Linear programming (LP) stands for an optimization of a linear objective function, subject to linear and non-negativity constraints. For this purpose many methods for LP emerged. The best known is Simplex Method. Another group of methods for LP is represented by Interior Point Methods (IPM). These methods are based on interior points of feasible region of a problem, while Simplex Method uses basic feasible solution of a problem. This thesis focuses on theoretical background of IPM and brings it into relation with algorithms based on IPM. KKT system and its significance are included and the algorithm solving Linear Complementarity Problem is discussed as well. In this thesis, two algorithms based on IPM are introduced and used for solving a sample LP problem.

Denna studie syftar till att, utifrån ett personal- och brukarperspektiv, undersöka vilka yttre och inre maktaspekter som kommer till uttryck och påverkar CM-teamets arbete samt hur dessa maktaspekter tar sig i uttryck i relations- och motivationsarbetet. CM-teamet är en verksamhet som arbetar för att samordna insatser från kommun och landsting för de individer som har ett vårdbehov för sitt missbruk och sin psykiska problematik och som faller mellan stolarna. Denna studie är baserad på en kvalitativ metod där materialet analyserades med hjälp av meningskoncentrering. Vi har gjort intervjuer med såväl personal som brukare på CM-teamet för att belysa två perspektiv av verksamhetens arbete. Resultatet visar på att de yttre maktaspekterna dels påverkar och begränsar CM-teamets arbete men även påverkar de inre maktaspekterna vilket tar sig uttryck i paternalism från personalens sida. Resultatet diskuteras med hjälp av tidigare forskning inom case management som visar på likheter och skillnader gentemot CM-teamets arbete. / This study aims to, from a professional and consumer perspective, examine the external and internal aspects of power that come to expression and affect the work of the CM-team and how these aspects of power affect the progress on relationships and motivation. The aim of CM-team’s work is to coordinate efforts by the municipality and county for those individuals who have a need for treatment for their substance abuse and their psychiatric problems, who often fall between the chairs. This study is based on qualitative methodology in which the data was analyzed with the help of sentence concentration. We have done interviews with both professionals and consumers of the CM-team. The results point out the external aspects of power that influence and limit the work of CM-team but also the affects the internal aspects of power as reflected in the paternalism of the professionals. The results are discussed with previous research in Case Management that shows both similarities and differences compared to CM-team's work.

The master’s thesis focuses on the optimization models in logistics with emphasis on the network interdiction problem. The brief introduction is followed by two overview chapters - graph theory and mathematical programming. Important definitions strongly related to network interdiction problems are introduced in the chapter named Basic concepts of graph theory. Necessary theorems used for solving problems are following the definitions. Next chapter named Introduction to mathematical programming firstly contains concepts from linear programming. Definitions and theorems are chosen with respect to the following maximum flow problem and the derived dual problem. Concepts of stochastic optimization follow. In the fifth chapter, we discuss deterministic models of the network interdiction. Stochastic models of the network interdiction follow in the next chapter. All models are implemented in programmes written in the programming language GAMS, the codes are attached.