90C10 Integer programming
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- combinatorial optimization (5)
- integer programming (5)
- line planning (4)
- Integer Programming (3)
- transfers (3)
- Kombinatorische Optimierung (2)
- Operations Research (2)
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Institute
Rapid Branching
(2012)
We propose rapid branching (RB) as a general branch-and-bound heuristic
for solving large scale optimization problems in traffic and transport.
The key idea is to combine a special branching rule and a greedy node selection
strategy in order to produce solutions of controlled quality rapidly
and efficiently. We report on three successful applications of the method
for integrated vehicle and crew scheduling, railway track allocation, and
railway vehicle rotation planning.
Duty Scheduling Templates
(2012)
We propose duty templates as a novel concept to produce similar duty
schedules for similar days of operation in public transit. Duty templates
can conveniently handle various types of similarity requirements, and
they can be implemented with ease using standard algorithmic techniques.
They have produced good results in practice.
Vehicle rotation planning is a fundamental problem in
rail transport. It decides how the railcars, locomotives, and
carriages are operated in order to implement the trips of the
timetable. One important planning requirement is operational
regularity, i.e., using the rolling stock in the same way on every
day of operation. We propose to take regularity into account by
modeling the vehicle rotation planning problem as a minimum cost
hyperassignment problem (HAP). Hyperassignments are generalizations
of assignments from directed graphs to directed hypergraphs.
Finding a minimum cost hyperassignment is
NP-hard.
Most instances arising from regular vehicle rotation planning, however, can
be solved well in practice. We show that, in particular, clique
inequalities strengthen the canonical LP relaxation substantially.
We propose a novel integer programming approach to transfer minimization for line planning problems in public transit. The idea is to incorporate penalties for transfers that are induced by “connection capacities” into the construction of the passenger paths. We show that such penalties can be dealt with by a combination of shortest and constrained shortest path algorithms such that the pricing problem for passenger paths can be solved efficiently. Connection capacity penalties (under)estimate the true transfer times. This error is, however, not a problem in practice. We show in a computational comparison with two standard models on a real-world scenario that our approach can be used to minimize passenger travel and transfer times for large-scale line planning problems with accurate results.
Robust Tail Assignment
(2010)
We propose an efficient column generation method to minimize the probability of delay propagations along aircraft rotations. In this way, delay resistant schedules can be constructed. Computational results for large-scale real-world problems demonstrate substantial punctuality improvements. The method can be generalized to crew and integrated scheduling problems.
The Vehicle Positioning Problem (VPP) is a classical combinatorial optimization problem in public transport planning. A number of models and approaches have been suggested in the literature, which work for small problems, but not for large ones. We propose in this article a novel set partitioning model and an associated column generation solution approach for the VPP. The model provides a tight linear description of the problem. The pricing problem, and hence the LP relaxation itself, can be solved in polynomial resp. pseudo-polynomial time for some versions of the problems.
The Vehicle Positioning Problem (VPP) consists of the assignment of vehicles (buses, trams or trains) of a public transport or railway company to parking positions in a depot and to timetabled trips. Such companies have many different types of vehicles, and each trip can be performed only by vehicles of some of these types. These assignments are non-trivial due to the topology of depots. The parking positions are organized in tracks, which work as one- or two-sided stacks or queues. If a required type of vehicle is not available in the front of any track, shunting movements must be performed in order to change vehicles' positions, which is undesirable and should be avoided. In this text we present integer linear and non-linear programming formulations for some versions of the problem and compare them from a theoretical and a computational point of view.
The mathematical treatment of planning problems in public transit has made significant advances in the last decade. Among others, the classical problems of vehicle and crew scheduling can nowadays be solved on a routine basis using combinatorial optimization methods. This is not yet the case for problems that pertain to the design of public transit networks, and for the problems of operations control that address the implementation of a schedule in the presence of disturbances. The article gives a sketch of the state and important developments in these areas, and it addresses important challenges. The vision is that mathematical tools of computer aided scheduling (CAS) will soon play a similar role in the design and operation of public transport systems as CAD systems in manufacturing.