+publisher:"University of Arizona" +contributor:("Bayraksan, Guzin")

University of Arizona

1. Love, David Keith. Data-Driven Methods for Optimization Under Uncertainty with Application to Water Allocation .

Degree: 2013, University of Arizona

► Stochastic programming is a mathematical technique for decision making under uncertainty using probabilistic statements in the problem objective and constraints. In practice, the distribution of… (more)

▼ Stochastic programming is a mathematical technique for decision making under uncertainty using probabilistic statements in the problem objective and constraints. In practice, the distribution of the unknown quantities are often known only through observed or simulated data. This dissertation discusses several methods of using this data to formulate, solve, and evaluate the quality of solutions of stochastic programs. The central contribution of this dissertation is to investigate the use of techniques from simulation and statistics to enable data-driven models and methods for stochastic programming. We begin by extending the method of overlapping batches from simulation to assessing solution quality in stochastic programming. The Multiple Replications Procedure, where multiple stochastic programs are solved using independent batches of samples, has previously been used for assessing solution quality. The Overlapping Multiple Replications Procedure overlaps the batches, thus losing the independence between samples, but reducing the variance of the estimator without affecting its bias. We provide conditions under which the optimality gap estimators are consistent, the variance reduction benefits are obtained, and give a computational illustration of the small-sample behavior. Our second result explores the use of phi-divergences for distributionally robust optimization, also known as ambiguous stochastic programming. The phi-divergences provide a method of measuring distance between probability distributions, are widely used in statistical inference and information theory, and have recently been proposed to formulate data-driven stochastic programs. We provide a novel classification of phi-divergences for stochastic programming and give recommendations for their use. A value of data condition is derived and the asymptotic behavior of the phi-divergence constrained stochastic program is described. Then a decomposition-based solution method is proposed to solve problems computationally. The final portion of this dissertation applies the phi-divergence method to a problem of water allocation in a developing region of Tucson, AZ. In this application, we integrate several sources of uncertainty into a single model, including (1) future population growth in the region, (2) amount of water available from the Colorado River, and (3) the effects of climate variability on water demand. Estimates of the frequency and severity of future water shortages are given and we evaluate the effectiveness of several infrastructure options. Advisors/Committee Members: Bayraksan, Guzin (advisor), Bayraksan, Guzin (committeemember), Brio, Moysey (committeemember), Kennedy, Thomas (committeemember), Son, Young-Jun (committeemember).

Subjects/Keywords: overlapping batches; phi divergence; Stochastic programming; water allocation; Applied Mathematics; Distributionally robust optimization

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Love, D. K. (2013). Data-Driven Methods for Optimization Under Uncertainty with Application to Water Allocation . (Doctoral Dissertation). University of Arizona. Retrieved from http://hdl.handle.net/10150/311177

Chicago Manual of Style (16^th Edition):

Love, David Keith. “Data-Driven Methods for Optimization Under Uncertainty with Application to Water Allocation .” 2013. Doctoral Dissertation, University of Arizona. Accessed December 07, 2019. http://hdl.handle.net/10150/311177.

MLA Handbook (7^th Edition):

Love, David Keith. “Data-Driven Methods for Optimization Under Uncertainty with Application to Water Allocation .” 2013. Web. 07 Dec 2019.

Vancouver:

Love DK. Data-Driven Methods for Optimization Under Uncertainty with Application to Water Allocation . [Internet] [Doctoral dissertation]. University of Arizona; 2013. [cited 2019 Dec 07]. Available from: http://hdl.handle.net/10150/311177.

Council of Science Editors:

Love DK. Data-Driven Methods for Optimization Under Uncertainty with Application to Water Allocation . [Doctoral Dissertation]. University of Arizona; 2013. Available from: http://hdl.handle.net/10150/311177

University of Arizona

2. Zhang, Weini. Water Network Design and Management via Stochastic Programming .

Degree: 2013, University of Arizona

URL: http://hdl.handle.net/10150/311556

► Water is an essential natural resource for life and economic activities. Water resources management is facing major challenges due to increasing demands caused by population… (more)

▼ Water is an essential natural resource for life and economic activities. Water resources management is facing major challenges due to increasing demands caused by population growth, increased industrial and agricultural use, and depletion of fresh water sources around the world. In addition to putting stress on our civilization, factors such as water supply availability, spatial population changes, industrial growth, etc. are all sources of major uncertainty in water resources management. There are also uncertainties regarding climate variability and how it affects both water demands and supplies. Stochastic programming is a mathematical tool to help make decisions under uncertainty that models the uncertain parameters using probability distributions and incorporates probabilistic statements in mathematical optimization. This dissertation applies stochastic programming to water resources management. In particular, we focus on reclaimed water distribution network design to effectively reuse water in a municipal system and a water allocation problem in an integrated water system under uncertainty. We first present a two-stage stochastic integer program with recourse for cost- effective reclaimed water network design. Unlike other formulations, uncertain demands, temporal, and spatial population changes are explicitly considered in our model. Selection of pipe and pump sizes are modeled using binary variables in order to linearize the nonlinear hydraulic equations and objective function terms. We then develop preprocessing methods to significantly reduce the problem dimension by exploiting the problem characteristics and network structure. We analyze the sensitivity of the network design under varying model parameters, present computational results, and discuss when the stochastic solution is most valuable. Next, we investigate the use of risk-averse approach in water resources management using the so-called conditional value-at-risk as a risk measure. We develop a multistage risk-averse stochastic program with recourse for long-term water allocation under uncertain demands and water supply variability. We propose a specialized decomposition-based algorithm to solve multistage risk-averse stochastic programs, and present both the single-cut and the multicut version of the algorithm. We then compare the solution methodologies with different ways of decomposing the resulting problem. We solve the multistage risk-averse water allocation problem with different risk aversion levels and model assumptions, present computational results to demonstrate the potential benefits of risk-averse approach, and provide a guideline for risk aversion level selection. Advisors/Committee Members: Bayraksan, Guzin (advisor), Bayraksan, Guzin (committeemember), Lansey, Kevin (committeemember), Liu, Jian (committeemember).

Subjects/Keywords: Systems & Industrial Engineering

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Zhang, W. (2013). Water Network Design and Management via Stochastic Programming . (Doctoral Dissertation). University of Arizona. Retrieved from http://hdl.handle.net/10150/311556

Chicago Manual of Style (16^th Edition):

Zhang, Weini. “Water Network Design and Management via Stochastic Programming .” 2013. Doctoral Dissertation, University of Arizona. Accessed December 07, 2019. http://hdl.handle.net/10150/311556.

MLA Handbook (7^th Edition):

Zhang, Weini. “Water Network Design and Management via Stochastic Programming .” 2013. Web. 07 Dec 2019.

Vancouver:

Zhang W. Water Network Design and Management via Stochastic Programming . [Internet] [Doctoral dissertation]. University of Arizona; 2013. [cited 2019 Dec 07]. Available from: http://hdl.handle.net/10150/311556.

Council of Science Editors:

Zhang W. Water Network Design and Management via Stochastic Programming . [Doctoral Dissertation]. University of Arizona; 2013. Available from: http://hdl.handle.net/10150/311556

University of Arizona

3. Zhou, Zhihong. Multistage Stochastic Decomposition and its Applications .

Degree: 2012, University of Arizona

URL: http://hdl.handle.net/10150/222892

► In this dissertation, we focus on developing sampling-based algorithms for solving stochastic linear programs. The work covers both two stage and multistage versions of stochastic… (more)

▼ In this dissertation, we focus on developing sampling-based algorithms for solving stochastic linear programs. The work covers both two stage and multistage versions of stochastic linear programs. In particular, we first study the two stage stochastic decomposition (SD) algorithm and present some extensions associated with SD. Specifically, we study two issues: a) are there conditions under which the regularized version of SD generates a unique solution? and b) in cases where a user is willing to sacrifice optimality, is there a way to modify the SD algorithm so that a user can trade-off solution times with solution quality? Moreover, we present our preliminary approach to address these questions. Secondly, we investigate the multistage stochastic linear programs and propose a new approach to solving multistage stochastic decision models in the presence of constraints. The motivation for proposing the multistage stochastic decomposition algorithm is to handle large scale multistage stochastic linear programs. In our setting, the deterministic equivalent problems of the multistage stochastic linear program are too large to be solved exactly. Therefore, we seek an asymptotically optimum solution by simulating the SD algorithmic process, which was originally designed for two-stage stochastic linear programs (SLPs). More importantly, when SD is implemented in a time-staged manner, the algorithm begins to take the flavor of a simulation leading to what we refer to as optimization simulation. As for multistage stochastic decomposition, there are a couple of advantages that deserve mention. One of the benefits is that it can work directly with sample paths, and this feature makes the new algorithm much easier to be integrated within a simulation. Moreover, compared with other sampling-based algorithms for multistage stochastic programming, we also overcome certain limitations, such as a stage-wise independence assumption. Advisors/Committee Members: Sen, Suvrajeet (advisor), Bayraksan, Guzin (advisor), Son, Young Jun (committeemember), Lin, Wei Hua (committeemember), Sen, Suvrajeet (committeemember), Bayraksan, Guzin (committeemember).

Subjects/Keywords: Optimization Simulation; Stage-wise Independence; Stochastic Decomposition; Stochastic Dual Dynamic Programming; Systems & Industrial Engineering; Multistage Stochastic Decomposition; Multistage Stochastic Program

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Zhou, Z. (2012). Multistage Stochastic Decomposition and its Applications . (Doctoral Dissertation). University of Arizona. Retrieved from http://hdl.handle.net/10150/222892

Chicago Manual of Style (16^th Edition):

Zhou, Zhihong. “Multistage Stochastic Decomposition and its Applications .” 2012. Doctoral Dissertation, University of Arizona. Accessed December 07, 2019. http://hdl.handle.net/10150/222892.

MLA Handbook (7^th Edition):

Zhou, Zhihong. “Multistage Stochastic Decomposition and its Applications .” 2012. Web. 07 Dec 2019.

Vancouver:

Zhou Z. Multistage Stochastic Decomposition and its Applications . [Internet] [Doctoral dissertation]. University of Arizona; 2012. [cited 2019 Dec 07]. Available from: http://hdl.handle.net/10150/222892.

Council of Science Editors:

Zhou Z. Multistage Stochastic Decomposition and its Applications . [Doctoral Dissertation]. University of Arizona; 2012. Available from: http://hdl.handle.net/10150/222892

University of Arizona

4. Basudhar, Anirban. Computational Optimal Design and Uncertainty Quantification of Complex Systems Using Explicit Decision Boundaries .

Degree: 2011, University of Arizona

URL: http://hdl.handle.net/10150/201491

► This dissertation presents a sampling-based method that can be used for uncertainty quantification and deterministic or probabilistic optimization. The objective is to simultaneously address several… (more)

▼ This dissertation presents a sampling-based method that can be used for uncertainty quantification and deterministic or probabilistic optimization. The objective is to simultaneously address several difficulties faced by classical techniques based on response values and their gradients. In particular, this research addresses issues with discontinuous and binary (pass or fail) responses, and multiple failure modes. All methods in this research are developed with the aim of addressing problems that have limited data due to high cost of computation or experiment, e.g. vehicle crashworthiness, fluid-structure interaction etc.The core idea of this research is to construct an explicit boundary separating allowable and unallowable behaviors, based on classification information of responses instead of their actual values. As a result, the proposed method is naturally suited to handle discontinuities and binary states. A machine learning technique referred to as support vector machines (SVMs) is used to construct the explicit boundaries. SVM boundaries can be highly nonlinear, which allows one to use a single SVM for representing multiple failure modes.One of the major concerns in the design and uncertainty quantification communities is to reduce computational costs. To address this issue, several adaptive sampling methods have been developed as part of this dissertation. Specific sampling methods have been developed for reliability assessment, deterministic optimization, and reliability-based design optimization. Adaptive sampling allows the construction of accurate SVMs with limited samples. However, like any approximation method, construction of SVM is subject to errors. A new method to quantify the prediction error of SVMs, based on probabilistic support vector machines (PSVMs) is also developed. It is used to provide a relatively conservative probability of failure to mitigate some of the adverse effects of an inaccurate SVM. In the context of reliability assessment, the proposed method is presented for uncertainties represented by random variables as well as spatially varying random fields.In order to validate the developed methods, analytical problems with known solutions are used. In addition, the approach is applied to some application problems, such as structural impact and tolerance optimization, to demonstrate its strengths in the context of discontinuous responses and multiple failure modes. Advisors/Committee Members: Missoum, Samy (advisor), Missoum, Samy (committeemember), Nikravesh, Parvis (committeemember), Haldar, Achintya (committeemember), Bayraksan, Guzin (committeemember).

Subjects/Keywords: explicit decision boundaries; multiple failure modes; reliability based design optimization; support vector machines; Mechanical Engineering; adaptive sampling; discontinuous and binary responses

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Basudhar, A. (2011). Computational Optimal Design and Uncertainty Quantification of Complex Systems Using Explicit Decision Boundaries . (Doctoral Dissertation). University of Arizona. Retrieved from http://hdl.handle.net/10150/201491

Chicago Manual of Style (16^th Edition):

Basudhar, Anirban. “Computational Optimal Design and Uncertainty Quantification of Complex Systems Using Explicit Decision Boundaries .” 2011. Doctoral Dissertation, University of Arizona. Accessed December 07, 2019. http://hdl.handle.net/10150/201491.

MLA Handbook (7^th Edition):

Basudhar, Anirban. “Computational Optimal Design and Uncertainty Quantification of Complex Systems Using Explicit Decision Boundaries .” 2011. Web. 07 Dec 2019.

Vancouver:

Basudhar A. Computational Optimal Design and Uncertainty Quantification of Complex Systems Using Explicit Decision Boundaries . [Internet] [Doctoral dissertation]. University of Arizona; 2011. [cited 2019 Dec 07]. Available from: http://hdl.handle.net/10150/201491.

Council of Science Editors:

Basudhar A. Computational Optimal Design and Uncertainty Quantification of Complex Systems Using Explicit Decision Boundaries . [Doctoral Dissertation]. University of Arizona; 2011. Available from: http://hdl.handle.net/10150/201491

University of Arizona

5. Celik, Nurcin. INTEGRATED DECISION MAKING FOR PLANNING AND CONTROL OF DISTRIBUTED MANUFACTURING ENTERPRISES USING DYNAMIC-DATA-DRIVEN ADAPTIVE MULTI-SCALE SIMULATIONS (DDDAMS) .

Degree: 2010, University of Arizona

URL: http://hdl.handle.net/10150/195427

► Discrete-event simulation has become one of the most widely used analysis tools for large-scale, complex and dynamic systems such as supply chains as it can… (more)

▼ Discrete-event simulation has become one of the most widely used analysis tools for large-scale, complex and dynamic systems such as supply chains as it can take randomness into account and address very detailed models. However, there are major challenges that are faced in simulating such systems, especially when they are used to support short-term decisions (e.g., operational decisions or maintenance and scheduling decisions considered in this research). First, a detailed simulation requires significant amounts of computation time. Second, given the enormous amount of dynamically-changing data that exists in the system, information needs to be updated wisely in the model in order to prevent unnecessary usage of computing and networking resources. Third, there is a lack of methods allowing dynamic data updates during the simulation execution. Overall, in a simulation-based planning and control framework, timely monitoring, analysis, and control is important not to disrupt a dynamically changing system. To meet this temporal requirement and address the above mentioned challenges, a Dynamic-Data-Driven Adaptive Multi-Scale Simulation (DDDAMS) paradigm is proposed to adaptively adjust the fidelity of a simulation model against available computational resources by incorporating dynamic data into the executing model, which then steers the measurement process for selective data update. To the best of our knowledge, the proposed DDDAMS methodology is one of the first efforts to present a coherent integrated decision making framework for timely planning and control of distributed manufacturing enterprises.To this end, comprehensive system architecture and methodologies are first proposed, where the components include 1) real time DDDAM-Simulation, 2) grid computing modules, 3) Web Service communication server, 4) database, 5) various sensors, and 6) real system. Four algorithms are then developed and embedded into a real-time simulator for enabling its DDDAMS capabilities such as abnormality detection, fidelity selection, fidelity assignment, and prediction and task generation. As part of the developed algorithms, improvements are made to the resampling techniques for sequential Bayesian inferencing, and their performance is benchmarked in terms of their resampling qualities and computational efficiencies. Grid computing and Web Services are used for computational resources management and inter-operable communications among distributed software components, respectively. A prototype of proposed DDDAM-Simulation was successfully implemented for preventive maintenance scheduling and part routing scheduling in a semiconductor manufacturing supply chain, where the results look quite promising. Advisors/Committee Members: Son, Young-Jun (advisor), Son, Young-Jun (committeemember), Szidarovszky, Ferenc (committeemember), Bayraksan, Guzin (committeemember), Ram, Sudha (committeemember).

Subjects/Keywords: Adaptive simulations; Distributed simulation; Dynamic data driven simulations; Particle filtering; Resampling rules; Simulation-based control

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Celik, N. (2010). INTEGRATED DECISION MAKING FOR PLANNING AND CONTROL OF DISTRIBUTED MANUFACTURING ENTERPRISES USING DYNAMIC-DATA-DRIVEN ADAPTIVE MULTI-SCALE SIMULATIONS (DDDAMS) . (Doctoral Dissertation). University of Arizona. Retrieved from http://hdl.handle.net/10150/195427

Chicago Manual of Style (16^th Edition):

Celik, Nurcin. “INTEGRATED DECISION MAKING FOR PLANNING AND CONTROL OF DISTRIBUTED MANUFACTURING ENTERPRISES USING DYNAMIC-DATA-DRIVEN ADAPTIVE MULTI-SCALE SIMULATIONS (DDDAMS) .” 2010. Doctoral Dissertation, University of Arizona. Accessed December 07, 2019. http://hdl.handle.net/10150/195427.

MLA Handbook (7^th Edition):

Celik, Nurcin. “INTEGRATED DECISION MAKING FOR PLANNING AND CONTROL OF DISTRIBUTED MANUFACTURING ENTERPRISES USING DYNAMIC-DATA-DRIVEN ADAPTIVE MULTI-SCALE SIMULATIONS (DDDAMS) .” 2010. Web. 07 Dec 2019.

Vancouver:

Celik N. INTEGRATED DECISION MAKING FOR PLANNING AND CONTROL OF DISTRIBUTED MANUFACTURING ENTERPRISES USING DYNAMIC-DATA-DRIVEN ADAPTIVE MULTI-SCALE SIMULATIONS (DDDAMS) . [Internet] [Doctoral dissertation]. University of Arizona; 2010. [cited 2019 Dec 07]. Available from: http://hdl.handle.net/10150/195427.

Council of Science Editors:

Celik N. INTEGRATED DECISION MAKING FOR PLANNING AND CONTROL OF DISTRIBUTED MANUFACTURING ENTERPRISES USING DYNAMIC-DATA-DRIVEN ADAPTIVE MULTI-SCALE SIMULATIONS (DDDAMS) . [Doctoral Dissertation]. University of Arizona; 2010. Available from: http://hdl.handle.net/10150/195427

University of Arizona

6. Keller, Brian. Models and Methods for Multiple Resource Constrained Job Scheduling under Uncertainty .

Degree: 2009, University of Arizona

URL: http://hdl.handle.net/10150/193630

► We consider a scheduling problem where each job requires multiple classes of resources, which we refer to as the multiple resource constrained scheduling problem(MRCSP). Potential… (more)

▼ We consider a scheduling problem where each job requires multiple classes of resources, which we refer to as the multiple resource constrained scheduling problem(MRCSP). Potential applications include team scheduling problems that arise in service industries such as consulting and operating room scheduling. We focus on two general cases of the problem. The first case considers uncertainty of processing times, due dates, and resource availabilities consumption, which we denote as the stochastic MRCSP with uncertain parameters (SMRCSP-U). The second case considers uncertainty in the number of jobs to schedule, which arises in consulting and defense contracting when companies bid on future contracts but may or may not win the bid. We call this problem the stochastic MRCSP with job bidding (SMRCSP-JB).We first provide formulations of each problem under the framework of two-stage stochastic programming with recourse. We then develop solution methodologies for both problems. For the SMRCSP-U, we develop an exact solution method based on the L-shaped method for problems with a moderate number of scenarios. Several algorithmic enhancements are added to improve efficiency. Then, we embed the L-shaped method within a sampling-based solution method for problems with a large number of scenarios. We modify a sequential sampling procedure to allowfor approximate solution of integer programs and prove desired properties. The sampling-based method is applicable to two-stage stochastic integer programs with integer first-stage variables. Finally, we compare the solution methodologies on a set of test problems.For SMRCSP-JB, we utilize the disjunctive decomposition (D2 ) algorithm for stochastic integer programs with mixed-binary subproblems. We develop several enhancements to the D2 algorithm. First, we explore the use of a cut generation problem restricted to a subspace of the variables, which yields significant computational savings. Then, we examine generating alternative disjunctive cuts based on the generalized upper bound (GUB) constraints that appear in the second-stage of the SMRCSP-JB. We establish convergence of all D2 variants and present computational results on a set of instances of SMRCSP-JB. Advisors/Committee Members: Bayraksan, Guzin (advisor), Head, Larry (committeemember), Kucukyavuz, Simge (committeemember), Baker, Ken (committeemember).

Subjects/Keywords: disjunctive decomposition; sampling; stochastic integer programming; stochastic scheduling

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Keller, B. (2009). Models and Methods for Multiple Resource Constrained Job Scheduling under Uncertainty . (Doctoral Dissertation). University of Arizona. Retrieved from http://hdl.handle.net/10150/193630

Chicago Manual of Style (16^th Edition):

Keller, Brian. “Models and Methods for Multiple Resource Constrained Job Scheduling under Uncertainty .” 2009. Doctoral Dissertation, University of Arizona. Accessed December 07, 2019. http://hdl.handle.net/10150/193630.

MLA Handbook (7^th Edition):

Keller, Brian. “Models and Methods for Multiple Resource Constrained Job Scheduling under Uncertainty .” 2009. Web. 07 Dec 2019.

Vancouver:

Keller B. Models and Methods for Multiple Resource Constrained Job Scheduling under Uncertainty . [Internet] [Doctoral dissertation]. University of Arizona; 2009. [cited 2019 Dec 07]. Available from: http://hdl.handle.net/10150/193630.

Council of Science Editors:

Keller B. Models and Methods for Multiple Resource Constrained Job Scheduling under Uncertainty . [Doctoral Dissertation]. University of Arizona; 2009. Available from: http://hdl.handle.net/10150/193630

University of Arizona

7. Reich, Daniel. Stochastic Networks: Tractable Approaches for Identifying Strategic Paths .

Degree: 2009, University of Arizona

URL: http://hdl.handle.net/10150/194439

► In Chapter 1, we present a stochastic shortest path problem that we refer to as the Most Likely Path Problem (MLPP). We prove that optimal… (more)

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Reich, D. (2009). Stochastic Networks: Tractable Approaches for Identifying Strategic Paths . (Doctoral Dissertation). University of Arizona. Retrieved from http://hdl.handle.net/10150/194439

Chicago Manual of Style (16^th Edition):

Reich, Daniel. “Stochastic Networks: Tractable Approaches for Identifying Strategic Paths .” 2009. Doctoral Dissertation, University of Arizona. Accessed December 07, 2019. http://hdl.handle.net/10150/194439.

MLA Handbook (7^th Edition):

Reich, Daniel. “Stochastic Networks: Tractable Approaches for Identifying Strategic Paths .” 2009. Web. 07 Dec 2019.

Vancouver:

Reich D. Stochastic Networks: Tractable Approaches for Identifying Strategic Paths . [Internet] [Doctoral dissertation]. University of Arizona; 2009. [cited 2019 Dec 07]. Available from: http://hdl.handle.net/10150/194439.

Council of Science Editors:

Reich D. Stochastic Networks: Tractable Approaches for Identifying Strategic Paths . [Doctoral Dissertation]. University of Arizona; 2009. Available from: http://hdl.handle.net/10150/194439

		in
And / Or
		in
And / Or
		in
And / Or
		in

Open Access Theses and Dissertations