National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
Risk measures in scheduling problems under uncertainty
Pohly, Jakub ; Branda, Martin (advisor) ; Procházka, Vít (referee)
In the presented work we deal with fixed interval scheduling problem with random delays. We present common formulations of the problem and introduce new ones. The aim is introduction of formulations where the actual cost or penalty is properly expres- sed and also risk of the schedule is taken into account. The main topic of the work is combining existing formulations for FIS problem with risk measures and creating mixed integer linear formulations of them. The new formulations are minimizing expected num- ber of unprocessed jobs which is better linked to penalties than number of overlaps. For formulations based on risk measures we presented mean-variance optimization of number of overlaps and CVaR optimization of both number of overlaps and number of unproces- sed jobs. All of the new formulations were reformulated as mixed integer linear problem. Finally we show a numerical study where we implemented two of the new formulations we presented in this work. 1
Voronoi tessellations
Pohly, Jakub ; Pawlas, Zbyněk (advisor) ; Beneš, Viktor (referee)
In the presented work we deal with the theory of Voronoi tessellations. We deal with the properties of general Voronoi tessellations, but we focus mainly on those tessellations that are randomly generated. We study the point processes that create random Voronoi tessellations. We define the most common Poisson process. We focus on the renewal pro- cesses, specifically the ordinary renewal process, the delayed process and the equilibrium renewal process. With the help of these processes, we build a one-dimensional version of the Poisson process. We examine Voronoi tessellations primarily on a semi-straight line. Later, we generalize the obtained results for the line and the plane. In the conclusion of the work we deal with Voronoi tessellations in space. 1

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