Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Graduate
SUBJECT

Code	Subject	
MO006	Operations Research	

Section	Semester	Hours: C+S+L	Category	Type	
Mathematics	7	2+2+0		compulsory	
Computer Science	7	2+2+0		compulsory	
Mathematics-Computer Science	7	2+2+0		compulsory	

Teaching Staff in Charge	Lect. POPOVICI Nicolae, Ph.D., popovici@math.ubbcluj.ro
Lect. BRECKNER Brigitte Erika, Ph.D., brigitte@math.ubbcluj.ro
Lect. BERINDE Stefan Gheorghe, Ph.D., sberinde@math.ubbcluj.ro
Lect. FINTA Zoltan, Ph.D., fzoltan@math.ubbcluj.ro	
Aims	This course is an introduction to operations research and to the mathematical theory of solving optimization problems.	
Content	General principles of operations research; interdisciplinary models. Convex analysis on the n-dimensional Euclidean space; characterizations of convex and generalized convex functions. Constrained and unconstrained optimization problems; properties of minimum points of convex functions; necessary and sufficient optimality conditions; saddle-point theorems; duality theorems. Numerical methods for solving linear and nonlinear optimization problems: Simplex method, cutting planes method, penalty and barier functions methods. Introduction to game theory; the solution of two-persons games by means of linear optimization technique.	
Bibliography	1. BOYD, S., VANDENBERGHE, L.: Convex Optimization. Cambridge University Press, Cambridge, 2004.
2. BRECKNER, B.E., POPOVICI, N.: Probleme de analiza convexa in R^n. Casa Cartii de Stiinta, Cluj-Napoca, 2003.
3. BRECKNER, B.E., POPOVICI, N.: Probleme de cercetare operationala. Editura EFES, Cluj-Napoca, 2006.
4. BRECKNER, W.W.: Cercetare operationala. Cluj-Napoca, Universitatea "Babes-Bolyai", Fac. de Matematica, 1981.
5. BRECKNER, W.W., DUCA, D.: Culegere de probleme de cercetare operationala. Cluj-Napoca, Universitatea, Fac. de Matematica, 1983.
6. DOMSCHKE, W., DREXL, A.: Einfuhrung in Operations Research. 3. Aufl. Berlin, Springer-Verlag, 1995.
7. DOMSCHKE, W., DREXL, A., SCHILDT, B., SCHOLL, A., VOSS, S.: Uebungsbuch Operations Research. 2. Aufl. Berlin, Springer-Verlag, 1997.
8. PREKOPA, A.: Linearis programozas. Bolyai Tarsulat, Budapest, 1968.
	
Assessment	Continuous evaluation (contributes 20% to the assesment), written and oral examination (contributes 80% to the assesment)