Vícestupňové úlohy stochastické optimalizace se zaměřením na generování scénářů pro dynamické diskrétní problémy

• Název práce v češtině: Vícestupňové úlohy stochastické optimalizace se zaměřením na generování scénářů pro dynamické diskrétní problémy
• Název v anglickém jazyce: Multistage Stochastic Integer Optimization with a Focus on Scenario Generation for Dynamic Discrete Problems
• Akademický rok vypsání: 2024/2025
• Typ práce: disertační práce
• Ústav: Katedra pravděpodobnosti a matematické statistiky (32-KPMS)
• Vedoucí / školitel: doc. RNDr. Martin Branda, Ph.D.
• Konzultanti: Ing. Vít Procházka, Ph.D.

Zásady pro vypracování

Multistage stochastic integer optimization problems are ubiquitous in various real-world applications, such as dynamic vehicle routing and scheduling problems. These problems involve making decisions over multiple stages in an uncertain environment, where future data is not known with certainty. An essential component of solving such problems is scenario generation, which involves generating representative scenarios for the uncertain parameters. The objective of this PhD thesis is to develop novel methods for multistage stochastic integer optimization with a special focus on scenario generation, and to apply these methods to dynamic discrete problems.
Research Questions:
1. What are the state-of-the-art methods for multistage stochastic integer optimization, and how can they be improved?
2. What are the current techniques for scenario generation in multistage stochastic optimization, and how can they be enhanced to generate more representative scenarios?
3. How can the developed methods be applied to dynamic vehicle routing and scheduling problems to improve their efficiency and effectiveness?

Seznam odborné literatury

[1] Branda, M., Matoušková, M. (2024). A Lagrangian relaxation algorithm for stochastic fixed interval scheduling problem with non-identical machines and job classes.
Computers & Operations Research 164, no. 106542.
[2] Branda, M., Novotný, J. and Olstad, A. (2016). Fixed interval scheduling under uncertainty - a tabu search algorithm for an extended robust coloring formulation. Computers & Industrial Engineering 93, 45-54.
[3] Lysgaard, J. (2012). Stochastic vehicle routing problems: models and solutions. European Journal of Operational Research, 223(2), 346-359.
[4] Prochazka, V., Wallace, S.W. (2020). Scenario tree construction driven by heuristic solutions of the optimization problem. Computational Management Science 17(2), 277–307.
[5] R. Rahmaniani, T.G. Crainic, M. Gendreau, W. Rei: The Benders decomposition algorithm: A literature review. European Journal of Operational Research 259(3), 801-817, 2017.
[6] A. Ruszczyński, A. Shapiro (eds.): Handbook of stochastic programming. Elsevier, 2003.
[7] A. Shapiro, D. Dentcheva, A. Ruszczyński: Lectures on stochastic programming. Modeling and theory. MPS/SIAM Series on Optimization 9. Philadelphia, 2009.
Wolsey, L.A. (1998). Integer Programming, Wiley, New York.
[8] Van den Akker, R., Vanberkel, P. T., & Zuidwijk, R. (2015). A two-stage stochastic integer programming approach for the integrated airline scheduling and aircraft routing problem. Transportation Science, 49(4), 806-822.