Optimization Models II (FSI-SO2-A)

Academic year 2025/2026
Supervisor: RNDr. Pavel Popela, Ph.D.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: English
Aims of the course unit:

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, 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.
Learning outcomes and competences:
 
Prerequisites:

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

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 also includes introductory information on the principles of modification and generalization of advanced optimization models (integer programs), which are further extended and deepened in the follow-up courses. The course was compiled on the basis of the author's experience with similar courses at foreign universities.
Teaching methods and criteria:
 
Assesment methods and criteria linked to learning outcomes:

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 model  properties, bounds, and approximations, modified and addvanced reformulations, etc. The attendance at seminars is required as well as active participation. Passive or missing students are required to work out additional assignments.
Controlled participation in lessons:
 
Type of course unit:
    Lecture  13 × 2 hrs. optionally                  
    Computer-assisted exercise  13 × 1 hrs. compulsory                  
Course curriculum:
    Lecture

1.-2. Integer programming and selected models in logistics.
3.-4. Advanced integer programming (indicator variables) models, their properties and basic ideas of solution methods.
5.-6. Underlying mathematical program and selected applications. WS and HN approach. IS and EV reformulations. EO, EEV, EVPI and VSS. Deterministic 
7.-8. MM and VO, the solution of the large problems in logistics. Multicriteria optimization. 
9.-10. PO and QO, relation to integer programming. Probabilistic constraints.
11.-12. The use of recourse.
13. Advanced applications of mathematical programming. 
    Computer-assisted exercise

Logistic examples and exercises on:
1.-2. Integer programming and selected models in logistics.
3.-4. Advanced integer programming (indicator variables) models, their properties and basic ideas of solution methods.
5.-6. Underlying mathematical program and selected applications. WS and HN approach. IS and EV reformulations. EO, EEV, EVPI and VSS. Deterministic
7.-8. MM and VO, the solution of the large problems in logistics. Multicriteria optimization.
9.-10. PO and QO, relation to integer programming. Probabilistic constraints.
11.-12. The use of recourse.
13. Advanced applications of mathematical programming. 
Course participance is obligatory.
Literature - fundamental:
1. Kall, P.-Wallace,S.W.: Stochastic Programming, 2nd edition (open access), Wiley 2003.
2. Birge,J.R.-Louveaux,F.: Introduction to Stochastic Programing, 3rd  edition, Springer, 2011.
3. Prekopa, A: Stochastic Programming, 2nd edition, Springer, 2010.
4. Shapiro, A., Dentcheva, D., and Ruszczyński, A.: Lectures on Stochastic Programming: Modeling and Theory (3rd Edition). SIAM, Philadelphia, 2021.
5. Williams,H.P.: Model Building in Mathematical Programming. Wiley and Sons, 2012
Literature - recommended:
1. King, A.J., Wallace, S.W.: Modeling with Stochastic Programming, Springer Verlag, 2014.
2. Kall, P.-Wallace,S.W.: Stochastic Programming, 2nd edition (open access), Wiley 2003.
3. Birge,J.R.-Louveaux,F.: Introduction to Stochastic Programing, 2nd edition, Springer, 2011.
4. Shapiro, A., Dentcheva, D., and Ruszczyński, A.: Lectures on Stochastic Programming: Modeling and Theory (3rd Edition). SIAM, Philadelphia, 2021.
5. Williams,H.P.: Model Building in Mathematical Programming. Wiley and Sons, 2012
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
N-LAN-A full-time study --- no specialisation -- Cr,Ex 4 Compulsory 2 1 S