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Stochastic programming models with applications
Novotný, Jan ; Michálek, Jaroslav (oponent) ; Popela, Pavel (vedoucí práce)
The thesis deals with stochastic programming and its application to aggregate blending, an optimization problem within the area of civil engineering. The theoretical part is devoted to the derivation of basic principles of stochastic programming (optimization under uncertainty). The applied part presents a development of suitable mathematical models for aggregate blending, their implementation and results. The thesis contains original results achieved in solution of the project GA CR reg. n. 103/08/1658 Advanced optimum design of composed concrete structures and it contains theoretical results of the project from MSMT of the Czech Republic no. 1M06047 Centre for Quality and Reliability of Production.
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Algoritmy pro řešení stochastických dvoustupňových úloh
Vlčková, Ivona ; Kopa, Miloš (vedoucí práce) ; Lachout, Petr (oponent)
V této práci se zabýváme algoritmy pro řešení dvoustupňových stochastických úloh. V první kapitole jsou uvedeny teoretické vlastnosti účelové funkce a množiny omezení, jenž jsou nezbytné pro pochopení fungování algoritmů. V závěru jsou diskutovány podmínky optimality. Druhá kapitola se zabývá algoritmy pro řešení úloh s lineární účelovou funkcí. V první části je podrobně vysvětlena základní forma L-shaped algoritmu. Druhá část je věnována algoritmu stochastické dekompozice včetně popisu regularizované verze. Poslední kapitola práce slouží k praktickému porovnání uvedených algoritmů na třech aplikačních příkladech. Každá úloha je nejprve teoreticky popsána a poté vyřešena oběma uvedenými algoritmy.
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Stochastic programming models with applications
Novotný, Jan ; Michálek, Jaroslav (oponent) ; Popela, Pavel (vedoucí práce)
The thesis deals with stochastic programming and its application to aggregate blending, an optimization problem within the area of civil engineering. The theoretical part is devoted to the derivation of basic principles of stochastic programming (optimization under uncertainty). The applied part presents a development of suitable mathematical models for aggregate blending, their implementation and results. The thesis contains original results achieved in solution of the project GA CR reg. n. 103/08/1658 Advanced optimum design of composed concrete structures and it contains theoretical results of the project from MSMT of the Czech Republic no. 1M06047 Centre for Quality and Reliability of Production.
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Day-ahead bidding on energy markets - a basic model and its extension to bidding curve
Branda, Martin
Wind resources energy production is highly influenced by uncertain weather conditions. We provide several simple models for bidding on day-ahead energy markets, which take into account the uncertainty. The obtained optimal bids and bidding curve are based not only on the point prediction, but also on the forecasted distribution of generated energy. We relate the resulting problems to two-stage stochastic programs with simple recourse.
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