Transportation infrastructure maintenance planning: An exact column enumeration approach

Abstract

Transportation infrastructure assets deteriorate over time due to natural hazards, heavy traffic, and aging, increasing their risk of failure. National transportation agencies must strategically invest in maintenance to avoid significant social and economic impacts. We address the infrastructure maintenance planning problem, in which a maintenance plan must be designed for each asset within a budget limit to maximize the weighted average asset condition over a planning horizon. We derive a knapsack-type mathematical formulation and propose an exact column enumeration algorithm to solve it. First, a column-and-cut generation algorithm computes a (dual) upper bound on the optimal value. The master problem selects a maintenance plan for each asset and is strengthened with extended $q$-cover inequalities. By representing maintenance plans as paths over a directed acyclic multigraph that captures asset deterioration and maintenance decisions, the pricing problems unveil feasible plans through a specialized labeling algorithm. Second, a relaxation-enforced neighborhood search finds a (primal) lower bound. Finally, using these bounds, we enumerate sufficient columns to find an optimal solution via a commercial MILP solver. Computational results on generated instances spanning a 10-year planning horizon demonstrate that our algorithm delivers optimal solutions for instances with up to 50 assets and near-optimal solutions (gap $<$ 0.18%) for instances with up to 100 assets within five hours.