|
| |
|
|
Transportation problem
Zymáková, Iva ; Lachout, Petr (advisor) ; Houda, Michal (referee)
As a transportation problem we usually denote one of the classical problems of the linear programming. This is just a very special case of more general problem, which is sometimes called Kantorovich transportation problem. I describe Kantorovich problem and its solution in some special cases in this work. Particularly, I describe the solution of the problem with quadratic cost and the solution of the problem with concave cost on the real line, in detail. At the end of the text, I show how the solution of the general problem could be approximated by the solutions of linear task. I solve the problem with some common distributions and with three typical cost functions { linear, strictly convex and strictly concave.
|
|
|
Use of the BCC and Range Directional DEA Models within an Efficiency Evaluation
Houda, Michal
The contribution deals with two data envelopment analysis (DEA) models, in particular the BCC model (radial DEA model with variable returns to scale), and the range directional model. The mathematical description of the models are provided and several properties reported. A numerical comparison of the two models on real industrial data is provided with discussion about possible drawbacks of simplifying modeling procedures.
|
|
|
Stochastic Optimization on Random Networks
Sigačevová, Jana ; Houda, Michal (advisor) ; Branda, Martin (referee)
The deterministic theory of graphs and networks is used successfully in cases where no random component is needed. However in practice, a number of decision-making and conflict situations require the inclusion of a stochastic element directly into the model. The objective of this thesis is the introduction of stochastic optimization and its application on random networks. The reader will become familiar with three approaches to stochastic optimization. Namely two-stage optimization, multi-stage optimization and chance constraint optimization. Finally, the studied issue is demonstrated on a real telecommunication network example.
|
|
|
Transportation problem
Zymáková, Iva ; Houda, Michal (referee) ; Lachout, Petr (advisor)
As a transportation problem we usually denote one of the classical problems of the linear programming. This is just a very special case of more general problem, which is sometimes called Kantorovich transportation problem. I describe Kantorovich problem and its solution in some special cases in this work. Particularly, I describe the solution of the problem with quadratic cost and the solution of the problem with concave cost on the real line, in detail. At the end of the text, I show how the solution of the general problem could be approximated by the solutions of linear task. I solve the problem with some common distributions and with three typical cost functions { linear, strictly convex and strictly concave.
|
|
| |
|
|
A note on the use of copulas in chance-constrained programming
Houda, Michal
In this paper we are concentrated on a problem of linear chanceconstrained programming where the constraint matrix is considered random with a known distribution of the matrix rows. The rows are not considered to be independent; instead, we make use of the copula notion to describe the dependence of the matrix rows. In particular, the distribution of the rows is driven by so-called Archimedean class of copulas. We provide a review of very basic properties of Archimedean copulas and describe how they can be used to transform the stochastic programming problem into a deterministic problem of second-order cone programming. Also the question of convexity of the problem is explored and importance of the selected class of copulas is commented. At the end of the paper, we provide a simple example to illustrate the concept used.
|
|
|
Convexity in stochastic programming model with indicators of ecological stability
Houda, Michal
We develop an optimization model dealing with construction expenses that are prescribed as a result of the EIA (Environmental Impact Assessment) process. The process is an obligatory part of every large construction project and evaluates possible influences of the project to the environment, including population health, natural and other socio-economic aspects; the result of the process is a set of recommendation and arrangements the construction must meet. Our optimization model incorporates uncertainties in model parameters; we represent them through their probabilistic distribution. Furthermore, to overcome a problem with quantifying subjective utility function of ecological impacts, we measure them by so-called indicators of ecological stability. The resulting problem is stochastic programming problem formulated as (C)VaR model used traditionally in finance area. In our contribution we deal with convexity properties of this problem – these are especially important from the theoretical as well as from the computational point of view.
|
|
|
Using indicators of ecological stability in stochastic programming
Houda, Michal
When building bigger construction the EU law impose the so-called EIA process - evaluation of possible influences of the construction on the environment and population health, grouped into several categories. Outputs of the EIA process are recommendations to the investors compensating the negative impacts of the constructions by additional arrangements. In our contribution we develop an innovative approach to model the expenses devoted to obey the EIA rules by stochastic programming tools: especially, we represent uncertainty in parameters by their probabilistic distributions, and subjective utility function representing the ecological demands is modelled via so-called indicators of ecological stability. The model takes into account budget limitations, several legislative obligations, and other ecological aspects; the goal is to help choose the optimal compensating constructions and arrangements. The resulting stochastic programming model is seen as parallel to V@R problem.
|
|
| |
guest ::
