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

SUBJECT

Code
Subject
MMA0008 Operations Research
Section
Semester
Hours: C+S+L
Category
Type
Mathematics
6
2+2+0
speciality
compulsory
Mathematics and Computer Science
6
2+2+0
speciality
compulsory
Teaching Staff in Charge
Prof. LUPSA Liana, Ph.D.,  llupsamath.ubbcluj.ro
Assoc.Prof. BRECKNER Brigitte Erika, Ph.D.,  brigittemath.ubbcluj.ro
Assoc.Prof. FINTA Zoltan, Ph.D.,  fzoltanmath.ubbcluj.ro
Aims
This course is an introduction to operations research and to the mathematical theory of solving optimization problems.
Content
Operations research principles; interdisciplinary models. Convex analysis on the n-dimensional Euclidean space; convex sets; convex cones; alternative theorems; 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: the Simplex method, the cutting planes method, penalty and barier functions methods. Introduction to game theory; the solution of two-persons games by means of linear optimization technique.
References
1. BLAGA, L., LUPSA, L.: Elemente de programare liniara. Risoprint, Cluj-Napoca, 2003.
2. BLAGA, L., LUPSA, L.: Cercetare operationala. Argonaut, Cluj-Napoca, 2006.
3. BRECKNER, B.E.: De la poliedre la jocuri matriceale. O introducere in optimizarea liniara. EFES, Cluj-Napoca, 2007.
4. BRECKNER, B.E., POPOVICI, N.: Probleme de analiza convexa in R^n. Casa Cartii de Stiinta, Cluj-Napoca, 2003.
5. BRECKNER, B.E., POPOVICI, N.: Probleme de cercetare operaţională, EFES, Cluj-Napoca, 2006.
6. BRECKNER, W.W.: Cercetare operationala. Cluj-Napoca, Universitatea $Babes-Bolyai$, Fac. de Matematica, 1981.
7. BRECKNER, W.W., DUCA, D.: Culegere de probleme de cercetare operationala. Cluj-Napoca, Universitatea, Fac. de Matematica, 1983.
8. DOMSCHKE, W., DREXL, A.: Einfuhrung in Operations Research. 3. Aufl. Berlin, Springer-Verlag, 1995.
9. DOMSCHKE, W., DREXL, A., SCHILDT, B., SCHOLL, A., VOSS, S.: Uebungsbuch Operations Research. 2. Aufl. Berlin, Springer-Verlag, 1997.
10. 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)
Links: Syllabus for all subjects
Romanian version for this subject
Rtf format for this subject