degradation process. We propose to model the degradation of a section of road based on the proliferation and growth of cracks. We utilize a combination of a Poisson and gamma process to account for the tremendous amount of uncertainty and difficulty in predicting the proliferation of cracks. Our policy defines the optimal inspection interval as well as the minimum threshold at which to perform crack repairs. Furthermore, our policy contains a safety constraint to prevent the probability of a "catastrophic" failure from exceeding a pre-determined reliability value. Numerical calculations have shown that our model will extend the lifecycle of the road by performing preventive, conditioned-based maintenance to slow down the growth of cracks. Classical preventive maintenance policies usually shorten the lifecycle by forcing earlier renewals.