A general iterative approach for the system-level joint optimization of pavement maintenance, rehabilitation, and reconstruction planning

We formulate a general bottom-up model for the joint optimization of maintenance, rehabilitation, and reconstruction (MR&R) schedules for a system of heterogeneous pavement segments under budget constraints. The objective is to minimize the total costs incurred to both the highway users and the pavement management agency. We propose a Lagrange multiplier approach together with derivative-free quasi-Newton algorithms to solve the problem for two scenarios: i) with a combined budget constraint for all the treatments; and ii) with one budget constraint for each treatment. The system-level solution approach has the following merits: i) it can be applied to problems with any forms of segment-level models for user and agency costs, deterioration process, and treatment effectiveness, given that the solution to the segment-level problem is available; ii) under the combined budget constraint, it ensures that the optimality gap of the system-level solution is bounded by a term that depends upon the optimality gap of the segment-level solutions; and iii) it exhibits linear complexity with the number of segments. At the segment level, a new maintenance effectiveness model fitted on empirical data is proposed and incorporated into the MR&R optimization program. A greedy heuristic algorithm is developed, which greatly reduces the computation time without compromising the solution quality. Combining the system- and segment-level models and solution algorithms, we examine a batch of numerical cases. The results show considerable cost savings from the incorporation of maintenance, and from jointly optimizing the use of a combined agency budget. A number of managerial insights stemmed from the numerical case studies are discussed, which can help highway agencies formulate more cost-efficient MR&R plans and budget allocation.