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Traffic assignment optimization models
Holešovský, Jan ; Mrázková, Eva (oponent) ; Popela, Pavel (vedoucí práce)
The class of network flow problems is one of the traditional applications of mathematical optimization. Such problems are widely applicable for example in logistics to achieve an optimal distribution of flow with respect to maximization of profit, or minimization of costs. This approach often leads to simplified models of real problems as it supposes the existence of only one decision maker. Such approach is possible in centralised networks, where an authority exists (such as railway network, military supply, or logistic network used by any company). The Traffic Assignment Problem (TAP) deals with impact of game theory to the network flow problem. Hence, we assume multiple decision makers, where each one of them wants to find his optimal behaviour. In this thesis, we focus on stochastic influences in TAP, for which we use methods of stochastic and multi-stage programming. Further, we concentrate on improvement options for the utilization of the system. Hereby, we consider possible actions of the master decision maker, and discuss them by the presence of multi-level mathematical programming.
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Stochastic Optimization of Network Flows
Málek, Martin ; Holešovský, Jan (oponent) ; Popela, Pavel (vedoucí práce)
The master's thesis focuses on the stochastic optimization in network flow problems. The theoretical part covers three topics - the graph theory, the optimization and the progressive hedging algorithm. Within the optimization the main part is devoted to the stochastic programming and the two-stage programming. The progressive hedging algorithm includes also the scenario aggregation and the modification of the general algorithm to two-stage problems. The practical part deals with models using real-world data of collection of municipal waste within the Czech Republic, which were provided by the Institute of Process Engineering.
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Stochastic Optimization of Network Flows
Málek, Martin ; Holešovský, Jan (oponent) ; Popela, Pavel (vedoucí práce)
The master's thesis focuses on the stochastic optimization in network flow problems. The theoretical part covers three topics - the graph theory, the optimization and the progressive hedging algorithm. Within the optimization the main part is devoted to the stochastic programming and the two-stage programming. The progressive hedging algorithm includes also the scenario aggregation and the modification of the general algorithm to two-stage problems. The practical part deals with models using real-world data of collection of municipal waste within the Czech Republic, which were provided by the Institute of Process Engineering.
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Traffic assignment optimization models
Holešovský, Jan ; Mrázková, Eva (oponent) ; Popela, Pavel (vedoucí práce)
The class of network flow problems is one of the traditional applications of mathematical optimization. Such problems are widely applicable for example in logistics to achieve an optimal distribution of flow with respect to maximization of profit, or minimization of costs. This approach often leads to simplified models of real problems as it supposes the existence of only one decision maker. Such approach is possible in centralised networks, where an authority exists (such as railway network, military supply, or logistic network used by any company). The Traffic Assignment Problem (TAP) deals with impact of game theory to the network flow problem. Hence, we assume multiple decision makers, where each one of them wants to find his optimal behaviour. In this thesis, we focus on stochastic influences in TAP, for which we use methods of stochastic and multi-stage programming. Further, we concentrate on improvement options for the utilization of the system. Hereby, we consider possible actions of the master decision maker, and discuss them by the presence of multi-level mathematical programming.
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