This thesis is about mathematical optimization for the efficient use of railway infrastructure. We address the optimal allocation of the available railway track capacity - the track allocation problem. This track allocation problem is a major challenge for a railway company, independent of whether a free market, a private monopoly, or a public monopoly is given. Planning and operating railway transportation systems is extremely hard due to the combinatorial complexity of the underlying discrete optimization problems, the technical intricacies, and the immense sizes of the problem instances. Mathematical models and optimization techniques can result in huge gains for both railway customers and operators, e.g., in terms of cost reductions or service quality improvements. We tackle this challenge by developing novel mathematical models and associated innovative algorithmic solution methods for large scale instances. This allows us to produce for the first time reliable solutions for a real world instance, i.e., the Simplon corridor in Switzerland.
Abstract: "The optimal track allocation problem (OPTRA) is to find, in a given railway network, a conflict free set of train routes of maximum value. We study two types of integer programming formulations for this problem: a standard formulation that models block conflicts in terms of packing constraints, and a novel formulation of the 'extended' type that is based on additional 'configuration' variables. The packing constraints in the standard formulation stem from an interval graph and can therefore be separated in polynomial time. It follows that the LP-relaxation of a strong version of this model, including all clique inequalities from block conflicts, can be solved in polynomial time. We prove that the LP-relaxation of the extended formulation can also be solved in polynomial time, and that it produces the same LP-bound. Albeit the two formulations are in this sense equivalent, the extended formulation has advantages from a computational point of view. It features a constant number of rows and is amenable to standard column generation techniques. Results of an empirical model comparison on mesoscopic data for the Hanover-Fulda-Kassel region of the German long distance railway network involving up to 570 trains are reported."
Faced with increasing challenges, railways around Europe have recently undergone major reforms aiming to improve the efficiency and competitiveness of the railway sector. New market structures such as vertical separation, deregulation and open access can allow for reduced public expenditures, increased market competition, and more efficient railway systems. However, these structures have introduced new challenges for managing infrastructure and operations. Railway capacity allocation, previously internally performed within monopolistic national companies, are now conferred to an infrastructure manager. The manager is responsible for transparent and efficient allocation of available capacity to the different (often competing) licensed railway undertakings. This thesis aims at developing a number of methods that can help allocate capacity in a deregulated (vertically separated) railway market. It focuses on efficiency in terms of social welfare, and transparency in terms of clarity and fairness. The work is concerned with successive allocation of capacity for publicly controlled and commercial traffic within a segmented railway market. The contributions include cost benefit analysis methods that allow public transport authorities to assess the social welfare of their traffic, and create efficient schedules. The thesis also describes a market-based transparent capacity allocation where infrastructure managers price commercial train paths to solve capacity conflicts with publicly controlled traffic. Additionally, solution methods are developed to help estimate passenger demand, which is a necessary input both for resolving conflicts, and for creating efficient timetables. Future capacity allocation in deregulated markets may include solution methods from this thesis. However, further experimentations are still required to address concerns such as data, legislation and acceptability. Moreover, future works can include prototyping and pilot projects on the proposed solutions, and investigating legal and digitalisation strategies to facilitate the implementation of such solutions. Med ökande utmaningar har järnvägar runt om i Europa genomgått stora reformer som syftar till att förbättra järnvägssektorns effektivitet och konkurrenskraft. Nya marknadsstrukturer såsom vertikal separering, avreglering och öppet tillträde för flera operatörer kan möjliggöra minskade offentliga kostnader, ökad marknadskonkurrens och effektivare järnvägssystem. Denna omreglering av järnvägsmarknaderna har dock skapat nya utmaningar för hanteringen av järnvägsinfrastruktur och drift. Tilldelning av järnvägskapacitet, vilket tidigare sköttes inom nationella monopolföretag, måste nu göras av en infrastrukturförvaltare (infrastructure manager). Förvaltarens kapacitetstilldelning till olika (ofta konkurrerande) licensierade järnvägsföretag (railway undertakings) måste samtidigt vara transparent, rättvis och leda till ett effektivt kapacitetsutnyttjande. I denna avhandling utvecklas metoder som kan användas av en infrastrukturförvaltare för att tilldela kapacitet i en avreglerad järnvägsmarknad. Den fokuserar på samhällsekonomiskt effektiva utfall men även transparens, tydlighet och rättvisa. Avhandlingens bidrag omfattar samhällsekonomiska analysmetoder som gör det möjligt för regionala kollektivtrafikmyndigheter att bedöma den samhällsekonomiska effektiviteten för deras trafikering och skapa ett effektivt utbud. Med dessa metoder som utgångspunkt beskrivs en marknadsbaserad och transparent tilldelningsprocess för kapacitet där infrastrukturförvaltare prissätter kommersiella tåglägen för att lösa kapacitetskonflikter med offentligt kontrollerad trafik. Dessutom utvecklas optimeringsmetoder för att estimera passagerarefterfrågan och för att skapa effektiva tågtidtabeller. Framtida kapacitetstilldelning på avreglerade marknader kan inkludera lösningsmetoder från denna avhandling. Ytterligare experiment krävs dock fortfarande för att hantera problem såsom data, lagstiftning och godtagbarhet. Dessutom kan framtida arbete omfatta prototyper och pilotprojekt av de föreslagna lösningarna och undersöka lagliga och digitaliseringsstrategier för att underlätta implementeringen av sådana lösningar.
Infrastructure managers in railway systems are striving to have as e?cient track utilization as possible. There are no unanimous interpretation of e?ciency in terms of track utilization, but the aim of the Swedish Transport Administration is to allocate track capacity such that societal bene?t is maximized. This means that the tracks should be used by as much tra?c as possible and by tra?c that provides as much bene?t for the society as possible. To allocate track capacity such that the track utilization is optimal would be an easy task if the track capacity were not a scarce resource. Today, many train operators share railway network and there are cases when two or more operators want to use the same track capacity at the same time. The infrastructure manager must then make priorities and reject some operators, and the question is which operators to reject. The guiding principle is to grant the operators that provide the highest societal bene?t access to the tracks. However, the question would then change into how to know which operator that provides the highest societal bene?t. In this thesis, the societal bene?t of publicly subsidized tra?c is estimated using social cost-bene?t analysis. Mathematical models and methods are developed for quantifying and computing the number of departures for the publicly subsidized tra?c and their distribution in time, i.e. a train timetable, that provides the maximal societal bene?t in a social cost-bene?t analysis setting. The societal bene?t of commercial tra?c is estimated using the market value for their requested train timetables. The market value is set using dynamic pricing. A suggestion of a dynamic pricing process that can be used in the train timetabling process is described. Mathematical models and methods for calculating the supply and demand of a track access request are developed and tested, which enables the use of a dynamic pricing process on track capacity
This book promotes the use of mathematical optimization and operations research methods in rail transportation. The editors assembled thirteen contributions from leading scholars to present a unified voice, standardize terminology, and assess the state-of-the-art. There are three main clusters of articles, corresponding to the classical stages of the planning process: strategic, tactical, and operational. These three clusters are further subdivided into five parts which correspond to the main phases of the railway network planning process: network assessment, capacity planning, timetabling, resource planning, and operational planning. Individual chapters cover: Simulation Capacity Assessment Network Design Train Routing Robust Timetabling Event Scheduling Track Allocation Blocking Shunting Rolling Stock Crew Scheduling Dispatching Delay Propagation
