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We present the problem of planning mobile tours of inspectors on German motorways to enforce the payment of the toll for heavy good trucks. This is a special type of vehicle routing problem with the objective to conduct as good inspections as possible on the complete network. In addition, we developed a personalized crew rostering model, to schedule the crews of the tours. The planning of daily tours and the rostering are combined in a novel integrated approach and formulated as a complex and large scale Integer Program. The main focus of this paper extends our previous publications on how different requirements for the rostering can be modeled in detail. The second focus is on a bi-criteria analysis of the planning problem to find the balance between the control quality and the roster acceptance. Finally, computational results on real-world instances show the practicability of our method and how different input parameters influence the problem complexity.
This paper proposes a highly integrated solution approach for rolling stock planning problems in the context of long distance passenger traffic between cities. The main contributions are a generic hypergraph-based mixed-integer programming model for the considered rolling stock rotation problem and an integrated algorithm for its solution. The newly developed algorithm is able to handle a large spectrum of industrial railway requirements, such as vehicle composition, maintenance constraints, infrastructure capacities, and regularity aspects. We show that our approach has the power to produce rolling stock rotations that can be implemented in practice. In this way, the rolling stock rotations at the largest German long distance operator Deutsche Bahn Fernverkehr AG could be optimized by an automated system utilizing advanced mathematical programming techniques.
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.