Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-51-15-M-7

Optimization in Public Transport (M, 9.0 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-51-15-M-7 Optimization in Public Transport 9.0 CP (270 h)


CP, Effort 9.0 CP = 270 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Module Manager
Area of study [MAT-OPT] Optimisation
Reference course of study [MAT-88.105-SG] M.Sc. Mathematics
Livecycle-State [NORM] Active


Type/SWS Course Number Title Choice in
Presence-Time /
SL SL is
required for exa.
PL CP Sem.
4V+2U MAT-51-15-K-7
Optimization in Public Transport
P 84 h 186 h - - PL1 9.0 irreg.
  • About [MAT-51-15-K-7]: Title: "Optimization in Public Transport"; Presence-Time: 84 h; Self-Study: 186 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester
  • Examination number: 86354 ("Optimization in Public Transport")

Evaluation of grades

The grade of the module examination is also the module grade.


In this lecture, the optimization of various planning stages in public transport will be discussed. In particular, the following is addressed:
  • site selection of stops, development of exact, heuristic and approximation methods,
  • modelling of line planning as a multi-covering problem and development of solution methods usinginteger optimization,
  • timetabling (periodic event scheduling problem) and its model as an integer programme, meaning of cycles and cycle bases,
  • modelling the vehicle scheduling problem as flow problem,
  • delay management, modelling and solution by integer programming.

Competencies / intended learning achievements

Upon successful completion of this module, the students are able to model practical problems from the field of traffic planning using suitable networks and formulate them as integer programmes. They are able to identify and prove characteristics of the problems and their optimal solutions. They are able to analyse the complexity classes of these problems. The students understand the solution methods presented in the lecture and are able to apply them. They are able to develop exact or heuristic methods for similar problems and assess their quality. They can assess the limitations of the use of the developed methods.

By completing the exercises, the students have deepened their knowledge of the subject, solved simple modelling tasks, proven some properties and adapted the algorithms to solve various problems. Examples are also discussed as a part of the exercises. Some algorithms have been implemented prototypically or solved by using suitable solvers.


The lecture is based on current research results. A textbook for the course is not available yet. Research papers corresponding to various chapters of the lecture will be made available. There are lecture notes for this module.


Registration for the exercise classes via the online administration system URM (

Requirements for attendance of the module (informal)

Basic knowledge of integer programming (e.g. from the module [MAT-50-11-M-4]) is helpful.


Requirements for attendance of the module (formal)


References to Module / Module Number [MAT-51-15-M-7]

Module-Pool Name
[MAT-52-MPOOL-7] Specialisation Mathematical Optimisation (M.Sc.)
[MAT-AM-MPOOL-7] Applied Mathematics (Advanced Modules M.Sc.)