1. komponenta

Lecture type	Total
Lectures	45

* 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 modeling approach in formulation and solving different problems, which can be formulated as some deterministic mathematical programming problems. During the course the corresponding methods for solving problems and some applications will be considered. Available software on PC's for algorithms and methods will be used in teaching.

COURSE DESCRIPTION AND SYLLABUS:
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 Modeling 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 optimisation 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. Introduction to Operations Research, 7th edition, F. S. Hillier, G. J. Lieberman, McGraw Hill, New York, 2001.
2. Operations Research Applications and Algorithms, 4th edition, W. L. Winston, Thomson - Brooks/Cole, London, 2004.
3. Matematičke metode za ekonomske analize, II. svezak, 3. izdanje, Lj. Martić, Narodne novine, Zagreb, 1979.
4. Višekriterijalno programiranje, Lj. Martić (redaktor), Informator, Zagreb, 1978.
5. Integer and Combinatorial Optimization, G. L. Nemhauser and L. A. Wolsey, John Wiley, New York, 1988.
6. Optimization in Operations Research, L. R. Rardin, Prentice Hall, Upper Saddle River, NJ, 1998.
7. Model Building in Mathematical Programming, 4th edition, H. P. Williams, Wiley, Chichester, 1999.

Enrollment :
Attended : Introduction to optimization

Examination :
Passed : Introduction to optimization

Izborni predmet 4, 5, 6, 7 - Regular study - Mathematical Statistics

Izborni predmet 4, 5, 6, 7 - Regular study - Mathematical Statistics