# TIØ4120 - Operations Research, Introduction

### Examination arrangement

Examination arrangement: School exam

Evaluation Weighting Duration Grade deviation Examination aids
School exam 100/100 4 hours C

### Course content

The course deals with the use of mathematical models for planning of corporate and governmental activities. Most of the planning problems will consist of an economic objective which we want to maximize under scarce resources. Operations Research consists of: - limiting and defining the current problem, - formulating a mathematical model of the problem, - calculating an optimal solution of the model, -and finally interpreting and implementing the found solution. This course deals with both deterministic and stochastic problems, and they will be analyzed based on the following models and methods: Linear and nonlinear programming, integer programming, network models, simple queuing theory and simulation. We will use spreadsheets to find numerical solutions for some of the analyzed problems.

### Learning outcome

By the end of the course the students should be able to:

• define what is meant by operations research, and account for which phases are normally part of a study applying operations research
• describe the assumptions on which linear programming (LP) is built
• formulate LP models on the basis of verbal problem descriptions
• solve LP problems graphically (for two variables), by using spreadsheets, and by hand using the simplex method, both algebraic and in tabular form
• perform sensitivity analysis on the basis of optimal simplex tableaus, and describe the economic information that can be drawn from the analysis
• formulate integer programming models and solve problems formulated using such models by using branch-and-bound or spreadsheets
• formulate non-linear programming models and identify classes of non-linear programming models based on properties of the objective function and the constraint set
• solve some types of non-linear problems using the method of Lagrangean multipliers, the KKT conditions, or spreadsheets
• formulate and solve a number of network models
• indicate which additional challenges arise for problems where the parameters are not known with certainty
• create queueing models based on verbal problem descriptions
• derive formulas for queueing models based on exponential distributions
• describe discrete event simulation and differentiate this from other types of simulation - implement simple simulation models in spreadsheets
• discuss the pros and cons of the different types of models and the associated solution methods in view of specific problems.

### Learning methods and activities

Lectures and exercises with and without computers.

• Exercises

### Further on evaluation

If there is a re-sit examination, the examination form may change from written to oral.

### Specific conditions

Compulsory activities from previous semester may be approved by the department.

### Course materials

Given at the start of the course.

### Credit reductions

Course code Reduction From To
SIS1012 7.5
TIØ4115 3.7 AUTUMN 2008
BØA2020 7.5 SPRING 2017
TIØ4126 3.7 AUTUMN 2018
More on the course

No

Facts

Version: 1
Credits:  7.5 SP
Study level: Third-year courses, level III

Coursework

Term no.: 1
Teaching semester:  AUTUMN 2022

Language of instruction: Norwegian

Location: Trondheim

Subject area(s)
• Technological subjects
Contact information
Course coordinator: Lecturer(s):

Department of Industrial Economics and Technology Management

# Examination

#### Examination arrangement: School exam

Term Status code Evaluation Weighting Examination aids Date Time Examination system
Autumn ORD School exam 100/100 2022-12-06 09:00
Summer UTS School exam 100/100
• * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.
Examination

For more information regarding registration for examination and examination procedures, see "Innsida - Exams"

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