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

Code	Subject	
MMA1011	Mathematical Foundations of Decision-Making Process	

Section	Semester	Hours: C+S+L	Category	Type	
Component-Based Programming - in English	1	2+2+0	speciality	compulsory	

Teaching Staff in Charge	Assoc.Prof. POPOVICI Nicolae, Ph.D., popovici@math.ubbcluj.ro	
Aims	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.	
Content	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.	
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.	
Assessment	Continuous evaluation (contributes 20% to the assesment), written and oral exam (contributes 80% to the assesment).