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

Fast Heuristics for Delay Management with Passenger Rerouting

Delay management models determine which connections should be maintained in case of a delayed feeder train. Recently, delay management models are developed that take into account that passengers will adjust their routes when they miss a connection. However, for large-scale real-world instances, these extended models become too large to be solved with standard integer programming techniques. We therefore develop several heuristics to tackle these larger instances. The dispatching rules that are used in practice are our first heuristic. Our second heuristic applies the classical delay management model without passenger rerouting. Finally, the third heuristic updates the parameters of the classical model iteratively. We compare the quality of these heuristic solution methods on real-life instances from Netherlands Railways. In this experimental study, we show that our iterative heuristic can solve large real-world instances within a short computation time. Furthermore, the solutions obtained by this iterative heuristic are of good quality

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

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

The path programming problem and a partial path relaxation

We introduce the class of path programming problems, which can be used to model many known optimization problems. A path programming problem can be formulated as a binary programming problem, for which the pricing problem can be modeled as a shortest path problem with resource constraints when column generation is used to solve its linear programming relaxation. Many optimization problems found in the literature belong to this class. We provide a framework for obtaining a partial path relaxation of a path programming problem. Like traditional path relaxations, the partial path relaxation allows the computational complexity of the pricing problem to be reduced, at the expense of a weaker linear programming bound. We demonstrate the versatility of this framework by providing different examples of partial path relaxations for a crew scheduling problem and vehicle routing problem

A p-step formulation for the capacitated vehicle routing problem

We introduce a _p_-step formulation for the capacitated vehicle routing problem (CVRP). The parameter _p_ indicates the length of partial paths corresponding to the used variables. This provides a family of formulations including both the traditional arc-based and path-based formulations. Hence, it is a generalization which unifies arc-based and path-based formulations, while also providing new formulations. We show that the LP bound of the _p_-step formulation is increasing in _p_, although not monotonically. Furthermore, we prove that computing the set partitioning bound is NP-hard. This is a meaningful result in itself, but combined with the _p_-step formulation this also allows us to show that there does not exist a strongest compact formulation for the CVRP, if _P ≠ NP_. While ending the search for a strongest compact formulation, we propose th

Solution methods for the tray optimization problem

In order to perform medical surgeries, hospitals keep large inventories of surgical in- struments. These instruments need to be sterilized before each surgery. Typically the instruments are kept in trays. Multiple trays may be required for a single surgery, while a single tray may contain instruments that are required for multiple surgical procedures. The tray optimization problem (TOP) consists of three main decisions: (i) the assignment of instruments to trays, (ii) the assignment of trays to surgeries, and (iii) the number of trays to keep in inventory. The TOP decisions have to be made such that total operating costs are minimized and such that for every surgery sufficient instruments are available. This paper presents and evaluates several exact and heuristic solution methods for the TOP. We compare solution methods on computation time and solution quality. Moreover, we conduct simulations to evaluate the performance of the solutions in the long run. The novel methods that are provided are the first methods that are capable of solving instances of realistic size. The most promising method consists of a highly scalable advanced greedy algorithm. Our results indicate that the outcomes of this method are, on average, very close to the outcomes of the other methods investigated, while it may be easily applied by (large) hospitals. The findings are robust with respect to fluctuations in long term OR schedules

Is Equality always desirable?

In this paper, we analyze the trade-off between perceived fairness and perceived attractiveness in crew rostering. First, we introduce the Fairness-oriented Crew Rostering Problem. In this problem, attractive cyclic rosters have to be constructed, while respecting a pre-specified fairness level. Then, we propose a flexible mathematical formulation, able to exploit problem specific knowledge, and develop an exact Branch-Price-and-Cut solution method. The solution method combines Branch-and-Bound with column generation, where profitable columns are separated by solving resource constrained shortest path problems with surplus variables. We also derive a set of valid inequalities to tighten the formulation. Finally, we demonstrate the benefit of our approach on practical instances from Netherlands Railways, the largest passenger railway operator in the Netherlands. We are able to construct the explicit trade-off curve between fairness and attractiveness and show that a sequential approach can lead to suboptimal results. In particular, we show that focusing solely on fairness leads to rosters that are disproportionally less attractive. Furthermore, this decrease in attractiveness is heavily skewed towards the most exible employees. Thus, in order to generate truly fair rosters, the explicit trade-off between fairness and attractiveness should be considered

Analysis of FPTASes for the Multi-Objective Shortest Path Problem

We propose a new FPTAS for the multi-objective shortest path problem. The algorithm uses elements from both an exact labeling algorithm and an FPTAS proposed by Tsaggouris and Zaroliagis (2009). We analyze the running times of these three algorithms both from a the- oretical and a computational point of view. Theoretically, we show that there are instances for which the new FPTAS runs an arbitrary times faster than the other two algorithms. Fur- thermore, for the bi-objective case, the number of approximate solutions generated by the proposed FPTAS is at most the number of Pareto-optimal solutions multiplied by the number of nodes. By performing a set of computational tests, we show that the new FPTAS performs best in terms of running ti