SC 98-09 Ralf Borndörfer, Martin Grötschel, Andreas Löbel: Optimization of Transportation Systems (Appeared in: 1.: ACTA FORUM ENGELBERG 98 und The Future of
Mobility \& Transportation in a Moving World, VDF
Hochschulverlag an der ETH Zürich, Schweiz, 1998)
Abstract: The world has experienced two hundred years of unprecedented
advances in vehicle technology, transport system development, and traffic
network extension. Technical progress continues but seems to have reached some
limits. Congestion, pollution, and increasing costs have created, in some parts
of the world, a climate of hostility against transportation technology.
Mobility, however, is still increasing. What can be done?
There is no panacea. Interdisciplinary cooperation is necessary, and we are
going to argue in this paper that Mathematics can contribute
significantly to the solution of some of the problems. We propose to employ
methods developed in the Theory of Optimization to make better use of
resources and existing technology. One way of optimization is better planning.
We will point out that Discrete Mathematics provides a suitable
framework for planning decisions within transportation systems. The
mathematical approach leads to a better understanding of problems. Precise and
quantitative models, and advanced mathematical tools allow for provable and
reproducible conclusions. Modern computing equipment is suited to put such
methods into practice.
At present, mathematical methods contribute, in particular, to the solution of
various problems of operational planning. We report about encouraging
results achieved so far.
Keywords: Transportation Systems,
Optimization,
Discrete Mathematics
MSC: 90B06