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Operational research

Code: 61511
ECTS: 5.0
Lecturers in charge: prof. dr. sc. Marko Vrdoljak
Lecturers: prof. dr. sc. Marko Vrdoljak - Exercises
English level:


All teaching activities will be held in Croatian. However, foreign students in mixed groups will have the opportunity to attend additional office hours with the lecturer and teaching assistants in English to help master the course materials. Additionally, the lecturer will refer foreign students to the corresponding literature in English, as well as give them the possibility of taking the associated exams in English.

1. komponenta

Lecture typeTotal
Lectures 30
Exercises 15
* Load is given in academic hour (1 academic hour = 45 minutes)
COURSE AIMS AND OBJECTIVES: The aim of the course is for students to learn about operational research modelling approach in formulation and solving different problems, which can be formulated as some deterministic mathematical programming problems. During the course the corresponding methods in solving problems and some applications will be considered. Available software on PC's for algorithms and methods will be used in teaching.

Topics for lectures:
1. Introduction. The origins of Operational Research (OR). The nature of OR. The impact of OR. Algorithms and software. ( 2 hours)
2. Operational Research Modelling Approach. Defining the problem and gathering data. Formulating a mathematical model. Deriving solutions from the model. Testing the model. Preparing to apply the model. Implementation. (2 hours)
3. The Transportation and Assignment Problems. Transportation problem. Solving transportation problem by simplex method. Assignment problem and its solution. Some generalizations of the transportation problem and applications. (4 hours)
4. Network optimization problems. Introduction. The shortest-path problem. The minimum spanning tree problem. The maximum flow problem. The minimum cost flow problem. The network simplex method. Planning and control of projects (PERT-CPM). (8 hours)
5. Integer Programming. Formulation of some integer programming models. The method of integer forms. Branch-and-bound method for binary integer programming. Branch-and-bound method for mixed integer programming. Some integer programming applications. (8 hours)
6. Multi-Objective Programming. Introduction. Some properties and characterizations of efficient solutions. Multi-objective linear programming. Goal programming. (6 hours)
  1. F. S. Hillier, G. J. Lieberman: Introduction to Operations Research, 7th edition
  2. W. L. Winston: Operations Research Applications and Algorithms, 4th edition
  3. Lj. Martić: Matematičke metode za ekonomske analize, II. svezak, 3. izdanje
  4. Lj. Martić (redaktor): Višekriterijalno programiranje
  5. G. L. Nemhauser and L. A. Wolsey: Integer and Combinatorial Optimization
  6. L. R. Rardin: Optimization in Operations Research
  7. H. P. Williams: Model Building in Mathematical Programming, 4th edition
Prerequisit for:
Enrollment :
Passed : Introduction to optimization
3. semester
Izborni predmeti 5, 6, 7 - Regular study - Mathematical Statistics

4. semester Not active
Izborni predmeti 5, 6, 7 - Regular study - Mathematical Statistics
Consultations schedule:


Link to the course web page: http://www.pmf.unizg.hr/math/predmet/opeist_a

All information and materials are available on Merlin.

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