Joint Optimal Policies for Pavement Maintenance, Repaving, and Reconstruction: A Static Optimization Approach

Research on optimal policies for infrastructure management has a long heritage. In this paper, we deviate from previous research and use a static optimization approach. To this end, we invoke the uniform network assumption. We show the resulting mathematical simplifications permit the derivation of a nearly complete analytic solution in closed form, that is, as directly executable expressions for each of the choice variables. The remaining choice variable can be found by a short integer program. Given the specified deterioration process, the optimal repaving intervals form a harmonic series. A fitting parameter allows a spectrum of specific patterns between sharply declining intervals to equal length intervals. Derivations depend on the insight that, at an optimum solution, the derivative of total cost with respect to repaving cycle lengths, at the close of each repaving cycle, must equal average total cost over the whole reconstruction cycle and, consequently, those derivatives must all be equal to one another. Thus, we conclude that the static optimization approach combined with the uniform network assumption yields surprisingly clear insights into this long-standing problem. The solutions are directly applicable to pavement management systems to derive optimal timings for interventions.