Strong Relaxations for the Train Timetabling Problem Using Connected Configurations

The task of the train timetabling problem or track allocation problem is to find conflict free schedules for a set of trains with predefined routes in a railway network. Especially for non-periodic instances models based on time expanded networks are often used. Unfortunately, the linear programming relaxation of these models is often extremely weak because these models do not describe combinatorial relations like overtaking possibilities very well. In this paper we extend the model by so called connected configuration subproblems. These subproblems perfectly describe feasible schedules of a small subset of trains (2-3) on consecutive track segments. In a Lagrangian relaxation approach we solve several of these subproblems together in order to produce solutions which consist of combinatorially compatible schedules along the track segments. The computational results on a mostly single track corridor taken from the INFORMS RAS Problem Solving Competition 2012 data indicate that our new solution approach is rather strong. Indeed, for this instance the solution of the Lagrangian relaxation is already integral

Generation of the transport service offer with application to timetable planning considering constraints due to maintenance work

Line planning is an important step in strategic timetable planning in public transport. In this step the transport offer for the customer is generated by the public transport operator, whereby the resulting costs for the operator should be as deep as possible. Mathematical models for line planning allow to create optimized line plans quickly. Planners can use these models to rate and select different alternatives. This is particularly valuable under the aspect of increasing maintenance and construction tasks of the railway infrastructure. We show, that in this case, it is possible to create functional requirements for automated timetable creation from the result of line planning step. The practical use of the involved models is illustrated by a real application example

A MILP model for quasi-periodic strategic train timetabling

In railways, the long-term strategic planning is the process of evaluating improvements to the railway network (e.g., upgrading a single track line to a double track line) and changes to the composition/frequency of train services (e.g., adding 1 train per hour along a certain route). The effects of different combinations of infrastructure upgrades and updated train services (also called scenarios), are usually evaluated by creating new feasible timetables followed by extensive simulation. Strategic Train Timetabling (STT) is indeed the task of producing new tentative timetables for these what-if scenarios. Unlike the more classic train timetabling, STT can often overlook (or at least give less importance to) some complementary aspects, such as crew and rolling stock scheduling. On the other hand, the different scenarios are likely to lead to very different timetables, hindering the common and effective practice of using existing timetables to warm start the solution process. We introduce the concept of quasi-periodic timetables, that are timetables where certain subsets of trains need to start at almost (rather than precisely) the same minute of every period. The additional flexibility offered by quasi-periodic timetables turned out to be crucial in real-life scenarios characterized by elevated train traffic. We describe a MILP based approach for strategic quasi-periodic train timetabling and we test it on 4 different realistic what-if scenarios for an important line in Norway. The timetables produced by our algorithm were ultimately used by the Norwegian Railway Directorate to select 3 out of the 4 scenarios for phasing the progressive expansion of the JȪren line.publishedVersio

Deutsche Bahn Schedules Train Rotations Using Hypergraph Optimization

Deutsche Bahn (DB) operates a large fleet of rolling stock (locomotives, wagons, and train sets) that must be combined into trains to perform rolling stock rotations. This train composition is a special characteristic of railway operations that distinguishes rolling stock rotation planning from the vehicle scheduling problems prevalent in other industries. DB models train compositions using hyperarcs. The resulting hypergraph models are addressed using a novel coarse-to-fine method that implements a hierarchical column generation over three levels of detail. This algorithm is the mathematical core of DB's fleet employment optimization (FEO) system for rolling stock rotation planning. FEO's impact within DB's planning departments has been revolutionary. DB has used it to support the company's procurements of its newest high-speed passenger train fleet and its intermodal cargo locomotive fleet for crossborder operations. FEO is the key to successful tendering in regional transport and to construction site management in daily operations. DB's planning departments appreciate FEO's high-quality results, ability to reoptimize (quickly), and ease of use. Both employees and customers benefit from the increased regularity of operations. DB attributes annual savings of 74 million euro, an annual reduction of 34,000 tons of CO2 emissions, and the elimination of 600 coupling operations in crossborder operations to the implementation of FEO

Operational Research: Methods and Applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes

Energy-aware Occupancy Scheduling

Buildings are the largest consumers of energy worldwide. Within a building, heating, ventilation and air-conditioning (HVAC) systems consume the most energy, leading to trillion dollars of electrical expenditure worldwide each year. With rising energy costs and increasingly stringent regulatory environments, improving the energy efficiency of HVAC operations in buildings has become a global concern. From a short-term economic point-of-view, with over 100 billion dollars in annual electricity expenditures, even a small percentage improvement in the operation of HVAC systems can lead to significant savings. From a long-term point-of-view, the need of fostering a smart and sustainable built environment calls for the development of innovative HVAC control strategies in buildings. In this thesis, we look at the potential for integrating building operations with room booking and occupancy scheduling. More specifically, we explore novel approaches to reduce HVAC consumption in commercial buildings, by jointly optimising the occupancy scheduling decisions (e.g. the scheduling of meetings, lectures, exams) and the building’s occupancy-based HVAC control. Our vision is to integrate occupancy scheduling with HVAC control, in such a way that the energy consumption is reduced, while the occupancy thermal comfort and scheduling requirements are addressed. We identify four unique research challenges which we simultaneously tackle in order to achieve this vision, and which form the major contributions of this thesis. Our first contribution is an integrated model that achieves high efficiency in energy reduction by fully exploiting the capability to coordinate HVAC control and occupancy scheduling. The core component of our approach is a mixed-integer linear programming (MILP) model which optimally solves the joint occupancy scheduling and occupancy-based HVAC control problem. Existing approaches typically solve these subproblems in isolation: either scheduling occupancy given conventional control policies, or optimising HVAC control using a given occupancy schedule. From a computation standpoint, our joint problem is much more challenging than either, as HVAC models are traditionally non-linear and non-convex, and scheduling models additionally introduce discrete variables capturing the time slot and location at which each activity is scheduled. We find that substantial reduction in energy consumption can be achieved by solving the joint problem, compared to the state of the art approaches using heuristic scheduling solutions and to more naïve integrations of occupancy scheduling and occupancy-based HVAC control. Our second contribution is an approach that scales to large occupancy scheduling and HVAC control problems, featuring hundreds of activity requests across a large number of offices and rooms. This approach embeds the integrated MILP model into Large Neighbourhood Search (LNS). LNS is used to destroy part of the schedule and MILP is used to repair the schedule so as to minimise energy consumption. Given sets of occupancy schedules with different constrainedness and sets of buildings with varying thermal response, our model is sufficiently scalable to provide instantaneous and near-optimal solutions to problems of realistic size, such as those found in university timetabling. The third contribution is an online optimisation approach that models and solves the online joint HVAC control and occupancy scheduling problem, in which activity requests arrive dynamically. This online algorithm greedily commits to the best schedule for the latest activity requests, but revises the entire future HVAC control strategy each time it considers new requests and weather updates. We ensure that whilst occupants are instantly notified of the scheduled time and location for their requested activity, the HVAC control is constantly re-optimised and adjusted to the full schedule and weather updates. We demonstrate that, even without prior knowledge of future requests, our model is able to produce energy-efficient schedules which are close to the clairvoyant solution. Our final contribution is a robust optimisation approach that incorporates adaptive comfort temperature control into our integrated model. We devise a robust model that enables flexible comfort setpoints, encouraging energy saving behaviors by allowing the occupants to indicate their thermal comfort flexibility, and providing a probabilistic guarantee for the level of comfort tolerance indicated by the occupants. We find that dynamically adjusting temperature setpoints based on occupants’ thermal acceptance level can lead to significant energy reduction over the conventional fixed temperature setpoints approach. Together, these components deliver a complete optimisation solution that is efficient, scalable, responsive and robust for online HVAC-aware occupancy scheduling in commercial buildings

Modelling, solution and evaluation techniques for Train Timetable Rescheduling via optimisation

It is common on railways for a single train delay to cause other trains to become delayed, multiplying the negative consequences of the original problem. However, making appropriate changes to the timetable in response to the initial delay can help to reduce the amount of further delay caused. In this thesis, we tackle the Train Timetable Rescheduling Problem (TTRP), the task of finding the best combination of timetable changes to make in any given traffic scenario. The TTRP can be formulated as an optimisation problem and solved computationally to aid the process of railway traffic control. Although this approach has received considerable research attention, the practical deployment of optimisation methods for the TTRP has hitherto been limited. In this thesis, we identify and address three outstanding research challenges that remain barriers to deployment. First, we find that existing TTRP models for large station areas are either not sufficiently realistic or cannot be solved quickly enough to be used in a real-time environment. In response, a new TTRP model is introduced that models the signalling system in station areas in fine detail. Using a new set of real instances from Doncaster station, we show that our tailored solution algorithm can obtain provably optimal or near-optimal solutions in sufficiently short times. Second, we argue that existing ways of modelling train speed in TTRP models are either unrealistic, overly complex, or lead to models that cannot be solved in real-time. To address this, innovative extensions are made to our TTRP model that allow speed to be modelled parsimoniously. Real instances for Derby station are used to demonstrate that these modelling enhancements do not incur any extra computational cost. Finally, a lack of evidence is identified concerning the fairness of TTRP models with respect to competing train operators. New evaluation techniques are developed to fill this gap, and these techniques are applied to a case study of Doncaster station. We find that unfairness is present when efficiency is maximised, and find that it mostly results from competition between a small number of operators. Moreover, we find that fairness can be improved up to a point by increasing the priority given to local trains. This work represents an important step forward in optimisation techniques for the TTRP. Our results, obtained using real instances from both Doncaster and Derby stations, add significantly to the body of evidence showing that optimisation is a viable approach for the TTRP. In the long run this will make deployment of such technology more likely

Modeling and Solution Approaches for Non-traditional Network Flow Problems with Complicating Constraints

In this dissertation, we model three network-based optimization problems. Chapter 2 addresses the question of what the operation plan should be for interdependent infrastructure systems in resource-constrained environments so that they collectively operate at the highest level. We develop a network-based operation model of these systems that accounts for interdependencies among them. To solve this large-scale model, a solution approach is proposed that relatively quickly generates high-quality solutions to the problem. Chapter 3 presents a routing model for a single train within a railyard with the objective of minimizing the total length traveled by train. The difference between this problem and the traditional shortest path is that the route must accommodate the length of the train at any time, subject to yard tracks’ configuration. This problem has application in the railway industry where they need to solve the single-train routing problem repeatedly for simulations of train movements in large complex yards. We develop an optimal polynomial-time algorithm that solves an important special case of the problem. Chapter 4 extends the problem defined in Chapter 3 to a two-train routing problem with the objective of minimizing the overall time possible to schedule the routes in a conflict-free manner. We propose a routing problem that indirectly aims to decrease the overall scheduling time for the two trains. We develop a scheduling model that compares the performance of the solution obtained by the proposed routing model with the solutions obtained by solving the problem as two separate single-train yard routing problems. The comparison indicates a better performance obtained by the proposed routing model for specific problems