Universitatea Babeş-Bolyai Cluj-Napoca
Facultatea de Matematică şi Informatică
Ciclul de studii: Masterat
Domeniul: Informatica
Programul de studii: Programare bazată pe componente - în limba engleză
Limba de predare: Engleză

SYLLABUS

I. General data
Code	Subject	
MMA1011	Mathematical Foundations of Decision-Making Process	

Semester	Hours: C+S+L	Category	Status	
1	2+2+0	speciality	compulsory	

II. Full status faculty members
Name and	Scientific	Didactic	Chair	Type of activity	
surname	title	title		C	S	L	
POPOVICI Nicolae	Ph.D.	Assoc.Prof.	Mathematical Analysis and Optimization	*			

Associated faculty members
Name and	Scientific	Institution	Type of	Type of activity	
surname	title		position	C	S	L	

III. Course objectives
The aim of the course is to introduce fundamental mathematical concepts and practical methods relevant to the study of decision-making processes as optimization problems.	

IV. Course contents
Partial ordered sets; linear preorder relations and their characterizations in terms of ordering cones. Preference relations induced by utility functions; optimality concepts; decisional processes as scalar or vector optimization problems. Convex sets and polyhedral sets; extreme points; convex functions and the properties of their minimum points. Necessary and sufficient optimality conditions for unconstrained and constrained optimization problems. Saddle point theorems. Duality theorems in linear optimization. Numerical methods for solving optimization problems: the Simplex algorithm in primal and dual form, the cutting planes method. Conflict and competition problems, two-player matrix games and their solution by means of linear programming.	

V. Bibliography
1. ANDERSON, D.R., SWEENEY, D.J., WILLIAMS, T.A., An Introduction to Management Science. Quantitative Approaches to Decision Making, South-Western College Publishing, Cincinnati, 2000.
2. BRECKNER, B.E., POPOVICI, N.: Probleme de cercetare operaţională, EFES, Cluj-Napoca, 2006.
3. BRECKNER, B.E., POPOVICI, N.: Convexity and Optimization. An Introduction, EFES, Cluj-Napoca, 2006. 
4. BRECKNER, W.W.: Cercetare operationala, Universitatea $Babes-Bolyai$, Facultatea de Matematica, Cluj-Napoca, 1981.
5. BRECKNER, W.W., DUCA, D.: Culegere de probleme de cercetare operationala,  Universitatea $Babes-Bolyai$, Facultatea de Matematica, Cluj-Napoca, 1983.
6. EHRGOT, M.: Multicriteria Optimization, Springer, Berlin Heidelberg New York, 2005.
7. POPOVICI, N.: Optimizare vectoriala, Casa Cartii de Stiinta, Cluj-Napoca, 2005.
8. YU, P.L.: Multiple Criteria Decision Making: Concepts, Techniques and Extensions, Plenum Press, New York - London, 1985.	

VI. Thematic of didactic activities per weeks

VII. Didactic methods used

VIII. Assessment
Continuous evaluation (contributes 20% to the assesment), written and oral exam (contributes 80% to the assesment).	

IX. Additional references

	Dean,							Chair head,

	Date,							Course responsible,
								Assoc.Prof. POPOVICI Nicolae, Ph.D.