Popis predmeta

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

Independent assignments

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) (3. semester)
Communication and Space Technologies (profile)
Free Elective Courses (1. semester) (3. semester)
Computational Modelling in Engineering (profile)
Free Elective Courses (1. semester) (3. semester)
Computer Engineering (profile)
Elective Course of the Profile (1. semester) Elective Courses of the Profile (3. semester)
Computer Science (profile)
Elective Courses of the Profile (1. semester) (3. semester)
Control Systems and Robotics (profile)
Free Elective Courses (1. semester) (3. semester)
Data Science (profile)
Free Elective Courses (1. semester) (3. semester)
Electrical Power Engineering (profile)
Free Elective Courses (1. semester) (3. semester)
Electric Machines, Drives and Automation (profile)
Free Elective Courses (1. semester) (3. semester)
Electronic and Computer Engineering (profile)
Free Elective Courses (1. semester) (3. semester)
Electronics (profile)
Free Elective Courses (1. semester) (3. semester)
Information and Communication Engineering (profile)
Free Elective Courses (1. semester) (3. semester)
Network Science (profile)
Free Elective Courses (1. semester) (3. semester)
Software Engineering and Information Systems (profile)
Elective Course of the profile (3. semester) Elective Course of the Profile (1. semester)

Literature

(.), D. Kalpić, V. Mornar (1996.), Operacijska istraživanja, Zeus - DRIP, Zagreb,
(.), Wayne L. Winston, Operations Research: Applications and Algorithms, 4th Edition. 2004.,
(.), F.S. Hillier, G.J. Lieberman (1974.), Operations Research, Holden Day,
(.), A. Ravindran, D.T. Phillips, J.J. Solberg (1987.), Operations Research - Principles and Practice, John Wiley & Sons,

For students

General

ID 222568
  Winter semester
5 ECTS
L3 English Level
L1 e-Learning
30 Lectures
15 Laboratory exercises

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

Independent assignments

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) (3. semester)
Communication and Space Technologies (profile)
Free Elective Courses (1. semester) (3. semester)
Computational Modelling in Engineering (profile)
Free Elective Courses (1. semester) (3. semester)
Computer Engineering (profile)
Elective Course of the Profile (1. semester) Elective Courses of the Profile (3. semester)
Computer Science (profile)
Elective Courses of the Profile (1. semester) (3. semester)
Control Systems and Robotics (profile)
Free Elective Courses (1. semester) (3. semester)
Data Science (profile)
Free Elective Courses (1. semester) (3. semester)
Electrical Power Engineering (profile)
Free Elective Courses (1. semester) (3. semester)
Electric Machines, Drives and Automation (profile)
Free Elective Courses (1. semester) (3. semester)
Electronic and Computer Engineering (profile)
Free Elective Courses (1. semester) (3. semester)
Electronics (profile)
Free Elective Courses (1. semester) (3. semester)
Information and Communication Engineering (profile)
Free Elective Courses (1. semester) (3. semester)
Network Science (profile)
Free Elective Courses (1. semester) (3. semester)
Software Engineering and Information Systems (profile)
Elective Course of the profile (3. semester) Elective Course of the Profile (1. semester)

Literature

(.), D. Kalpić, V. Mornar (1996.), Operacijska istraživanja, Zeus - DRIP, Zagreb,
(.), Wayne L. Winston, Operations Research: Applications and Algorithms, 4th Edition. 2004.,
(.), F.S. Hillier, G.J. Lieberman (1974.), Operations Research, Holden Day,
(.), A. Ravindran, D.T. Phillips, J.J. Solberg (1987.), Operations Research - Principles and Practice, John Wiley & Sons,

For students

General

ID 222568
  Winter semester
5 ECTS
L3 English Level
L1 e-Learning
30 Lectures
15 Laboratory exercises