Operations Research

Course Description

*Applied mathematical and algorithmic optimization.* - Approaches regarding variable domains: continuous, discrete and mixed-discrete, with focus on discrete (combinatorial) optimization. - Approaches regarding available information: deterministic, stochastic and robust optimization. - Approaches for solving big-scale optimization problems: delayed generation and decompositions. *Methods and topics.* Linear programming. Simplex method. Duality, dual simplex method. Interior point methods. Mixed-integer programming, solving strategies and applications. Combinatorial optimization. Network planning and scheduling. Constraint satisfaction and constraint programming (backtracking and local search). Decision trees (from decision theory, not machion learning). Stochastic programming. (Stochastic) dynamic programming and Markov decision processes. Robust linear optimization and polyhedral uncertainty. Delayed generation of columns and rows. Decompositions: Dantzig-Wolfe and Benders. *Practical work* Solution and analysis of prepared problems by using available software. Applications: machine learning, optimization of business processes, project scheduling, timetabling, financial mathematics…

Learning Outcomes

  1. Explain the concept of mathematical modelling.
  2. Explain when and why optimisation is applicable.
  3. Identify in real life possibilities for optimisation.
  4. Explain the production goals in a factory.
  5. Identify the need for discrete programming in real life.
  6. Apply network planning for proposing, leading and auditing of projects.
  7. Explain the need to optimise stock levels.
  8. Apply for decion making in industry.

Forms of Teaching

Lectures

Materials and presentations are on course web page.

Laboratory

complex laboratory assignments which includes algorithms from the lectures

Grading Method

Continuous Assessment Exam
Type Threshold Percent of Grade Threshold Percent of Grade
Laboratory Exercises 0 % 30 % 10 % 20 %
Mid Term Exam: Written 0 % 30 % 0 %
Final Exam: Written 0 % 30 %
Final Exam: Oral 10 %
Exam: Written 50 % 50 %
Exam: Oral 30 %
Comment:

short examinations are added above the basic 100%

Week by Week Schedule

  1. Convexity; Polyhedra, convex hulls, polytopes, The simplex method
  2. Duality and sensitivity, Primal-dual interior-point method for linear programming
  3. Primal-dual interior-point method for linear programming, Deterministic and heuristic approaches, Knapsack problem, Vehicle routing problem
  4. Basics of decision making under uncertainty; Newsvendor problem, Decision Trees
  5. Stochastic programming
  6. The integer hull of a polyhedron, Unimodular transformations; Totally unimodular matrices, Cutting planes, Lagrangean relaxation
  7. Mixed integer programming - branch and bound method
  8. Midterm exam
  9. Max-flow min-cut theorem, Menger's theorem, Finding a maximum flow, Minimum cost flows
  10. Critical path problem; Algorithms
  11. Robust linear optimization; Ellipsoidal and polyhedral uncertainty
  12. Constraint satisfaction (backtracking and local search methods), Markov decision processes (MDP)
  13. Delayed column generation; The cutting stock problem, Delayed constraint generation
  14. Dantzig-Wolfe decomposition, Benders decomposition
  15. Final exam

Study Programmes

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[FER3-HR] Software Engineering and Information Systems - profile
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[FER2-HR] Electrical Engineering Systems and Technologies - profile
Recommended elective courses (3. semester)
[FER2-HR] Electrical Power Engineering - profile
Recommended elective courses (3. semester)
[FER2-HR] Electronic and Computer Engineering - profile
Recommended elective courses (3. semester)
[FER2-HR] Electronics - profile
Recommended elective courses (3. semester)
[FER2-HR] Information Processing - profile
Recommended elective courses (3. semester)
[FER2-HR] Software Engineering and Information Systems - profile
Specialization Course (1. semester) (3. semester)
[FER2-HR] Telecommunication and Informatics - profile
Recommended elective courses (3. semester)

Literature

D. Kalpić, V. Mornar (1996.), Operacijska istraživanja, Zeus - DRIP
Ronald L. Rardin (2016.), Optimization in Operations Research, Prentice Hall
Frederick S. Hillier, Gerald J. Lieberman (2021.), ISI Introduction to Operations Research, 11th ed, McGraw-Hill Education
Hamdy A. Taha (2016.), Operations Research, Pearson
Michael Carter, Camille C. Price, Ghaith Rabadi (2018.), Operations Research, CRC Press
Richard S. Sutton, Andrew G. Barto (2018.), Reinforcement Learning, A Bradford Book
Francesca Rossi, Peter Van Beek, Toby Walsh (2006.), Handbook of Constraint Programming, Elsevier Science Limited

Associate Lecturers

Laboratory exercises

For students

General

ID 222568
  Winter semester
5 ECTS
L0 English Level
L1 e-Learning
30 Lectures
0 Seminar
0 Exercises
15 Laboratory exercises
0 Project laboratory

Grading System

90 Excellent
75 Very Good
60 Good
50 Acceptable