Single cars in rail freight service are bundled into trains at classification yards. On the way from their respective origins via intermediate yards to their destinations, they are reclassified several times, which is a time-consuming and personally consuming procedure. The single-car routing problem asks for the design of such routes for a given set of orders (origin-destination pairs with associated data) on an infrastructure network, such that the number of trains and their travel distances are minimal. A number of hard restrictions must be obeyed, such as restrictions for the train length and weight, and capacity restrictions for the yards, as well as further operational rules. We present a mixed-integer linear programming (MILP) formulation for this car-routing problem arising at Deutsche Bahn, one of the largest European railway companies. In a further step, we refine the handling of the turnover waiting time for the cars in the yards, which leads to the inclusion of nonlinear constraints in the model. Using adequate linearization techniques, this model can be reduced to a MILP again. Instances of this model turn out to be hard to solve. Further techniques are thus presented to speed up the numerical solution process, among them a tree-based reformulation and heuristic cuts. The different model formulations are computationally compared on a test set of randomly generated instances whose sizes are comparable to real-world instances. Using state-of-the-art MILP solvers, optimal or near-optimal solutions can be computed within a reasonable time frame.

We consider the following freight train routing problem (FTRP). Given is a transportation network with fixed routes for passenger trains and a set of freight trains (requests), each defined by an origin and destination station pair. The objective is to calculate a feasible route for each freight train such that the sum of all expected delays and all running times is minimal. Previous research concentrated on microscopic train routings for junctions or inside major stations. Only recently approaches were developed to tackle larger corridors or even networks. We investigate the routing problem from a strategic perspective, calculating the routes in a macroscopic transportation network of Deutsche Bahn AG. In this context, macroscopic refers to an aggregation of complex and large real-world structures into fewer network elements. Moreover, the departure and arrival times of freight trains are approximated. The problem has a strategic character since it asks only for a coarse routing through the network without the precise timings. We provide a mixed-integer nonlinear programming (MINLP) formulation for the FTRP, which is a multicommodity flow model on a time-expanded graph with additional routing constraints. The model’s nonlinearities originate from an algebraic approximation of the delays of the trains on the arcs of the network by capacity restraint functions. The MINLP is reduced to a mixed-integer linear model (MILP) by piecewise linear approximation. The latter is solved by a state-of-the art MILP solver for various real-world test instances.

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In this work we develop methods to optimize an industriallyrelevant logistics problem using quantum computing. We consider the scenario of partially filled trucks transporting shipments between a network of hubs. By selecting alternative routes for some shipment paths, we optimize the trade-off between merging partially filled trucks using fewer trucks in total and the increase in distance associated with shipment rerouting. The goal of the optimization is thus to minimize the total distance travelled for all trucks transporting shipments. The problem instances and techniques used to model the optimization are drawn from real-world data describing an existing shipment network in Europe. We show how to construct this optimization problem as a quadratic unconstrained binary optimization (QUBO) problem. We then solve these QUBOs using classical and hybrid quantum-classical algorithms, and explore the viability of these algorithms for this logistics problem.

In this work, we report about the results of a joint research project between Friedrich–Alexander–Universität Erlangen–Nürnberg and Deutsche Bahn AG on the optimal expansion of the German railway network until 2030. The need to increase the throughput of the network is given by company-internal demand forecasts that indicate an increase in rail freight traffic of about 50% over the next two decades. Our focus is to compute an optimal investment strategy into line capacities given an available annual budget, i.e., we are to choose the most profitable lines to upgrade with respect to the demand scenario under consideration and to provide a schedule according to which the chosen measures are implemented. This leads to a multiperiod network design problem—a class of problems that has received increasing interest over the past decade. We develop a mixed-integer programming formulation to model the situation and solve it via a novel decomposition approach that we call multiple-knapsack decomposition. The method can both be used as a quick heuristic and allows for the extension to an exact algorithm for the problem. We demonstrate its potential by solving a real-world problem instance provided by Deutsche Bahn AG and use the results as the basis for a broad case study for the expansion of the German railway network until 2030.