Dissertation--Humboldt-Universität zu Berlin, 2009. / Includes bibliographical references and index.

A dissertation submitted to the Faculty of Arts, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Arts. / Real-life decision-making problems can often be modelled by mathematical programs (or optimization models). It is common for there to be uncertainty about the parameters of such optimization models. Usually, this uncertainty is ignored and a simplified deterministic program is obtained. Stochastic programs take account of this uncertainty by including a probabilistic description of the uncertain parameters in the model. Stochastic programs are therefore more appropriate or valuable than deterministic programs in many situations, and this is emphasized throughout the dissertation. The dissertation contains a development of the theory of stochastic programming, and a number of illustrative examples are formulated and solved. As a real-life application, a stochastic model for the unit commitment problem facing Eskom (one of the world's largest producers of electricity) is formulated and solved, and the solution is compared with that of the current strategy employed by Eskom. / AC 2018

Multistage stochastic programming is an important tool in medium to long term planning where there are uncertainties in the data. In this thesis, we consider a special case of multistage stochastic programming in which each subprogram is a convex quadratic program. The results are also applicable if the quadratic objectives are replaced by convex piecewise quadratic functions. Convex piecewise quadratic functions have important application in financial planning problems as they can be used as very flexible risk measures. The stochastic programming problems can be used as multi-period portfolio planning problems tailored to the need of individual investors. Using techniques from convex analysis and sensitivity analysis, we show that each subproblem of a multistage quadratic stochastic program is a polyhedral piecewise quadratic program with convex Lipschitz objective. The objective of any subproblem is differentiable with Lipschitz gradient if all its descendent problems have unique dual variables, which can be guaranteed if the linear independence constraint qualification is satisfied. Expression for arbitrary elements of the subdifferential and generalized Hessian at a point can be calculated for quadratic pieces that are active at the point. Generalized Newton methods with linesearch are proposed for solving multistage quadratic stochastic programs. The algorithms converge globally. If the piecewise quadratic objective is differentiable and strictly convex at the solution, then convergence is also finite. A generalized Newton algorithm is implemented in Matlab. Numerical experiments have been carried out to demonstrate its effectiveness. The algorithm is tested on random data with 3, 4 and 5 stages with a maximum of 315 scenarios. The algorithm has also been successfully applied to two sets of test data from a capacity expansion problem and a portfolio management problem. Various strategies have been implemented to improve the efficiency of the proposed algorithm. We experimented with trust region methods with different parameters, using an advanced solution from a smaller version of the original problem and sorting the stochastic right hand sides to encourage faster convergence. The numerical results show that the proposed generalized Newton method is a highly accurate and effective method for multistage quadratic stochastic programs. For problems with the same number of stages, solution times increase linearly with the number of scenarios.

Wildfires have become more destructive and are seriously threatening societies and our ecosystems throughout the world. Once a wildfire escapes from its initial suppression attack, it can easily develop into a destructive huge fire that can result in significant loss of lives and resources. Some human-caused wildfires may be prevented; however, most nature-caused wildfires cannot. Consequently, wildfire suppression and contain- ment becomes fundamentally important; but suppressing and containing wildfires is costly. Since the budget and resources for wildfire management are constrained in reality, it is imperative to make important decisions such that the total cost and damage associated with the wildfire is minimized while wildfire containment effectiveness is maximized. To achieve this objective, wildfire attack-bases should be optimally located such that any wildfire is suppressed within the effective attack range from some bases. In addition, the optimal fire-fighting resources should be deployed to the wildfire location such that it is efficiently suppressed from an economic perspective. The two main uncertain/stochastic factors in wildfire management problems are fire occurrence frequency and fire growth characteristics. In this thesis two models for wildfire management planning are proposed. The first model is a strategic model for the optimal location of wildfire-attack bases under uncertainty in fire occurrence. The second model is a tactical model for the optimal deployment of fire-fighting resources under uncertainty in fire growth. A stochastic mixed-integer programming approach is proposed in order to take into account the uncertainty in the problem data and to allow for robust wildfire management decisions under uncertainty. For computational results, the tactical decision model is numerically experimented by two different approaches to provide the more efficient method for solving the model.

Stochastic programming facilitates decision making under uncertainty. It is usually impractical or impossible to find the optimal solution to a stochastic problem, and approximations are required. Sampling-based approximations are simple and attractive, but the standard point estimate of optimization and the Monte Carlo approximation. We provide a method to reduce this bias, and hence provide a better, i.e., tighter, confidence interval on the optimal value and on a candidate solution's optimality gap. Our method requires less restrictive assumptions on the structure of the bias than previously-available estimators. Our estimators adapt to problem-specific properties, and we provide a family of estimators, which allows flexibility in choosing the level of aggressiveness for bias reduction. We establish desirable statistical properties of our estimators and empirically compare them with known techniques on test problems from the literature.

No description available.

Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of New South Wales, 1999. / Also available online.

Thesis (Ph.D. - Civil Engineering and Engineering Mechanics)--University of Arizona. / There are two pages numbered "70". Includes bibliographical references (leaves 184-188).

Thesis (Ph. D. in Operations Research)--Naval Postgraduate School, Sept. 2004. / Thesis Advisor(s): R. Kevin Wood. Includes bibliographical references (p. 71-80). Also available online.