Course detail

Linear and Non-linear Optimization in Logistics

FSI-SLN-AAcad. year: 2024/2025

The course presents fundamental optimization models and methods for solving of logistic problems. The principal ideas of mathematical programming are discussed: problem analysis, model building, solution search, and the interpretation of results. The course mainly deals with linear programming (polyhedral sets, simplex method, duality) and introduction to nonlinear programming (convex sets and functions, Karush-Kuhn-Tucker conditions, selected algorithms). The course was built on the basis of the author's experience with similar courses at foreign universities.

Language of instruction

English

Number of ECTS credits

3

Mode of study

Not applicable.

Guarantor

RNDr. Pavel Popela, Ph.D.

Department

Institute of Mathematics (ÚM)

Entry knowledge

Basic knowledge of principal concepts of Calculus and Linear Algebra in the scope of the engineering curriculum is assumed.

Rules for evaluation and completion of the course

Graded course-unit credit is awarded based on the result in a written exam involving modelling-related (Question 1), computational-based (Question 2 LP and Question 3 NLP), and theoretical questions (Question 4 LP and Question 5 NLP). The written part of exam has the form of open book exam, so the related short oral exam is also included.


The attendance at seminars is required as well as active participation. Passive or missing students are required to work out additional assignments.

Aims

The course objective is to emphasize optimization modelling together with solution methods. It involves problem analysis, model building, model description and transformation, and the choice of the algorithm. Introduced methods are based on the theory and illustrated by geometrical point of view.


The course is designed for students of logistics and it is also useful for students of applied science and engineering. Students will learn the theoretical background of fundamental topics in linear and non-linear programming. They will also become familiar with useful algorithms and interesting applications.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Bazaraa, M.S. et al.: Linear Programming and Network Flows, 4th edition, Wiley, 2009. (EN)
Bazaraa, M.S. et al.: Nonlinear Programming: Theory and Algorithms, 3rd edition, Wiley, 2012. (EN)
Vanderbei, R.J. Linear Programming: Foundations and Extensions, 5th edition, Springer, 2020. (EN)
Luenberger D.G. and Ye, Y., Linear and Nonlinear Programming, 5th edition, Springer, 2021. (EN)

Recommended reading

Hillier, F.S. and Lieberman, G.J. Introduction to Operations Research, 9th edition, McGraw-Hill, 2009. (EN)
Solow, D. Linear Programming: An Introduction to Finite Improvement Algorithms, 2nd edition, Dover Publications, 2014. (EN)
Gass, S.I. Linear Programming: Methods and Applications, 5th edition, Dover Publications, 2010. (EN)
Panik, M.J., Linear Programming and Resource Allocation Modeling, 1st edition, Wiley, 2018. (EN)
Boyd, S.and Vandenberghe, L. Convex Optimization, 1st edition, Cambridge University Press, 2004. (recent www stanford updates 2020). (EN)

Classification of course in study plans

  • Programme N-LAN-A Master's, 1. year of study, winter semester, compulsory-optional

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

RNDr. Pavel Popela, Ph.D.

Syllabus

1.-2. Introductory optimization: problem formulation and analysis, model building, theory.
3. Visualisation, algorithms, software, postoptimization.
4.-5. Linear programming (LP): Selected applications in logistics. 
6. LP: Convex and polyhedral sets. Feasible sets and related theory.
7.-8. LP: The simplex method.
9.-10. LP: Duality, sensitivity and parametric analysis.
11. Nonlinear programming (NLP): Selected applications in logistics. Convex functions and unconstrained optimization. 
12. NLP: Selected applications in logistics. Constrained optimization and KKT conditions.
13. NLP: Constrained optimization and related numerical methods.

Exercise

13 hours, compulsory

Teacher / Lecturer

RNDr. Pavel Popela, Ph.D.

Syllabus

Introductory problems (1-3)

Linear problems (4-10)

Nonlinear problems (11-13)

Course participance is obligatory.