Course detail
Linear and Non-linear Optimization in Logistics
FSI-SLN-A Acad. year: 2024/2025 Winter semester
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
Supervisor
Department
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.
The study programmes with the given course
Programme N-LAN-A: Logistics Analytics, Master's, compulsory-optional
Programme C-AKR-P: , Lifelong learning
specialization CZS: , elective
Type of course unit
Lecture
26 hours, optionally
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
Syllabus
Introductory problems (1-3)
Linear problems (4-10)
Nonlinear problems (11-13)
Course participance is obligatory.