Introduction to Operations Research, 4 credits

Optimeringslära, grundkurs, 4 hp

TAOP52

Main field of study

Mathematics Applied Mathematics

Course level

First cycle

Course type

Programme course

Examiner

Nils-Hassan Quttineh

Director of studies or equivalent

Ingegerd Skoglund

Education components

Preliminary scheduled hours: 50 h
Recommended self-study hours: 57 h
ECV = Elective / Compulsory / Voluntary
Course offered for Semester Period Timetable module Language Campus ECV
6CIEI Industrial Engineering and Management - International, M Sc in Engineering - Chinese 2 (Spring 2017) 2 3 Swedish Linköping C
6CIEI Industrial Engineering and Management - International, M Sc in Engineering - French 2 (Spring 2017) 2 3 Swedish Linköping C
6CIEI Industrial Engineering and Management - International, M Sc in Engineering - German 2 (Spring 2017) 2 3 Swedish Linköping C
6CIEI Industrial Engineering and Management - International, M Sc in Engineering - Japanese 2 (Spring 2017) 2 3 Swedish Linköping C
6CIEI Industrial Engineering and Management - International, M Sc in Engineering - Spanish 2 (Spring 2017) 2 3 Swedish Linköping C
6CIII Industrial Engineering and Management, M Sc in Engineering 2 (Spring 2017) 2 3 Swedish Linköping C

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level

G1X

Course offered for

  • Industrial Engineering and Management - International, M Sc in Engineering
  • Industrial Engineering and Management, M Sc in Engineering

Entry requirements

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.

Prerequisites

Calculus, Linear Algebra.

Intended learning outcomes

Optimization deals with mathematical theory and methods aiming at analyzing and solving decision problems that arise in technology, economy, medicine, etc. The course gives a broad orientation of the field of optimization, with emphasis on basic theory and methods for continuous optimization problems in finite dimension, and it also gives some insight into its use for analyzing practical optimization problems. After the course, the student shall:

  • be able to explain important classes of ptimization problems and to be able to classify them according to their properties, into, for example, linear and nonlinear problems
  • model mathematical models of simple optimization problems
  • be able to explain basic concepts, such as, for example, local and global optimality, convexity, weak and strong duality
  • have knowledge about and be able to apply basic theory for some common types of optimization problems, such as, for example, duality theory for linear optimization problems, and have knowledge about and be able to use optimality conditions, such as, for example, KKT-conditions, to determine the optimality of a given solution
  • be able to explain and to apply basic principles for solving some common types of optimization problems, such as, for example, the simplex method for linear problems
  • be able to estimate the optimal objective value through lower and upper bounds
  • be able to use commonly available software for solving optimization problems of standard type
  • have some knowledge of practical applications of optimization

Course content

Linear programming: the simplex method, sensitivity analysis, duality. Nonlinear programming, convex functions and sets, iterative methods for problems with or without constraints, optimality conditions (Karush-Kuhn-Tucker conditions) 

Teaching and working methods

Lectures which include theory, problem solving and applications. Exercises which are intended to give individual training in problem solving. A laboratory course with emphasis on modelling and the use of optimization software.

Examination

TEN1Written examination3 creditsU, 3, 4, 5
LAB1Laboratory Work1 creditsU, G

Grades

Four-grade scale, LiU, U, 3, 4, 5

Other information

Supplementary courses:
Operations Research, extended course, Economic Analysis: Economic Theory, Economic Analysis: Decision- and Financial Methodology, Production and Operations Management

Department

Matematiska institutionen

Director of Studies or equivalent

Ingegerd Skoglund

Examiner

Nils-Hassan Quttineh

Course website and other links

Education components

Preliminary scheduled hours: 50 h
Recommended self-study hours: 57 h

Course literature

Lundgren J, Rönnqvist M, Värbrand P: Optimeringslära. Studentlitteratur (2003, reviderad 2008), ISBN: 9789144053141 Henningsson M, Lundgren J, Rönnqvist M, Värbrand P: Optimeringslära övningsbok (2010), ISBN: 9789144067605
Code Name Scope Grading scale
TEN1 Written examination 3 credits U, 3, 4, 5
LAB1 Laboratory Work 1 credits U, G
Lundgren J, Rönnqvist M, Värbrand P: Optimeringslära. Studentlitteratur (2003, reviderad 2008), ISBN: 9789144053141 Henningsson M, Lundgren J, Rönnqvist M, Värbrand P: Optimeringslära övningsbok (2010), ISBN: 9789144067605

Note: The course matrix might contain more information in Swedish.

I = Introduce, U = Teach, A = Utilize
I U A Modules Comment
1. DISCIPLINARY KNOWLEDGE AND REASONING
1.1 Knowledge of underlying mathematics and science (G1X level)
X
X
TEN1

                            
1.2 Fundamental engineering knowledge (G1X level)
X
TEN1

                            
1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level)

                            
1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level)

                            
1.5 Insight into current research and development work

                            
2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES
2.1 Analytical reasoning and problem solving
X
X
X
LAB1
TEN1

                            
2.2 Experimentation, investigation, and knowledge discovery

                            
2.3 System thinking
X
X
LAB1
TEN1

                            
2.4 Attitudes, thought, and learning
X

                            
2.5 Ethics, equity, and other responsibilities

                            
3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION
3.1 Teamwork
X
LAB1

                            
3.2 Communications
X
LAB1

                            
3.3 Communication in foreign languages

                            
4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT
4.1 External, societal, and environmental context

                            
4.2 Enterprise and business context

                            
4.3 Conceiving, system engineering and management
X
LAB1
TEN1

                            
4.4 Designing

                            
4.5 Implementing

                            
4.6 Operating

                            
5. PLANNING, EXECUTION AND PRESENTATION OF RESEARCH DEVELOPMENT PROJECTS WITH RESPECT TO SCIENTIFIC AND SOCIETAL NEEDS AND REQUIREMENTS
5.1 Societal conditions, including economic, social, and ecological aspects of sustainable development for knowledge development

                            
5.2 Economic conditions for knowledge development

                            
5.3 Identification of needs, structuring and planning of research or development projects
X
X
LAB1

                            
5.4 Execution of research or development projects
X
X
LAB1

                            
5.5 Presentation and evaluation of research or development projects
X
X
LAB1

                            

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