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Deterministic approximations in stochastic programming with applications to a class of portfolio allocation problemsDokov, Steftcho Pentchev 09 March 2011 (has links)
Not available / text

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Task Optimization and Workforce SchedulingShateri, Mahsa 31 August 2011 (has links)
This thesis focuses on task sequencing and manpower scheduling to develop robust schedules for an aircraft manufacturer. The production of an aircraft goes through a series of multiple workstations, each consisting of a large number of interactive tasks and a limited number of working zones. The duration of each task varies from operator to operator, because most operations are performed manually. These factors limit the ability of managers to balance, optimize, and change the statement of work in each workstation. In addition, engineers spend considerable amount of time to manually develop schedules that may be incompatible with the changes in the production rate.
To address the above problems, the current state of work centers are first analyzed. Then, several deterministic mathematical programming models are developed to minimize the total production labour cost for a target cycle time. The mathematical models seek to find optimal schedules by eliminating and/or considering the effect of overtime on the production cost. The resulting schedules decrease the required number of operators by 16% and reduce production cycle time of work centers by 53% to 67%. Using these models, the time needed to develop a schedule is reduced from 36 days to less than a day.
To handle the stochasticity of the task durations, a twostage stochastic programming model is developed to minimize the total production labour cost and to find the number of operators that are able to work under every scenario. The solution of the twostage stochastic programming model finds the same number of operators as that of the deterministic models, but reduces the time to adjust production schedules by 88%.

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Statistical modeling of the value function in highdimensional, continuousstate SDPTsai, Julia ChiaChieh 08 1900 (has links)
No description available.

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Behavior of forkjoin networks, and effect of variability in service systemsKo, SungSeok 08 1900 (has links)
No description available.

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Simulationbased methods for stochastic optimizationHomem de Mello, Tito 08 1900 (has links)
No description available.

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Approximate method for solving twostage stochastic programming and its application to the groundwater managementWang, Maili. January 1999 (has links)
Stochastic twostage programming, a main branch of stochastic programming, offers models and methods to find the optimal objective function and decision variables under uncertainty. This dissertation is concerned with developing an approximate procedure to solve the stochastic twostage programming problem and applying it in relative field. Five methods used in evaluating the expected value of function for distribution problem are discussed and their basic characteristics and performances are compared to choose the most effective approach for use in a twostage program. Then the stochastic twostage programming solving method has been established with the combination of a genetic algorithm (GA) and point estimation (PE) procedure. This approach avoids the inherent limitations of other methods by using PE to estimate the expected value of recourse function and the GA to search optimal solution of the problem. To extend the advantage of GA the modified genetic algorithm (MGA) is built to improve the performance of GA. Finally, the whole procedure is used in several examples with different kinds of variable and linear or nonlinear style objective functions. A stochastic twostage programming model for an aquifer management problem is set up with considering conductivity and local random recharge as the source of uncertainty in the system. The designed procedure includes the response matrix process that replaces the partial differential flow equation, Girinski potential process and a presetup process that makes the response matrix process application in general aquifer random field possible. Other chosen problems are solved with designed approach to illustrate the effects of uncertainty source in the stochastic programming model and compared with results with ones given in literatures.

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Stochastic programming for hydrothermal unit commitmentSchulze, Tim January 2015 (has links)
In recent years the deregulation of energy markets and expansion of volatile renewable energy supplies has triggered an increased interest in stochastic optimization models for thermal and hydrothermal scheduling. Several studies have modelled this as stochastic linear or mixedinteger optimization problems. Although a variety of efficient solution techniques have been developed for these models, little is published about the added value of stochastic models over deterministic ones. In the context of dayahead and intraday unit commitment under wind uncertainty, we compare twostage and multistage stochastic models to deterministic ones and quantify their added value. We show that stochastic optimization models achieve minimal operational cost without having to tune reserve margins in advance, and that their superiority over deterministic models grows with the amount of uncertainty in the relevant wind forecasts. We present a modification of the WILMAR scenario generation technique designed to match the properties of the errors in our wind forcasts, and show that this is needed to make the stochastic approach worthwhile. Our evaluation is done in a rolling horizon fashion over the course of two years, using a 2020 central scheduling model of the British National Grid with transmission constraints and a detailed model of pump storage operation and systemwide reserve and response provision. Solving stochastic problems directly is computationally intractable for large instances, and alternative approaches are required. In this study we use a DantzigWolfe reformulation to decompose the problem by scenarios. We derive and implement a column generation method with dual stabilisation and novel primal and dual initialisation techniques. A fast, novel schedule combination heuristic is used to construct an optimal primal solution, and numerical results show that knowing this solution from the start also improves the convergence of the lower bound in the column generation method significantly. We test this method on instances of our British model and illustrate that convergence to within 0.1% of optimality can be achieved quickly.

38 
Essays on bounding stochastic programming problemsEdirisinghe, Nalin Chanaka Perera January 1991 (has links)
Many planning problems involve choosing a set of optimal decisions for a system in the face of uncertainty of elements that may play a central role in the way the system is analyzed and operated. During the past decade, there has been a renewed interest in the modelling, analysis, and solution of such problems due to a remarkable development of both new theoretical results and novel computational techniques in stochastic optimization. A prominent approach is to develop upper and lower bounding approximations to the problem along with procedures to sharpen bounds until an acceptable tolerance is satisfied. The contributions of this dissertation are concerned with the latter approach.
The thesis first studies the stochastic linear programming problem with randomness in both the objective coefficients and the constraints. A convexconcave saddle property of the value function is utilized to derive new bounding techniques which generalize previously known results. These approximations require discretizing bounded domains of the random variables in such a way that tight upper and lower bounds result. Such techniques will prove attractive with the recent advances in largescale linear programming.
The above results are also extended to obtain new upper and lower bounds when the domains of random variables are unbounded. While these bounds are tight, the approximating models are largescale deterministic linear programs. In particular, with a proposed ordercone decomposition for the domains, these linear programs are wellstructured, thus enabling one to use efficient techniques for solution, such as parallel computation.
The thesis next considers convex stochastic programs. Using aggregation concepts from the deterministic literature, new bounds are developed for the problem which are
computable using standard convex programming algorithms. Finally, the discussion is focused on a stochastic convex program arising in a certain resource allocation problem. Exploiting the problem structure, bounds are developed via the KarushKuhnTucker conditions. Rather than discretizing domains, these approximations advocate replacing difficult multidimensional integrals by a series of simple univariate integrals. Such practice allows one to preserve differentiability properties so that smooth convex programming methods can be applied for solution. / Business, Sauder School of / Graduate

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Stochastic hub and spoke networksHult, Edward Eric January 2011 (has links)
Transportation systems such as mail, freight, passenger and even telecommunication systems most often employ a hub and spoke network structure since correctly designed they give a strong balance between high service quality and low costs resulting in an economically competitive operation. In addition, consumers are increasingly demanding fast and reliable transportation services, with services such as next day deliveries and fast business and pleasure trips becoming highly sought after. This makes finding an efficient design of a hub and spoke network of the utmost importance for any competing transportation company. However real life situations are complicated, dynamic and often require responses to many different fixed and random events. Therefore modeling the question of what is an optimal hub and spoke network structure and finding an optimal solution is very difficult. Due to this, many researchers and practitioners alike make several assumptions and simplifications on the behavior of such systems to allow mathematical models to be formulated and solved optimally or near optimally within a practical timeframe. Some assumptions and simplifications can however result in practically poor network design solutions being found. This thesis contributes to the research of hub and spoke networks by introducing new stochastic models and fast solution algorithms to help bridge the gap between theoretical solutions and designs that are useful in practice. Three main contributions are made in the thesis. First, in Chapter 2, a new formulation and solution algorithms are proposed to find exact solutions to a stochastic phub center problem. The stochastic phub center problem is about finding a network structure, where travel times on links are stochastic, which minimizes the longest path in the network to give fast delivery guarantees which will hold for some given probability. Second, in Chapter 3, the stochastic phub center problem is looked at using a new methodological approach which gives more realistic solutions to the network structures when applied to real life situations. In addition a new service model is proposed where volume of flow is also accounted for when considering the stochastic nature of travel times on links. Third, in Chapter 4, stochastic volume is considered to account for capacity constraints at hubs and, de facto, reduce the costs embedded in excessive hub volumes. Numerical experiments and results are conducted and reported for all models in all chapters which demonstrate the efficiency of the new proposed approaches.

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Twostage stochastic linear programming: Stochastic decomposition approaches.Yakowitz, Diana Schadl. January 1991 (has links)
Stochastic linear programming problems are linear programming problems for which one or more data elements are described by random variables. Twostage stochastic linear programming problems are problems in which a first stage decision is made before the random variables are observed. A second stage, or recourse decision, which varies with these observations compensates for any deficiencies which result from the earlier decision. Many applications areas including water resources, industrial management, economics and finance lead to twostage stochastic linear programs with recourse. In this dissertation, two algorithms for solving stochastic linear programming problems with recourse are developed and tested. The first is referred to as Quadratic Stochastic Decomposition (QSD). This algorithm is an enhanced version of the Stochastic Decomposition (SD) algorithm of Higle and Sen (1988). The enhancements were designed to increase the computational efficiency of the SD algorithm by introducing a quadratic proximal term in the master program objective function and altering the manner in which the recourse function approximations are updated. We show that every accumulation point of an easily identifiable subsequence of points generated by the algorithm are optimal solutions to the stochastic program with probability 1. The various combinations of the enhancements are empirically investigated in a computational experiment using operations research problems from the literature. The second algorithm is an SD based algorithm for solving a stochastic linear program in which the recourse problem appears in the constraint set. This algorithm involves the use of an exact penalty function in the master program. We find that under certain conditions every accumulation point of a sequence of points generated by the algorithm is an optimal solution to the recourse constrained stochastic program, with probability 1. This algorithm is tested on several operations research problems.

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