C61 - Optimization Techniques; Programming Models; Dynamic AnalysisNávrat zpět

Smartcities are, among other things, well-known for solving optimization problems. One of the problems could be an optimal location of a central warehouse, which supplies branches. The branches are not the same; they naturally have a different location and a volume of traffic. The central warehouse must be situated in the area within the optimal distance that allows for minimal transportation costs. It can happen that the optimal solution to the abovementioned problem lies in a prohibited area such as forests, military areas. This paper deals with the problem of an optimal location of the central warehouse that must not lie in the prohibited area. The aim of the article is to present a mathematical model based on nonlinear principle, which can offer a solution to the mentioned problem. The main principle in modelling is to create a user-friendly and affordable model and to find an optimal solution to a particular situation. Such a model must take into consideration the dynamic development of logistics, construction of distribution warehouses and the chain stores nearby. The model gives results for the first phase of the planning optimal positioning. The mathematical solution must be implemented into a realistic situation. The actual location of the central warehouse must be adapted to, for example the reach of the highway.

Public universities in the Czech Republic suffer from insufficient funding for many years. One possibility for an increased funding of Czech public universities is an introduction of a low administrative fee called enrollment fee for each semester of a study. The aim of this article is to show how to find the optimal level of the enrollment fee for a given university so the total revenue of a university for enrolling students is maximal. This is done via mathematical model encompassing parameters such as maximal enrollment fee, sensitivity of enrolling students to the level of the enrollment fee, the number of enrolling students, etc. By improperly adjusted enrollment fee a university can lose millions or tens of millions crowns per year. Thus, the determination of the optimal level of the enrollment fee has high practical value, as it enables a university to maximize its combined revenue from the enrollment fee and the number of enrolling students.

Při řešení úloh optimalizace portfolia se většinou využívají metody matematického programování. Tyto metody však nemohou být použity, pokud zavedeme omezení počtu držených aktiv. K řešení takto definovaného problému je nutno použít jednu z mnoha heuristických metod (genetické algoritmy, neuronové sítě nebo algrotimus rojení částic). V tomto příspěvku je využito binárního algoritmu rojení částic a metody kvadratického programování při hledání efektivní množiny řešení při optimalizaci portfolia. V článku jsou použity dvě množiny vstupních dat. První množinu tvoří akcie zahrnuté do indexu Dow Jones Industrial Average, druhou pak akcie zahrnuté do indexu Standard & Poor's 500. V závěru příspěvku jsou graficky srovnány nalezené efektivní množiny pro různá omezení počtu držených akcií.