C44 - Operations Research; Statistical Decision TheoryReturn

Two levels can be identified in the article. The first one is related to a theoretical introduction to the known stochastic dominance approach and the interactive multi-objective programming method; in the second we apply the aforesaid quantitative approaches to making an "optimal" portfolio structure of shares funds. We use the draft of stochastic dominance for a reduction in a relatively huge set of investment opportunities. The application of the stochastic dominance principle is determined by the stochastic character of the studied problem. The yield rate of shares funds is stated as a random variable. We also apply the Monte Carlo method in the investment decision-making procedure. For finding an "optimal" portfolio form, we use the interactive multi-criteria programming method, the computational algorithm of which is based on maximization of positive deviation from aspiration levels of separate objective functions (criteria). After all the procedures, including successive revision of solutions offered by analysts according to decision-maker preferences, we obtain a final portfolio form of shares funds.

DEA (Data Envelopment Analysis) models are usually used to find the relative efficiency among homogenous units according to selected criteria (inputs and outputs). Homogenous units are the units (companies, institutions, states) that produce equivalent outputs via using the same inputs but with different intensity. As the number of inputs and outputs included in the model can be higher, the DEA models rank among the methods of multi-criteria decision-making. In this article we try to compare the not-for-profit hospitals that are situated in Vysocina Region in these towns: Jihlava, Havlickuv Brod, Trebic and Nove Mesto na Morave. In this article we compare only the Departments of Ophthalmology in the hospitals named above. All the criteria for the comparison were selected in cooperation with the Section of Health Care of the Vysocina Region which also has given all the data. This article describes results of DEA models and suggestions how to improve the efficiency of the departments.

The paper deals with two methods of solving optimization programs where uncertainties occur: stochastic (in particular chance-constrained) programming and robust programming. We review briefly how these two methods deal with uncertainty and what approximations are commonly used. Furthermore, we are concentrated on approximations based on sample sets where some type of weak dependence occurs. We demonstrate that such kind of dependence does not imply any important malfunction of optimization methods used there. Numerical illustration on simple optimization program is given.

Economic activities developing over time are very often influenced simultaneously by a random factor (modeled mostly by a stochastic process) and a "decision" parameter (that has to be chosen according to economic possibilities). Theory of multistage stochastic programming, controlled Markov processes as well as empirical processes can be employed to treat the economic processes. We focus on the multistage stochastic problems with the individual probability constraints and random element following an autoregressive (generally) nonlinear sequence.

Optimization techniques enter often as a mathematical tool into many economic applications. In these models, uncertainty is modelled via probability distribution that is approximated or estimated in real cases. Then we ask for a stability of solutions with respect to changes in the probability distribution. The work illustrates one of possible approaches (using probability metrics), underlying numerical challenges and a backward glance to economical interpretation.

Economic and social phenomena develop over time, they are mostly influenced by random factors and, moreover, it is very often necessary to evaluate them simultaneously by several "objective" functions. Multistage stochastic programming problems, control Markov chains, empirical processes as well as stochastic multiobjective problems can serve to model them. We focus to cases that can be treated by multistage stochastic programming models with Markov type of dependence.