A two-stage stochastic programming approach for strategic rolling stock scheduling in passenger railway transport

Abstract

Conventional railway planning follows a sequential approach in which rolling stock scheduling is performed only after timetables are constructed, forcing early-stage line-planning decisions to rely on simplified rolling stock cost approximations. The lack of precise cost information hampers line-plan evaluation and limits the design of cost-efficient services. This study considers rolling stock scheduling in a strategic setting, aiming to estimate fleet size and operational costs for a given line plan without solving the timetabling problem. Since predefined train services are unavailable at this level, unlike in tactical planning, we introduce a network representation incorporating shunting movements like coupling and uncoupling. To account for demand uncertainty, a two-stage stochastic programming approach is proposed, in which first-stage decisions determine fleet acquisition and second-stage decisions optimize rolling stock circulation, including shunting, under each demand scenario. Two models are developed, differing in whether the fleet size is estimated using a flow-based or circulation-based approach. The applicability of the proposed models is demonstrated using instances derived from the Dutch Intercity network. Compared to a trip-based benchmark, the circulation-based model yields more accurate cost estimates, while short and simple cycles retain most of its value at much lower computational cost. Moreover, stochastic planning better captures the procurement–service trade-off under demand uncertainty and produces more robust fleet plans than a deterministic approach. Under strong emphasis on investment costs, fleet choices are dominated by flexible, cost-effective unit types. Allowing shunting enables flexible capacity redistribution, reducing fleet requirements and investment costs while maintaining comparable service levels.