Browsing by Subject "Stochastic Programming"
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Item A stochastic mixed integer programming approach to wildfire management systems(2009-06-02) Lee, Won JuWildfires 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.Item Bio-energy Logistics Network Design Under Price-based Supply and Yield Uncertainty(2014-12-10) Memisoglu, GokhanIn this dissertation, we study the design and planning of bio-energy supply chain networks. This dissertation consists of 3 studies that focus on different aspects of bio-energy supply chain systems. In the first study, we consider planning and design of an extended supply chain for bio-energy networks in an integrated fashion while simultaneously addressing strategic and tactical decisions pertaining to location, production, inventory, and distribution in a multi-period planning horizon setting. For an efficient solution of our model, we suggest a Benders Decomposition based algorithm that can handle realistic size problems for design and analysis purposes. We provide computational results that demonstrate the efficiency of the solution approach on a wide ranging set of problem instances. Furthermore, we develop a realistic case by utilizing data pertaining to the state of Texas and conduct an extensive analysis on the effects of varying input parameters on the design outcomes for a bio-energy supply chain network. In the second study, we consider a two-stage stochastic problem to model farm-to-biorefinery biomass logistics while designing a policy that encourages farmers to plant biomass energy crops by offering them a unit wholesale price. In the first-stage, the model determines the supply chain network structure as well as the policy parameter, which is the biomass wholesale price offered to farmers. Second-stage problem is to determine the logistical decisions such as transportation, salvaging and out-sourcing. To solve this problem, we propose a solution framework that uses an algorithm based on the L-shaped method along with a Sample Average Approximation (SAA) approach. An extensive case study by varying some of the problem input parameters is conducted in Texas and the effects on the policy parameter (wholesale price), supply chain network design and expected total system cost are observed. In the last study, we propose a two-stage stochastic program to model a multi-period biomass-biofuel supply chain system to maximize the expected total system profit. We utilize a similar policy used in the second study to stimulate biomass energy crop production. Our model determines the policy parameter and the supply chain network structure in the first-stage and the tactical decisions for every time period in the second-stage. To solve this problem efficiently, we propose a solution algorithm based on the L-shaped method. Moreover, we also employ SAA approach in our solution methodology to statistically justify our solution quality. A case study is conducted in Texas for different biofuel prices and we analyze changes in the expected system profit the policy parameter and the supply chain network structure. Our case study results indicate that biofuel price needs to be at least $2.62/gal for the system to have a profit.Item Development and Evaluation of An Adaptive Transit Signal Priority System Using Connected Vehicle Technology(2014-12-15) Zeng, XiaosiTransit signal priority (TSP) can be a very effective preferential treatment for transit vehicles in congested urban networks. There are two problems with the current practice of the transit signal priority. First, random bus arrival time is not sufficiently accounted for, which?ve become the major hindrance in practice for implementing active or adaptive TSP strategies when a near-side bus stop is present. Secondly, most research focuses on providing bus priority at local intersection level, but bus schedule reliability should be achieved at route level and relevant studies have been lacking. In the first part of this research, a stochastic mixed-integer nonlinear programming (SMINP) model is developed to explicitly to account for uncertain bus arrival time. A queue delay algorithm is developed as the supporting algorithm for SMINP to capture the delays caused by the interactions between vehicle queues and buses entering and exiting near-side bus stops. A concept of using signal timing deviations to approximate the impacts of TSP operations on other traffic is proposed for the first time in this research. In the second part of the research, the deterministic version of the SMINP model is extended to the arterial setting, where a route-based TSP (R-TSP) model is develop to optimize for schedule-related bus performances on the corridor level. The R-TSP model uses the real-time data available only from the connected vehicle communications technology. Based on the connected vehicle technology, a real-time signal control system that implements the proposed TSP models is prototyped in the simulation environment. The connected vehicle technology is also used as the main detection and monitoring mechanism for the real-time control of the adaptive TSP signal system. The adaptive TSP control module is designed as a plug-in module that is envisioned to work with a modern fixed-time or adaptive signal controller with connected vehicle communications capabilities. Using this TSP-enabled signal control system, simulation studies were carried out in both a single intersection setting and a five-intersection arterial setting. The effectiveness of the SMINP model to handle uncertain bus arrival time and the R-TSP model to achieve corridor-level bus schedule reliability were studied. Discussions, conclusions and future research on the topic of adaptive TSP models were made.Item Mathematical Programming Formulations for the Optimal Placement of Imperfect Detectors with Applications to Flammable Gas Detection and Mitigation Systems(2014-11-13) Benavides Serrano, Alberto J.The placement of detectors in mitigation systems is a difficult problem usually addressed in the industry via qualitative and semiquantative approaches. Simplifications are used to circumvent difficulties regarding problem size, parameter uncertainty, and lack of information concerning leak development. Given recent improvement of consequence modeling tools, the use of a stochastic Mixed-Integer Linear Programming (MILP) formulation (SP) was previously proposed to quantitatively approach this problem. This formulation minimizes the expected damage over a large set of gas leak scenarios while assuming perfect detectors. In reality gas detectors are prone to false positives and false negatives. Two solutions are usually implemented in the process industries. First, additional confirmation from several detectors (i.e., voting) is required before emergency actions are triggered in order to avoid false positives. Second, in order to avoid false negatives, the unavailability of the detectors is considered in the placement strategy. Unavailability corresponds to the probability that the detector will not be able to perform its intended function when required. In the first part of this dissertation, two problem formulations were developed and validated to address the issue of imperfect detectors: minimization of expected damage considering unavailability (SP-U) and minimization of the expected damage considering unavailability and voting (SP-UV). SP-U and SP-UV placement results were compared with those obtained assuming perfect detectors. Results demonstrate that explicit consideration of unavailability and voting effects alters the final detector placement. Quantitative risk can be significantly higher if we neglect these issues when solving for the optimal placement. Furthermore, SP-UV placement results were compared with those of four existing approaches for gas detector placement using three different performance metrics in accordance to the objectives of gas detection systems. Results provide further evidence on the effectiveness of the use of dispersion simulations, and mathematical programming, to supplement the gas detector placement problem. Formulation SP-U assumes a uniform unavailability across all detector types and locations. In the second part of this work, this assumption is relaxed via formulation SPqt, which considers non-uniform dynamic detector unavailabilities. Relaxing this assumption results in a Mixed-Integer NonLinear Programming (MINLP) formulation. SPqt, being an extension of SP-U, explicitly considers di?erent backup detection levels, allowing an approximation where the maximum degree of the nonlinear products considered can be determined by the modeler. The effect of reducing the number of detection levels was analyzed. For the problem, results shown that two detection levels are sufficient to find objective values within 1% of the optimal solution. Considering two detection levels reduces the MINLP formulation to a zero-one quadratic formulation (SPqt-Q). A solution quality comparison between SPqt-Q and approximate solution strategies previously proposed in the literature demonstrates its suitability to obtain approximate answers for the general nonlinear problem. Two exact linear reformulation strategies (SPqt-L1 and SPqt-L2) were proposed for SPqt-Q and validated from the computationally efficiency perspective. All the results presented were obtained by using four real data sets provided by Gex-Con. The data corresponds to FLACS CFD dispersion simulations including the full geometric features of an offshore facility and capturing the uncertainty in the leak characteristics. Additionally, real unavailability values were obtained from industry gas detector reliability databases. The work presented here constitutes a step forward toward the achievement of a realistic detector placement formulation that includes current industrial practice for these important safety systems.Item Stochastic Programming Approach to Hydraulic Fracture Design for the Lower Tertiary Gulf of Mexico(2013-07-27) Podhoretz, SethIn this work, we present methodologies for optimization of hydraulic fracturing design under uncertainty specifically with reference to the thick and anisotropic reservoirs in the Lower Tertiary Gulf of Mexico. In this analysis we apply a stochastic programming framework for optimization under uncertainty and apply a utility framework for risk analysis. For a vertical well, we developed a methodology for making the strategic decisions regarding number and dimensions of hydraulic fractures in a high-cost, high-risk offshore development. Uncertainty is associated with the characteristics of the reservoir, the economics of the fracturing cost, and the fracture height growth. The method developed is applicable to vertical wells with multiple, partially penetrating fractures in an anisotropic formation. The method applies the utility framework to account for financial risk. For a horizontal well, we developed a methodology for making the strategic decisions regarding lateral length, number and dimensions of transverse hydraulic fractures in a high-cost, high-risk offshore development, under uncertainty associated with the characteristics of the reservoir. The problem is formulated as a mixed-integer, nonlinear, stochastic program and solved by a tailored Branch and Bound algorithm. The method developed is applicable to partially penetrating horizontal wells with multiple, partially penetrating fractures in an anisotropic formation.Item Stochastic Programming Approaches for the Placement of Gas Detectors in Process Facilities(2013-05-21) Legg, Sean WThe release of flammable and toxic chemicals in petrochemical facilities is a major concern when designing modern process safety systems. While the proper selection of the necessary types of gas detectors needed is important, appropriate placement of these detectors is required in order to have a well-functioning gas detection system. However, the uncertainty in leak locations, gas composition, process and weather conditions, and process geometries must all be considered when attempting to determine the appropriate number and placement of the gas detectors. Because traditional approaches are typically based on heuristics, there exists the need to develop more rigorous optimization based approaches to handling this problem. This work presents several mixed-integer programming formulations to address this need. First, a general mixed-integer linear programming problem is presented. This formulation takes advantage of precomputed computational fluid dynamics (CFD) simulations to determine a gas detector placement that minimizes the expected detection time across all scenarios. An extension to this formulation is added that considers the overall coverage in a facility in order to improve the detector placement when enough scenarios may not be available. Additionally, a formulation considering the Conditional-Value-at-Risk is also presented. This formulation provides some control over the shape of the tail of the distribution, not only minimizing the expected detection time across all scenarios, but also improving the tail behavior. In addition to improved formulations, procedures are introduced to determine confidence in the placement generated and to determine if enough scenarios have been used in determining the gas detector placement. First, a procedure is introduced to analyze the performance of the proposed gas detector placement in the face of ?unforeseen? scenarios, or scenarios that were not necessarily included in the original formulation. Additionally, a procedure for determine the confidence interval on the optimality gap between a placement generated with a sample of scenarios and its estimated performance on the entire uncertainty space. Finally, a method for determining if enough scenarios have been used and how much additional benefit is expected by adding more scenarios to the optimization is proposed. Results are presented for each of the formulations and methods presented using three data sets from an actual process facility. The use of an off-the-shelf toolkit for the placement of detectors in municipal water networks from the EPA, known as TEVA-SPOT, is explored. Because this toolkit was not designed for placing gas detectors, some adaptation of the files is necessary, and the procedure for doing so is presented.