Delay Management including Capacities of Stations

The question of delay management (DM) is whether trains should wait for delayed feeder trains or should depart on time. Solutions to this problem strongly depend on the capacity constraints of the tracks making sure that no two trains can use the same piece of track at the same time. While these capacity constraints have been included in integer programming formulations for DM, the capacity constraints of the stations (only offering a limited number of platforms) have been neglected so far. This can lead to highly infeasible solutions. In order to overcome this problem we suggest two new formulations for DM both including the stations\u27 capacities. We present numerical results showing that the assignment-based formulation is clearly superior to the packing formulation. We furthermore propose an iterative algorithm in which we improve the platform assignment with respect to the current delays of the trains at each station in each step. We will show that this subproblem asks for coloring the nodes of a graph with a given number of colors while minimizing the weight of the conflicts. We show that the graph to be colored is an interval graph and that the problem can be solved in polynomial time by presenting a totally unimodular IP formulation

Analyzing a Family of Formulations for Cyclic Crew Rostering

In this paper, we analyze a family of formulations for the Cyclic Crew Rostering Problem (CCRP), in which a cyclic roster has to be constructed for a group of employees. Each formulation in the family is based on a partition of the roster. Intuitively, finer partitions give rise to a formulation with fewer variables, but possibly more constraints. Coarser partitions lead to more variables, but might allow to incorporate many of the constraints implicitly. We derive analytical results regarding the relative strength of the different formulations, which can serve as a guideline for formulating a given problem instance. Furthermore, we propose a column generation approach, and use it to compare the strength of the formulations empirically. Both the theoretical and computational results demonstrate the importance of choosing a suitable formulation. In particular, for practical instances of Netherlands Railways, stronger lower bounds are obtained, and more than 90% of the roster constraints can be modeled implicitly

Delay Management and Dispatching in Railways

Passenger railway transportation plays a crucial role in the mobility in Europe. Since the privatization of the railway sector in the 90s, passenger satisfaction has become an important performance indicator in this sector. A key aspect for passengers is the reliability of transfers between trains. When a train arrives at the station with a delay, passengers might miss their connection if the next train departs on time. These passengers then prefer the connecting train to wait, but this introduces delays for many other passengers. Delay Management is a field in railway operations that deals with this situation. It determines whether a connecting train should wait for the passengers that arrive with a delayed train or should depart on time. In this thesis, we apply techniques from Operations Research to develop models and solution approaches for Delay Management. The objective in our models is the minimization of passenger delay. First, we extend the classical delay management model with passenger rerouting. This allows us to compute the exact delays for passengers. We develop an exact algorithm and several heuristics to solve this extension. Then, we incorporate the limited capacity of the stations in our models. Stations are the bottlenecks of the railway infrastructure, where delays of one train can easily propagate to other trains. When optimizing the wait-depart decisions, these secondary delays should be considered. We therefore develop an integrated model that includes headway constraints for trains on the same track in the station and an iterative approach that evaluates the timetable microscopically

Spare parts inventory control for an aircraft component repair shop

We study spare parts inventory control for a repair shop for aircraft components. Defect components that are removed from the aircraft are sent to such a shop for repair. Only after inspection of the component, it becomes clear which specific spare parts are needed to repair it, and in what quantity they are needed. Market requirements on shop performance are reflected in fill rate requirements on the turn around times of the repairs for each component type. The inventory for spare parts is controlled by independent min-max policies. Because parts may be used in the repair of different component types, the resulting optimization problem has a combinatorial nature. Practical instances may consist of 500 component types and 4000 parts, and thus pose a significant computational challenge. We propose a solution algorithm based on column generation. We study the pricing problem, and develop a method that is very efficient in (repeatedly) solving this pricing problem. With this method, it becomes feasible to solve practical instances of the problem in minutes

Reducing passenger delays by rolling stock rescheduling

Delays are a major nuisance to railway passengers. The extent to which a delay propagates, and thus affects the passengers, is influenced by the assignment of rolling stock. We propose to reschedule the rolling stock in such a way that the passenger delay is minimized and such that objectives on passenger comfort and operational efficiency are taken into account. We refer to this problem as the passenger delay reduction problem. We propose two models for this problem, which are based on two dominant streams of literature for the traditional rolling stock rescheduling problem. The first model is an arc formulation of the problem, whereas the second model is a path formulation. We test the effectiveness of these models on instances from Netherlands Railways (Nederlandse Spoorwegen). The results show that the rescheduling of rolling stock can significantly decrease passenger delays in the system. Especially, allowing flexibility in the assignment of rolling stock at terminal stations turns out to be effective in reducing the delays. Moreover, we show that the arc formulation–based model performs best in finding high-quality solutions within the limited time that is available in the rescheduling phase

Delay management including capacities of stations

The question of delay management (DM) is whether trains should wait for delayed feeder trains or should depart on time. Solutions to this problem strongly depend on the capacity constraints of the tracks making sure that no two trains can use the same piece of track at the same time. While these capacity constraints have been included in integer programming formulations for DM, the capacity constraints of the stations (only offering a limited number of platforms) have been neglected so far. This can lead to highly infeasible solutions. In order to overcome this problem we suggest two new formulations for DM both including the stations' capacities. We present numerical results showing that the assignment-based formulation is clearly superior to the packing formulation. We furthermore propose an iterative algorithm in which we improve the platform assignment with respect to the current delays of the trains at each station in each step. We will show that this subproblem asks for coloring the nodes of a graph with a given number of colors while minimizing the weight of the conflicts. We show that the graph to be colored is an interval graph and that the problem can be solved in polynomial time by presenting a totally unimodular IP formulation

Integrating Timetabling and Crew

We investigate to what degree we can integrate a Train Timetabling / Engine Scheduling Problem with a Crew Scheduling Problem. In the Timetabling Problem we design a timetable for the desired lines by fixing the departure and arrival times. Also, we allocate time-slots in the network to secure a feasible timetable. Next, we assign engines in the Engine Scheduling Problem to the lines in accordance with the timetable. The overall integration is achieved by obtaining an optimal solution for the Timetabling / Engine Scheduling Problem. We exploit the fact that numerous optimal, and near optimal solutions exists. We consider all solutions that can be obtained from the optimal engine schedule by altering the timetable, while keeping the order of demands in the schedules intact. The Crew Scheduling model is allowed to re-time the service of demands if the additional cost is outweighed by the crew savings. This information is implemented in a mathematical model for the Crew Scheduling Problem. The model is solved using a column generation scheme. Hereby it is possible for the Crew Scheduling algorithm to adjust the timetable and achieve a better overall solution. We perform computational experiments based on a case at a freight railway operator, DB Schenker Rail Scandinavia, and show that significant cost savings can be achieved

An adjustable robust optimization approach for periodic timetabling

In this paper, we consider the Robust Periodic Timetabling Problem (RPTP), the problem of designing a periodic timetable that can easily be adjusted in case of small periodic disturbances. We develop a solution method for a parametrized class of uncertainty regions. This class relates closely to uncertainty regions known in the robust optimization literature, and naturally defines a metric for the robustness of the timetable. The proposed solution method combines a linear decision rule with well-known reformulation techniques and cutting-plane methods. We show that the RPTP can be solved for practical-sized instances by applying the solution method to practical cases of Netherlands Railways (NS). In particular, we show that the trade-off between the efficiency and robustness of a timetable can be analyzed using our solution method