Operations Research

Course Description

History and development of operational research. Mathematical modelling. 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.

General Competencies

The course should indicate to students the existence of multiple feasible solutions to practical problems, what opens the possibility of choice and accordingly to optimization. The students should learn mathematical modelling, solving, analysis and correct interpretation and acting in real world situations. Some quantitative business practices are connected to computing procedures as a base for decision-making. The main goal is to bridge the gap between the mathematical programming theory and practical problems. Practical problems are often of interdisciplinary nature. Many graduates will in their professional career deal with economics related problems. The course should improve their ability to recognize and understand these not primarily technical problems and to apply successfully their knowledge in mathematics and computing to solve them.

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 are performed classically, using chalk and blackboard, enhanced with PowerPoint presentations and software demonstrations.


During lectures, short tests are applied. Homework is assigned, a midterm examination, final examination and oral examination are held.


Exercises are embedded into the schedule of lectures. They consist of 6 auditory sessions for practicing of examination problems.


Students can ask appointment for consultations via e-mail. Prerequisite is to be able to precisely formulate what is not clear. Wishes for consultation like “I have not attended your lectures, so please give me a quick overview what is mixed-integer programming all about” are dismissed.

Other Forms of Group and Self Study

Students individually solve 3 homework assignments.

Grading Method

Continuous Assessment Exam
Type Threshold Percent of Grade Comment: Percent of Grade
Homeworks 0 % 20 % 0 % 0 %
Quizzes 0 % 10 % 0 % 0 %
Mid Term Exam: Written 0 % 30 % 0 %
Final Exam: Written 0 % 30 %
Final Exam: Oral 10 %
Exam: Written 0 % 70 %
Exam: Oral 30 %

Week by Week Schedule

  1. History and development of operational research. Mathematical modelling.
  2. Graphical solution to simple production problem. Solution using simplex.
  3. All bound types, free variables, negative valued variables, types of solution. Dual simplex, duality.
  4. Characteristics of duality. Programming system LPE. Models and interpretation of results for the simple production problem. Sensitivity analysis. Exercises (1 hour): Linear programming, simplex, graphical method.
  5. Multiphase production. Sensitivity analysis for different statuses of variables in the solution.
  6. Optimum mix. Transportation problem as linear program. Method MODI to solve the transportation problem. Assignment problem. Minimax and maxmin. Branch and bound.
  7. Exercises (2 hours): Preparation for midterm examination.
  8. Midterm examination.
  9. Midterm examination.
  10. Mixed-integer programming. Solving strategies. Example for application in agriculture.
  11. Example for application of mixed-integer programming in planning of power lines. Separable programming. Progressive/regressive profit in separable program. Lead time for adjustments. Separable program formulated as mixed-integer. Production scheduling. Costs of stocks for raw materials and intermediate products.
  12. Principles of network planning. Activities in nodes. MS Project as example for application software for network planning. Calculation of earliest and latest times using the critical path method. Activity ranks and drawing of network plan. Resources. Basic policies of stock replenishment. Deterministic and stochastic models.
  13. Discounting. Problem of equipment replacement. Selection of equipment. Dynamic programming. Nonlinear programming.
  14. Exercises: Mixed-integer programming, discounting.
  15. Exercises: Preparation for final examination.

Study Programmes

University graduate
Computer Engineering (profile)
Recommended elective courses (3. semester)
Computer Science (profile)
Recommended elective courses (3. semester)
Electrical Engineering Systems and Technologies (profile)
Recommended elective courses (3. semester)
Electrical Power Engineering (profile)
Recommended elective courses (3. semester)
Electronic and Computer Engineering (profile)
Recommended elective courses (3. semester)
Electronics (profile)
Recommended elective courses (3. semester)
Information Processing (profile)
Recommended elective courses (3. semester)
Software Engineering and Information Systems (profile)
Specialization Course (1. semester) (3. semester)
Telecommunication and Informatics (profile)
Recommended elective courses (3. semester)


D. Kalpić, V. Mornar (1996.), Operacijska istraživanja, Zeus - DRIP, Zagreb
A. Ravindran, D.T. Phillips, J.J. Solberg (1987.), Operations Research - Principles and Practice, John Wiley & Sons
F.S. Hillier, G.J. Lieberman (1974.), Operations Research, Holden Day
A. Kaufmann, R, Faure (1970.), Invitation a la recherche operationnelle, Dunod, Paris

Lecturers in Charge