Data-driven robust strategies for joint optimization of rail renewal and maintenance planning

We study the problem of rail renewal and maintenance planning. The problem is to determine when and what type of maintenance tasks or rail renewal are required to be performed on different segments to maintain the rail in a safe and reliable condition. This problem is formulated as a Mixed Integer Linear Programming (MILP) model. The model applies Track Quality Index and also defines a new index to represent the current condition of the rail. Maintenance recovery effect is intrinsically uncertain; therefore, we develop data-driven uncertainty set approximation approaches and leverage robust optimization to handle the uncertainty. Data-driven uncertainty sets are constructed by approximating convex hulls of uncertain data points and by adding cutting planes to mix of classic robust uncertainty sets. We also obtained the robust counterpart formulations of the proposed MILP model for constructed uncertainty sets. Furthermore, a heuristic algorithm is developed to facilitate solving large-scale instances. Applicability and efficiency of the proposed approach are demonstrated through an illustrative case study of a Class I freight railroad network in the United States. Our analyses reveal that the proposed approaches introduce efficient strategies to deal with uncertainties in rail networks at the reasonable cost of increasing the budget.