Theses and Dissertations (Decision Sciences)

Satisticing solutions for multiobjective stochastic linear programming problems

Wed, 01 Jun 2011 00:00:00 GMT

Satisticing solutions for multiobjective stochastic linear programming problems Adeyefa, Segun Adeyemi Multiobjective Stochastic Linear Programming is a relevant topic. As a matter of fact, many real life problems ranging from portfolio selection to water resource management may be cast into this framework. There are severe limitations in objectivity in this field due to the simultaneous presence of randomness and conflicting goals. In such a turbulent environment, the mainstay of rational choice does not hold and it is virtually impossible to provide a truly scientific foundation for an optimal decision. In this thesis, we resort to the bounded rationality and chance-constrained principles to define satisficing solutions for Multiobjective Stochastic Linear Programming problems. These solutions are then characterized for the cases of normal, exponential, chi-squared and gamma distributions. Ways for singling out such solutions are discussed and numerical examples provided for the sake of illustration. Extension to the case of fuzzy random coefficients is also carried out.

Local times of Brownian motion

Wed, 01 Sep 2010 00:00:00 GMT

Local times of Brownian motion Mukeru, Safari After a review of the notions of Hausdorff and Fourier dimensions from fractal geometry and Fourier analysis and the properties of local times of Brownian motion, we study the Fourier structure of Brownian level sets. We show that if δa(X) is the Dirac measure of one-dimensional Brownian motion X at the level a, that is the measure defined by the Brownian local time La at level a, and μ is its restriction to the random interval [0, L−1 a (1)], then the Fourier transform of μ is such that, with positive probability, for all 0 ≤ β < 1/2, the function u → |u|β|μ(u)|2, (u ∈ R), is bounded. This growth rate is the best possible. Consequently, each Brownian level set, reduced to a compact interval, is with positive probability, a Salem set of dimension 1/2. We also show that the zero set of X reduced to the interval [0, L−1 0 (1)] is, almost surely, a Salem set. Finally, we show that the restriction μ of δ0(X) to the deterministic interval [0, 1] is such that its Fourier transform satisfies E (|ˆμ(u)|2) ≤ C|u|−1/2, u 6= 0 and C > 0. Key words: Hausdorff dimension, Fourier dimension, Salem sets, Brownian motion, local times, level sets, Fourier transform, inverse local times.

The interplay of sector regulators and competition authorities in regulating competition in telecomunications : the south African case

Wed, 01 Apr 2009 00:00:00 GMT

The interplay of sector regulators and competition authorities in regulating competition in telecomunications : the south African case Khosa, Miyelani The privatisation and liberalisation of telecommunications throughout the world has resulted in the growing involvement of competition authorities in telecommunications regulation, alongside telecommunications sector-specific regulators. The existence of both sector specific rules and competition rules has brought about a critical institutional challenge. The increased role of competition authorities in the telecommunications sector raises the issue of inconsistent jurisdiction in the sector. Conflicts are therefore inevitable in the absence of clear delineation of jurisdiction. The South African model for regulation in the telecommunications sector entails a sharing of jurisdiction between the sector-specific regulator, the Independent Communications Authority of South Africa (ICASA), and the competition-wide regulator, the Competition Commission. The study thus determines the interplay between the Competition Commission and ICASA as well as the competitiveness of South African telecommunications.

A decision support system for multi-objective programming problems

Sun, 01 Nov 2009 00:00:00 GMT

A decision support system for multi-objective programming problems Rangoaga, Moeti Joseph Many concrete problems may be cast in a multi-objective optimisation framework. The redundancy of existing methods for solving multi-objective programming problems susceptible to inconsistencies, coupled with the necessity for making in- herent assumptions before using a given method, make it hard for a nonspecialist to choose a method that ¯ts the situation at hand well. Moreover, using a method blindly, as suggested by the hammer principle (when you only have a hammer, you want everything in your hand to be a nail) is an awkward approach at best and a caricatural one at worst. This brings challenges to the design, development, implementation and deployment of a Decision Support System able to choose a method that is appropriate for a given problem and to apply the chosen method to solve the problem under consideration. The choice of method should be made according to the structure of the problem and the decision maker's opinion. The aim here is to embed a sample of methods representing the main multi-objective programming techniques and to help the decision maker find the most appropriate method for his problem.