Operations Research

Course Description

Linear programming. Linear programming models. Graphical solution and sensitivity analysis. Simplex method. Duality. Dual simplex method. Multiphase production. Business aspects of production planning. The role of variable and fixed costs, contribution. Optimum mix. Assignment problem. Transportation problem. Branch and bound algorithms. Mixed integer programming, solving strategies and applications. Separable programming. Production scheduling. Network planning. Optimisation of stocks. Renewal and selection of equipment. Dynamic programming. Allocation of investment. Nonlinear programming using steepest ascent method. Practical work: Solution and analysis of prepared problems by using available software.

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

University graduate
Audio Technologies and Electroacoustics (profile)
Free Elective Courses (1. semester)
Communication and Space Technologies (profile)
Free Elective Courses (1. semester)
Computational Modelling in Engineering (profile)
Free Elective Courses (1. semester)
Computer Engineering (profile)
Elective Course of the Profile (1. semester) Recommended elective courses (3. semester)
Computer Science (profile)
Elective Courses of the Profile (1. semester) Recommended elective courses (3. semester)
Control Systems and Robotics (profile)
Free Elective Courses (1. semester)
Data Science (profile)
Free Elective Courses (1. semester)
Electrical Engineering Systems and Technologies (profile)
Recommended elective courses (3. semester)
Electrical Power Engineering (profile)
Free Elective Courses (1. semester) Recommended elective courses (3. semester)
Electric Machines, Drives and Automation (profile)
Free Elective Courses (1. semester)
Electronic and Computer Engineering (profile)
Free Elective Courses (1. semester) Recommended elective courses (3. semester)
Electronics (profile)
Free Elective Courses (1. semester) Recommended elective courses (3. semester)
Information and Communication Engineering (profile)
Free Elective Courses (1. semester)
Information Processing (profile)
Recommended elective courses (3. semester)
Network Science (profile)
Free Elective Courses (1. semester)
Software Engineering and Information Systems (profile)
Elective Course of the Profile (1. semester) Specialization Course (1. semester) (3. semester)
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
L3 English Level
L1 e-Learning
30 Lectures
15 Laboratory exercises

Grading System

90 Excellent
75 Very Good
60 Good
50 Acceptable