Freight train scheduling with elastic demand

Abstract

A train slot selection model based on multicommodity network flow concepts is developed for determining freight train timetables for scheduling rail services along multiple interconnected routes. The model seeks to minimize operating costs incurred by carriers and delays incurred by shippers while ensuring that the schedules and demand levels are mutually consistent. A column generation-based methodology is proposed for train slot selection to meet frequency requirements. This methodology is embedded in a simulation-based iterative framework, where demand for rail services is re-computed in accordance with the train schedule obtained by solving the freight train scheduling problem.

Introduction

The assignment of freight trains to track segment-time pairs comprising a timetable over the railway infrastructure can be viewed as a track capacity allocation problem, where shipments delivered by the trains compete for track capacity with the goal of meeting preferred delivery times. Timetables resulting from such an allocation specify a departure and arrival time for each train at intermediate and final destinations and are used in making customer commitments. While the timetable may be set to meet expected demand, this demand depends on the services that are offered as a function of the timetable. That is, one cannot assume that the demand is fixed, because the demand is a function of the frequency of service, which determines waiting times at terminals, delays and ultimate delivery times. Furthermore, demand is formed given the level of provided transportation services. To address this elasticity in demand, a freight scheduling methodology that equilibrates between the performance of the freight transport system given schedules, delays and user costs under different demand levels and demand given level of service provided is needed. A scheduling tool that explicitly considers the simultaneity between setting the schedule (supply), which determines service levels experienced by shippers, and the associated demand is proposed in this paper.

This work was motivated by interoperability legislation imposed by the European Commission on all European Union member states, designed to aid in transforming European railways from nationally fragmented systems into an internationally integrated intermodal (IM) freight transport system. While numerous obstacles exist, harmonization of these fragmented systems is crucial to creating a competitive and profitable international system. The competitiveness of IM rail-based service relative to other modes, especially transport by truck, depends on its efficiency as measured by both carriers and shippers. The development of services, including associated timetables to serve this international freight business, needs to consider both shippers and carriers. In addition to its standalone application for rail carriers, the problem addressed in this paper also arises in network analysis and demand forecasting exercises at the strategic planning and policy assessment levels.

The methodology proposed for addressing the freight train scheduling problem with elastic demand is comprised of a train slot selection model (a multicommodity network flow model), with supporting tools, and a column generation-based solution technique employed in an iterative simulation-based framework. The model and solution technique seek an optimal or near-optimal operational cost-saving periodic rail timetable based on given demand and delay estimates. The resulting schedule is evaluated in a microscopic simulation-assignment platform from which demand estimates can be adjusted and delays can be re-estimated. Revised schedules are developed in response to new demand and delay predictions. This iterative procedure is repeated until stopping criteria are met or convergence is achieved.

The train slot selection model considers objectives of both shippers and carriers. The shipper, on the one hand, seeks a schedule that provides the quickest, most reliable service at the lowest cost; the carrier, on the other hand, seeks a schedule that maximizes profit. In the proposed methodology, profit maximization is sought by minimizing operating costs, and thus maximizing the profit margin, while seeking to capture the greatest market share. Ideally, the resulting timetable will consider both decision-makers’ objectives simultaneously. The objective employed in the model, thus, seeks to minimize a function of both operating costs and delays in delivery from scheduled arrival times. Operating costs consist of infrastructure charges and track access costs.

Previous works on freight train scheduling are discussed in Section 2. Nomenclature and the space–time network representation used in this study to create the train timetables are introduced in Section 3. The process of creating a timetable for fixed demand is introduced in Section 4 first. In Section 5, the iterative simulation-based framework is described. This framework produces a timetable for elastic demand, employing techniques from Section 4 and a freight train shipment–assignment microscopic simulation platform. This iterative process was applied on a real-world, pan-European network spanning 11 countries, results from which are discussed in Section 6. Conclusions are given in Section 7. The proposed train scheduling tool enables more efficient utilization of track capacity, improved delivery times and reduced operating costs.