Thesis (Ph. D.)--Industrial & Systems Engineering, Georgia Institute of Technology, 2005. / Barnes, Earl, Committee Member ; Shapiro, Alex, Committee Member ; Realff, Matthew, Committee Member ; Al-Khayyal, Faiz, Committee Chair ; Ahmed, Shabbir, Committee Co-Chair. Includes bibliographical references.

Thesis (Ph. D. in Operations Research)--Naval Postgraduate School, March 2005. / Thesis Advisor(s): R. Kevin Wood, Moshe Kress. Includes bibliographical references (p. 91-93). Also available online.

Thesis (Ph. D.)--University of Texas at Austin, 2005. / Vita. Includes bibliographical references.

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 hydro-thermal scheduling. Several studies have modelled this as stochastic linear or mixed-integer 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 day-ahead and intraday unit commitment under wind uncertainty, we compare two-stage and multi-stage 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 system-wide 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 Dantzig-Wolfe 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.

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 p-hub center problem. The stochastic p-hub 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 p-hub 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.

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 convex-concave 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 large-scale 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 large-scale deterministic linear programs. In particular, with a proposed order-cone decomposition for the domains, these linear programs are well-structured, 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 Karush-Kuhn-Tucker 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

Since the 1990s, facing increasing competition and mass customization, many companies including Dell have chosen to adopt the assemble-to-order (ATO) model in order to increase products offering and reduce the life cycles of products. Inventory management is a key challenge for ATO systems, in particular determination of inventory replenishment levels without full demand information, component allocations based on available component inventories, and realizations of product demands. ATO systems are usually modeled as a two-stage stochastic integer program. However, such programs are typically hard to solve, especially for stochastic integer nonlinear programs used for the joint optimization. In this thesis, we describe two ATO models proposed by Ackay and Xu (2004) and by Huang (2014). Both models include a nonlinear term in the right hand side of the inventory availability constraints. We discuss the techniques used to linearize the original problem and to estimate the impact of the linearization. In addition, we investigate another key element of ATO systems called component commonality used to reduce inventory costs. An extensive literature review regarding component commonality is provided. / Thesis / Master of Science (MSc)

Runway systems at airports have been identified as a major source of delay in the aviation system and efficient runway operations are, therefore, important to maintain and/or increase the capacity of the entire aviation system. The goal of the airport runway scheduling problem is to schedule a set of aircraft and minimize a given objective while maintaining separation requirements and enforcing other operational constraints. Uncertain factors such as weather, surrounding traffic and pilot behavior affect when aircraft can be scheduled, and these factors need to be considered in planning models. In this thesis we propose two stochastic programs to address the stochastic airport runway scheduling problem and similarly structured machine scheduling problems. In the first part, we develop a two-stage stochastic integer programming model and analyze it by developing alternative formulations and solution methods. As part of our analysis, we first show that a restricted version of the stochastic runway scheduling problem is equivalent to a machine scheduling problem on a single machine with sequence dependent setup times and stochastic due dates. We then extend this restricted model by considering characteristics specific to the runway scheduling problem and present two different stochastic integer programming models. We derive some tight valid inequalities for these formulations, and we propose a solution methodology based on sample average approximation and Lagrangian based scenario decomposition. Realistic data sets are then used to perform a detailed computational study involving implementations and analyses of several different configurations of the models. The results from the computational tests indicate that practically implementable truncated versions of the proposed solution algorithm almost always produce very high quality solutions. In the second part, we propose a sampling based stochastic program for a general machine scheduling problem with similar characteristics as the airport runway scheduling problem. The sampling based approach allows us to capture more detailed aspects of the problem, such as taxiway operations crossing active runways. The model is based on the stochastic branch and bound algorithm with several enhancements to improve the computational performance. More specifically, we incorporate a method to dynamically update the sample sizes in various parts of the branching tree, effectively decreasing the runtime without worsening the solution quality. When applied to runway scheduling, the algorithm is able to produce schedules with makespans that are 5% to 7% shorter than those obtained by optimal deterministic methods. Additional contributions in this thesis include the development of a global cost function, capturing all relevant costs in airport runway scheduling and trading off different, sometimes conflicting, objectives. We also analyze the impact of including environmental factors in the scheduling process.

Diplomová práce se zabývá stochastickým programováním a jeho aplikací na problém mísení kameniva z oblasti stavebního inženýrství. Teoretická část práce je věnována odvození základních přístupů stochastického programování, tj. optimalizace se zohledněním náhodných vlivů v modelech. V aplikované části je prezentována tvorba vhodných optimalizačních modelů pro mísení kameniva, jejich implementace a výsledky. Práce zahrnuje původní aplikační výsledky docílené při řešení projektu GA ČR reg. čís. 103/08/1658 Pokročilá optimalizace návrhu složených betonových konstrukcí a teoretické výsledky projektu MŠMT České republiky čís. 1M06047 Centrum pro jakost a spolehlivost výroby.

A stochastic dynamic programming model (called P.B.S.D.P.) based on the consideration of peak discharge and time between peaks as two stochastic variables has been used to model and to solve a reservoir operation problem. This conceptualization of the physical reality allows to solve, in this order, the tactical and strategic operation of surface reservoirs. This P.B.S.D.P. model has been applied to the Sau reservoir in the Northeastern corner of Spain. The results showed a significant improvement over the currently used operation procedure, yielding values of yearly average electricity production that are somewhat under 6% of what could have been the maximum electricity production.