Course detail

Optimization II

FSI-SO2-AAcad. year: 2024/2025

The course focuses on advanced optimization models and methods of solving problems in logistics and related engineering problems. It includes foundations of stochastic programming (deterministic reformulations, theoretical properties, and selected algorithms for one stage and basic two stage problems) with applications in logistics. The course was compiled on the basis of the author's experience with similar courses at foreign universities.

Language of instruction

English

Number of ECTS credits

4

Mode of study

Not applicable.

Guarantor

RNDr. Pavel Popela, Ph.D.

Department

Institute of Mathematics (ÚM)

Entry knowledge

The presented topics require basic knowledge of optimization concepts. Standard knowledge of probabilistic and statistical concepts is assumed.

Rules for evaluation and completion of the course

There is an exam based on presentation of a written paper accompanied by oral discussion of results. Formulation, calculation and theoretical aspects of the work are evaluated. The related themes are based on logistic applications of recourse properties, bounds, and approximations, efficient decompostion algorithms, modified and addvanced deterministic reformulations, scenario generation and reduction, etc.


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 develop the advanced knowledge of sophisticated optimization techniques as well as the understanding and applicability of principal concepts.


The course is mainly designated for students of logistics and mathematical engineers, however it might be useful for applied sciences and engineering students as well. Students will learn of the recent topics in advanced optimization modelling and related optimization algorithms. They will also develop their ideas about suitable models for typical applications.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Kall, P.-Wallace,S.W.: Stochastic Programming, 2nd edition (open access), Wiley 2003. (EN)
Birge,J.R.-Louveaux,F.: Introduction to Stochastic Programing, 3rd  edition, Springer, 2011. (EN)
Prekopa, A: Stochastic Programming, 2nd edition, Springer, 2010. (EN)
Shapiro, A., Dentcheva, D., and Ruszczyński, A.: Lectures on Stochastic Programming: Modeling and Theory (3rd Edition). SIAM, Philadelphia, 2021. (EN)

Recommended reading

King, A.J., Wallace, S.W.: Modeling with Stochastic Programming, Springer Verlag, 2014. (EN)
Kall, P.-Wallace,S.W.: Stochastic Programming, 2nd edition (open access), Wiley 2003. (EN)
Birge,J.R.-Louveaux,F.: Introduction to Stochastic Programing, 2nd edition, Springer, 2011. (EN)
Shapiro, A., Dentcheva, D., and Ruszczyński, A.: Lectures on Stochastic Programming: Modeling and Theory (3rd Edition). SIAM, Philadelphia, 2021. (EN)
Ruszczyński, A. and Shapiro, A. (Editors): Stochastic Programming, Handbook in Operations Research and Management Science. Elsevier Science, Amsterdam, 2003. (EN)
Prekopa, A: Stochastic Programming, 2nd edition, Springer, 2010. (EN)

Classification of course in study plans

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

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

RNDr. Pavel Popela, Ph.D.

Syllabus

1.-2. Underlying mathematical program and selected applications.
3. WS and HN approach.
4. IS and EV reformulations.
5. EO, EEV, EVPI and VSS.
6.-7. MM and VO, the solution of the large problems in logistics.
8.-9. PO and QO, relation to integer programming.
10.-11. Deterministic and probabilistic constraints, the use of recourse.
12.-13. Applied twostage programming.

Computer-assisted exercise

13 hours, compulsory

Teacher / Lecturer

RNDr. Pavel Popela, Ph.D.

Syllabus

Logistic examples and exercises on:
1.-2. Underlying mathematical program.
3. WS and HN approach.
4. IS and EV reformulations.
5. EO, EEV, EVPI and VSS.
6.-7. MM and VO, the solution of the large problems.
8.-9. PO and QO, relation to integer programming.
10.-11. Deterministic and probabilistic constraints, the use of recourse.
12.-13. Applied two-stage programming.

Course participance is obligatory.