To wait or not to wait? Delay management in public transportation<BR>

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Anita Schoebel, Georg-August Universitaet Goettingen<BR>

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Abstract:<BR>
Should connecting trains wait for delayed feeder trains? 
Or is it better for the passengers if trains depart on time?

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Questions of this type are the subject of the delay management
problem, which will be treated in this talk from the point of view of 
the customers. The wait/depart decision is easy at one single station,
however, in a public transportation network the problem belongs to the
class of NP hard problems. In this talk we will sketch two approaches
for finding wait/depart decisions: 

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- Minimizing the average delay of the customers will be treated 
by mixed-integer programming. We present two different integer
programming formulations, develop an approximate linearization and
solution methods based on these results.

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- The problem can be formulated as bicriteria optimization problem
with respect to the two objectives ``number of missed connections''
and ``delay of the vehicles''. In our solution approaches we use
methods of project planning.<BR> 

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To apply these approaches in the practice of railways, delay
management gets more complex due to the limited capacity of the
tracks. In the second part of the talk we will hence show how capacity
constraints can be taken into account and transfer some of the results
of the uncapacitated case. We will finally discuss robustness of delay
management solutions and point out recent developments and open
research questions.