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This paper proposes the first model for toll enforcement optimization
on German motorways. The enforcement is done by mobile control teams and our
goal is to produce a schedule achieving network-wide control, proportional to
spatial and time-dependent traffic distributions. Our model consists of two
parts. The first plans
control tours using a vehicle routing approach with profits and some side
constraints. The second plans feasible rosters for the control teams. Both
problems can be modeled as Multi-Commodity Flow Problems. Adding additional
coupling constraints produces a large-scale integrated integer programming
formulation. We show that this model can be solved to optimality for real
world instances associated with a control area in East Germany.
Today the railway timetabling process and the track allocation
is one of the most challenging problems to solve by a railway company.
Especially due to the deregulation of the transport market in the recent years several
suppliers of railway traffic have entered the market in Europe. This leads to more
potential conflicts between trains caused by an increasing demand of train paths.
Planning and operating railway transportation systems is extremely hard due
to the combinatorial complexity of the underlying discrete optimization problems,
the technical intricacies, and the immense size of the problem instances.
In order to make best use of the infrastructure and to ensure economic operation,
efficient planning of the railway operation is indispensable.
Mathematical optimization models and algorithms can help
to automatize and tackle these challenges.
Our contribution in this paper is to present a renewed planning process
due to the liberalization in Europe and an associated concept for track allocation, that consists
of three important parts, simulation, aggregation, and optimization.
Furthermore, we present results of our general framework for real world data.
In this paper a bottom-up approach of automatic simplification of a railway network is presented. Starting from a very detailed, microscopic level, as it is used in railway simulation, the network is transformed by an algorithm to a less detailed level (macroscopic network), that is sufficient for long-term planning and optimization. In addition running and headway times are rounded to a pre-chosen time discretization by a special cumulative method, which we will present and analyse in this paper. After the transformation we fill the network with given train requests to compute an optimal slot allocation. Then the optimized schedule is re-transformed into the microscopic level and can be simulated without any conflicts occuring between the slots. The algorithm is used to transform the network of the very dense Simplon corridor between Swiss and Italy. With our aggregation it is possible for the first time to generate a profit maximal and conflict free timetable for the corridor across a day by a simultaneously optimization run.