Browsing by Subject "stochastic programming"
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Item Computational Study of Mean-Risk Stochastic Programs(2013-05-01) Cotton, Tanisha GreenMean-risk stochastic programs model uncertainty by including risk measures in the objective function. This allows for modeling risk averseness for many problems in science and engineering. This dissertation addresses gaps in the literature on stochastic programs with mean-risk objectives. This includes a need for a computational study of the few available algorithms for this class of problems. The study was aimed at implementing and performing an empirical investigation of decomposition algorithms for stochastic linear programs with absolute semideviation (ASD) and quantile deviation (QDEV) as mean-risk measures. Specifically, the goals of the study were to analyze for specific instances how algorithms perform across different levels of risk, investigate the effect of using ASD and QDEV as risk measures, and understand when it is appropriate to use the risk-averse approach over the risk-neutral one. We derive two new subgradient based algorithms for the ASD and QDEV models, respectively. These algorithms are based on decomposing the stochastic program stage-wise and using a single (aggregated) cut in the master program to approximate the mean and deviation terms of the mean-risk objective function. We also consider a variant of each of the algorithms from the literature in which the mean-risk objective function is approximated by separate optimality cuts, one for the mean and one for the deviation term. These algorithms are implemented and applied to standard stochastic programming test instances to study their comparative performance. Both the aggregated cut and separate cut algorithms have comparable computational performance for ASD, while the separate cut algorithm outperforms its aggregate counterpart for QDEV. The computational study also reveals several insights on mean-risk stochastic linear programs. For example, the results show that for most standard test instances the risk-neutral approach is still appropriate. We show that this is the case due to the test instances having random variables with uniform marginal distributions. In contrast, when these distributions are changed to be non-uniform, the risk-averse approach is preferred. The results also show that the QDEV mean-risk measure has broader flexibility than ASD in modeling risk.Item Nonlinear Programming Approaches for Efficient Large-Scale Parameter Estimation with Applications in Epidemiology(2013-07-09) Word, Daniel PaulThe development of infectious disease models remains important to provide scientists with tools to better understand disease dynamics and develop more effective control strategies. In this work we focus on the estimation of seasonally varying transmission parameters in infectious disease models from real measles case data. We formulate both discrete-time and continuous-time models and discussed the benefits and shortcomings of both types of models. Additionally, this work demonstrates the flexibility inherent in large-scale nonlinear programming techniques and the ability of these techniques to efficiently estimate transmission parameters even in very large-scale problems. This computational efficiency and flexibility opens the door for investigating many alternative model formulations and encourages use of these techniques for estimation of larger, more complex models like those with age-dependent dynamics, more complex compartment models, and spatially distributed data. However, the size of these problems can become excessively large even for these powerful estimation techniques, and parallel estimation strategies must be explored. Two parallel decomposition approaches are presented that exploited scenario based decomposition and decomposition in time. These approaches show promise for certain types of estimation problems.Item Stochastic Programming Model for Fuel Treatment Management(2014-04-28) Kabli, Mohannad Reda ADue to the increased number and intensity of wild fires, the need for solutions that minimize the impact of fire are needed. Fuel treatment is one of the methods used to mitigate the effects of fire at a certain area. In this thesis, a two-stage stochastic programming model for fuel treatment management is constructed. The model optimizes the selection of areas for fuel treatment under budget and man-hour constraints. The process makes use of simulation tools like PHYGROW, which mimics the growth of vegetation after treatment, and FARSITE, which simulates the behavior of fire. The model minimizes the costs of fuel treatment as well as the potential losses when fire occurs. Texas Wild re Risk Assessment Model (TWRA) used by Texas Forest Service (TFS) is used to quantify risk at each area. The model is applied at TX 12, which is a re planning unit under the administration of TFS. Results show that the total of the expenditures on fuel treatment and the expected impact justify the efforts of fuel treatment.