C61 - Optimization Techniques; Programming Models; Dynamic AnalysisReturn

Nowadays, consumers can find basic information about a wide range of offers with almost no effort. For example, Internet sites give information about second-hand cars regarding the mark, age, price, engine type/size and distance travelled. This information suffices to assess whether a car is potentially attractive, but is not sufficient to make a final decision. The authors have developed an automatic procedure for selecting a shortlist of offers that aims to maximize a weighted average of the attractiveness and diversity of the offers on the shortlist. The consumer determines the number of offers to be placed on the shortlist and the relative importance of the traits considered. The authors have compared the results obtained by applying two methods of multicriteria assessment.

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.

Mathematical programming methods dominate in the portfolio optimization problems, but they cannot be used if we introduce a constraint limiting the number of different assets included in the portfolio. To solve this model some of the heuristics methods (such as genetic algorithm, neural networks and particle swarm optimization algorithm) must be used. In this paper we utilize binary particle swarm optimization algorithm and quadratic programming method to find an efficient frontier in portfolio optimization problem. Two datasets are utilized. First dataset consists of the stocks incorporated in the Dow Jones Industrial Average, second dataset contains stocks from the Standard & Poor's 500. The comparison of found efficient frontiers for different limitation on the number of stock held is made at the close of the paper.