Operational research

2022/2023
Programme:
Financial mathematics, First Cycle
Year:
2 year
Semester:
second
Kind:
mandatory
ECTS:
5
Language:
slovenian
Hours per week – 2. semester:
Lectures
2
Seminar
0
Tutorial
2
Lab
0
Prerequisites

Completed courses Optimization methods, Introduction to programming and Discrete structures.

Content (Syllabus outline)

Modelling real-world problems.
Integer linear programming.
Dynamic programming.
Shortest paths in graphs. Topological sorting.
Basic decision theory.
Additional topics selected from the following list:
Stable matchings.
Data presentation.
Project management (CPM/PERT).
Fair division.
Inventory theory.
Multicriteria Optimization.
Scheduling.
Facility location.
Applications of Markov chains.
Simulations.
Forecasting.
Design of experiments.

Readings

V. Batagelj: Operacijske raziskave. Skripta v pripravi. http://vlado.fmf.uni-lj.si/vlado/or/or.htm
D. C. Montgomery: Design and analysis of experiments. John Wiley & Sons, 1997.
F.S. Hillier in G.J. Lieberman: Introduction to operations research. McGraw-Hill Higher Education, 2010.
W.L. Winston: Operation Research, Applications and Algorithms. PWS-KENT, Boston, MA 1991.
F.S. Roberts: Discrete Mathematical Models. Prentice-Hall, Englewood Cliffs, New Jersey, 1976.
T. H. Cormen, C. E. Leiserson, R. L. Rivest, C. Stein: Introduction to Algorithms, 2. izdaja, MIT Press, Cambridge, 2001.

Objectives and competences

Introduction to the models, methodology and tools used in operations research.

Intended learning outcomes

Knowledge and understanding: Understanding of models, methodologies and tools used in operations research
Applications: Methodical approach to problem solving related to optimal managing of systems in everyday life.
Reflection: The relation between theoretical predictions on the optimal management and the actual behavior of the system
Transferable skills: Relevance of a methodical approach to problem solving.

Learning and teaching methods

Lectures, exercises, homework, consultations

Assessment

Written exam
Oral exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Lecturer's references

Sergio Cabello:
CABELLO, Sergio, ROTE, Günter. Obnoxious centers in graphs. SIAM journal on discrete mathematics, ISSN 0895-4801, 2010, vol. 24, no. 4, str. 1713-1730. [COBISS-SI-ID 15762265]
BUCHIN, Kevin, CABELLO, Sergio, GUDMUNDSSON, Joachim, LÖFFLER, Maarten, LUO, Jun, ROTE, Günter, SILVEIRA, Rodrigo I., SPECKMANN, Bettina, WOLLE, Thomas. Finding the most relevant fragments in networks. Journal of graph algorithms and applications, ISSN 1526-1719, 2010, vol. 14, no. 2, str. 307-336. [COBISS-SI-ID 15629401]
CABELLO, Sergio, DÍAZ-BÁÑEZ, José Miguel, LANGERMAN, Stefan, SEARA, Carlos, VENTURA, Inma. Facility location problems in the plane based on reverse nearest neighbor queries. European journal of operational research, ISSN 0377-2217. [Print ed.], 2010, vol. 202, iss. 1, str. 99-106. [COBISS-SI-ID 15160921]
Matjaž Konvalinka:
KONVALINKA, Matjaž, PAK, Igor. Geometry and complexity of O'Hara's algorithm. Advances in applied mathematics, ISSN 0196-8858, 2009, vol. 42, iss. 2, str. 157-175. [COBISS-SI-ID 15545945]
KONVALINKA, Matjaž, PAK, Igor. Triangulations of Cayley and Tutte polytopes. Advances in mathematics, ISSN 0001-8708, 2013, vol. 245, str. 1-33. [COBISS-SI-ID 16706905]
DOLŽAN, David, KONVALINKA, Matjaž, OBLAK, Polona. Diameters of connected components of commuting graphs. The electronic journal of linear algebra, ISSN 1081-3810, 2013, vol. 26, str. 433-445. [COBISS-SI-ID 16707161]