Anita Schöbel is a Professor for Applied Mathematics at the Technical University in Kaiserslautern and head of the Fraunhofer Institute for Industrial Mathematics (ITWM). She studied Mathematics in Kaiserslautern, received her Diploma degree in 1994, her PhD in 1998 and her Habilitation in 2003. From 2003 to 2018 she was Professor in Göttingen and 2008/09 guest professor in Auckland. She is a member of the scientific senate of the National Research Data Infrastructure (NFDI) Germany, and speaker of the DFG Research Group on Integrated Optimization in Public Transport. In 2022/23, she will be President Elect of the Association of European Operational Research Societies (EURO). Her research interests are in the area of multicriteria optimization, robust optimization, and transport and logistic applications.
Integrated versus sequential planning: The case of public transport optimization
Many real-world problems are treated sequentially. One prominent example
for such a sequential process is public transport optimization:
One starts with network design, then plans lines and their
frequencies. Based on these, the timetable is determined,
and later on the vehicles’ and drivers’ schedules.
The sequential procedure sketched above can be regarded as a
Greedy approach: in each planning stage one aims at the best one can
do. This usually leads to suboptimal solutions. On the other hand,
in public transport optimization many of the mentioned single steps
are already NP hard such that solving the
integrated problem to optimality seems to be out of scope.
We introduce a general framework to analyze integrated versus sequential
planning. We define the price of sequentiality to measure how much can be
gained by integrated approaches. We present results under which conditions
the price of sequentiality is bounded or even zero. We also develop
different approaches for integrated optimization, among them partial
integration or the Eigenmodel. We illustrate our findings
for the case of public transport optimization.