Academic Commons Search Results
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Academic Commons Search Resultsen-usCutting Planes for Convex Objective Nonconvex Optimization
http://academiccommons.columbia.edu/catalog/ac:166569
Michalka, Alexanderhttp://hdl.handle.net/10022/AC:P:22000Thu, 17 Oct 2013 00:00:00 +0000This thesis studies methods for tightening relaxations of optimization problems with convex objective values over a nonconvex domain. A class of linear inequalities obtained by lifting easily obtained valid inequalities is introduced, and it is shown that this class of inequalities is sufficient to describe the epigraph of a convex and differentiable function over a general domain. In the special case where the objective is a positive definite quadratic function, polynomial time separation procedures using the new class of lifted inequalities are developed for the cases when the domain is the complement of the interior of a polyhedron, a union of polyhedra, or the complement of the interior of an ellipsoid. Extensions for positive semidefinite and indefinite quadratic objectives are also studied. Applications and computational considerations are discussed, and the results from a series of numerical experiments are presented.Industrial engineeringadm2148Industrial Engineering and Operations ResearchDissertationsResource Cost Aware Scheduling Problems
http://academiccommons.columbia.edu/catalog/ac:166566
Carrasco, Rodrigohttp://hdl.handle.net/10022/AC:P:21999Thu, 17 Oct 2013 00:00:00 +0000Managing the consumption of non-renewable and/or limited resources has become an important issue in many different settings. In this dissertation we explore the topic of resource cost aware scheduling. Unlike the purely scheduling problems, in the resource cost aware setting we are not only interested in a scheduling performance metric, but also the cost of the resources consumed to achieve a certain performance level. There are several ways in which the cost of non-renewal resources can be added into a scheduling problem. Throughout this dissertation we will focus in the case where the resource consumption cost is added, as part of the objective, to a scheduling performance metric such as weighted completion time and weighted tardiness among others. In our work we make several contributions to the problem of scheduling with non-renewable resources. For the specific setting in which only energy consumption is the important resource, our contributions are the following. We introduce a model that extends the previous energy cost models by allowing more general cost functions that can be job-dependent. We further generalize the problem by allowing arbitrary precedence constraints and release dates. We give approximation algorithms for minimizing an objective that is a combination of a scheduling metric, namely total weighted completion time and total weighted tardiness, and the total energy consumption cost. Our approximation algorithm is based on an interval-and-speed-indexed IP formulation. We solve the linear relaxation of this IP and we use this solution to compute a schedule. We show that these algorithms have small constant approximation ratios. Through experimental analysis we show that the empirical approximation ratios are much better than the theoretical ones and that in fact the solutions are close to optimal. We also show empirically that the algorithm can be used in additional settings not covered by the theoretical results, such as using flow time or an online setting, with good approximation and competitiveness ratios.Industrial engineering, Applied mathematicsIndustrial Engineering and Operations ResearchDissertationsRapid Advance: High Technology in China in the Global Electronic Age
http://academiccommons.columbia.edu/catalog/ac:161506
Mays, Susan Kayhttp://hdl.handle.net/10022/AC:P:20447Thu, 23 May 2013 00:00:00 +0000This study examines how a critical high technology industry in China, the semiconductor industry, advanced from being an isolated, centrally planned industry in the mid 1980s to being an important participant in the competitive global semiconductor industry after 2000. The research examines the most important trends, projects, and enterprises in China, with attention to China's global partners and China's rapidly growing role in the world economy. In the 1990s, semiconductor enterprises in China proactively made key structural changes and global linkages that set the stage for the industry's growth after 2000. The study thus provides an industry level assessment of how reforms and technological upgrading occurred in contemporary China, including the degree and character of so-called state led development. This research also shows that the development of this high technology industry had direct and positive effects on China's larger business environment and trade policies. Finally, this study compares the development of the semiconductor industry in China with its development in Japan, South Korea, and Taiwan, identifying differences in national approaches and the effects of the global information revolution.Economic history, Asian studies, Industrial engineeringsm2075History, East Asian Languages and CulturesDissertationsLeveraging the mining industry’s energy demand to improve host countries’ power infrastructure
http://academiccommons.columbia.edu/catalog/ac:156324
Toledano, Perrinehttp://hdl.handle.net/10022/AC:P:18962Thu, 07 Feb 2013 00:00:00 +0000The World Bank estimates that African investment needs in infrastructure would cost US$93 billion per year, only half of which is for the power sector. In the same time, the availability of power lies at the core of a mine’s development strategy; mining operators need to make sure that the energy demand of mining operations is met. This is especially the case in remote areas, where mining companies are developing large projects with little or no connectivity to national grids and very limited options for electricity supply. To address these energy problems, the mining industry has adopted different solutions depending on the power situation of the country, the projects’ energy demand, and the projects’ distance from the grid: When sourcing from the grid is too expensive or when there is no grid, industry finances and builds its own power generation facilities or sources from a third-party that is a private power generator. When sourcing from the grid is less expensive than own generation, industry either sources from the grid or finances/co-finances the upgrade of the power assets under various arrangements with the public utility. For a mining company, the goal is to maximize cost-savings. For a host country, the challenge is to maximize welfare gains by leveraging any investment in power infrastructure development for the electrification needs of the country. This could be through connecting the mine to the grid and incentivizing the company to produce extra capacity to sell to the public utility in order to increase supply and reduce the electricity cost, or by requiring that the privately-financed network is open to third-party access, so that towns and populations between the mine and the grid benefit from the privately financed distribution lines as well. Both, cost savings and welfare gains can be met simultaneously if sound regulations and efficient coordination mechanisms are in place. Without appropriate regulation, the opportunity for the country will be missed. Without appropriate coordination mechanisms within the mining industry or between the industry and the government, scale economies will be lost. Therefore to take advantage of the opportunity of the investments of the mining industry in power infrastructure, and make sure that the country benefits from those investments, an appropriate planning, regulatory and commercial framework is needed. If power assets are leveraged and designed to contribute to the development of public infrastructure at the national, regional or community levels, the incremental capital cost of building additional capacity could be reduced and the economic and social spillover effects can extend far beyond the mining sector. The purpose of this working paper is to distill good practice principles observed in power infrastructure development leveraging the mining industry’s energy demand around the world, informed by expert opinion.Economics, Industrial engineeringpt2179Vale Columbia Center on Sustainable International InvestmentWorking papersChance Constrained Optimal Power Flow: Risk-Aware Network Control under Uncertainty
http://academiccommons.columbia.edu/catalog/ac:156182
Bienstock, Daniel; Chertkov, Michael; Harnett, Seanhttp://hdl.handle.net/10022/AC:P:18933Tue, 05 Feb 2013 00:00:00 +0000When uncontrollable resources fluctuate, Optimum Power Flow (OPF), routinely used by the electric power industry to re-dispatch hourly controllable generation (coal, gas and hydro plants) over control areas of transmission networks, can result in grid instability, and, potentially, cascading outages. This risk arises because OPF dispatch is computed without awareness of major uncertainty, in particular fluctuations in renewable output. As a result, grid operation under OPF with renewable variability can lead to frequent conditions where power line flow ratings are significantly exceeded. Such a condition, which is borne by simulations of real grids, would likely resulting in automatic line tripping to protect lines from thermal stress, a risky and undesirable outcome which compromises stability. Smart grid goals include a commitment to large penetration of highly fluctuating renewables, thus calling to reconsider current practices, in particular the use of standard OPF. Our Chance Constrained (CC) OPF corrects the problem and mitigates dangerous renewable fluctuations with minimal changes in the current operational procedure. Assuming availability of a reliable wind forecast parameterizing the distribution function of the uncertain generation, our CC-OPF satisfies all the constraints with high probability while simultaneously minimizing the cost of economic re-dispatch. CC-OPF allows efficient implementation, e.g. solving a typical instance over the 2746-bus Polish network in 20 seconds on a standard laptop.Industrial engineering, Operations researchdb17, srh2144Applied Physics and Applied Mathematics, Industrial Engineering and Operations ResearchArticlesChance Constrained Optimal Power Flow: Risk-Aware Network Control under Uncertainty
http://academiccommons.columbia.edu/catalog/ac:153902
Bienstock, Daniel; Chertkov, Michael; Harnett, Seanhttp://hdl.handle.net/10022/AC:P:15118Mon, 29 Oct 2012 00:00:00 +0000When uncontrollable resources fluctuate, Optimum Power Flow (OPF), routinely used by the electric power industry to redispatch hourly controllable generation (coal, gas and hydro plants) over control areas of transmission networks, can result in grid instability, and, potentially, cascading outages. This risk arises because OPF dispatch is computed without awareness of major uncertainty, in particular fluctuations in renewable output. As a result, grid operation under OPF with renewable variability can lead to frequent conditions where power line flow ratings are significantly exceeded. Such a condition, which is borne by simulations of real grids, would likely resulting in automatic line tripping to protect lines from thermal stress, a risky and undesirable outcome which compromises stability. Smart grid goals include a commitment to large penetration of highly fluctuating renewables, thus calling to reconsider current practices, in particular the use of standard OPF. Our Chance Constrained (CC) OPF corrects the problem and mitigates dangerous renewable fluctuations with minimal changes in the current operational procedure. Assuming availability of a reliable wind forecast parameterizing the distribution function of the uncertain generation, our CCOPF satisfies all the constraints with high probability while simultaneously minimizing the cost of economic redispatch. CCOPF allows efficient implementation, e.g. solving a typical instance over the 2746bus Polish network in 20s on a standard laptop.Industrial engineering, Operations researchdb17Applied Physics and Applied Mathematics, Industrial Engineering and Operations ResearchArticlesMultiproduct Pricing Management and Design of New Service Products
http://academiccommons.columbia.edu/catalog/ac:144706
Wang, Ruxianhttp://hdl.handle.net/10022/AC:P:12603Fri, 17 Feb 2012 00:00:00 +0000In this thesis, we study price optimization and competition of multiple differentiated substitutable products under the general Nested Logit model and also consider the designing and pricing of new service products, e.g., flexible warranty and refundable warranty, under customers' strategic claim behavior. Chapter 2 considers firms that sell multiple differentiated substitutable products and customers whose purchase behavior follows the Nested Logit model, of which the Multinomial Logit model is a special case. In the Nested Logit model, customers make product selection decision sequentially: they first select a class or a nest of products and subsequently choose a product within the selected class. We consider the general Nested Logit model with product-differentiated price coefficients and general nest-heterogenous degrees. We show that the adjusted markup, which is defined as price minus cost minus the reciprocal of the price coefficient, is constant across all the products in each nest. When optimizing multiple nests of products, the adjusted nested markup is also constant within a nest. By using this result, the multi-product optimization problem can be reduced to a single-dimensional problem in a bounded interval, which is easy to solve. We also use this result to simplify the oligopolistic price competition and characterize the Nash equilibrium. Furthermore, we investigate its application to dynamic pricing and revenue management. In Chapter 3, we investigate the flexible monthly warranty, which offers flexibility to customers and allow them to cancel it at anytime without any penalty. Frequent technological innovations and price declines severely affect sales of extended warranties as product replacement upon failure becomes an increasingly attractive alternative. To increase sales and profitability, we propose offering flexible-duration extended warranties. These warranties can appeal to customers who are uncertain about how long they will keep the product as well as to customers who are uncertain about the product's reliability. Flexibility may be added to existing services in the form of monthly-billing with month-by-month commitments, or by making existing warranties easier to cancel, with pro-rated refunds. This thesis studies flexible warranties from the perspectives of both the customer and the provider. We present a model of the customer's optimal coverage decisions under the objective of minimizing expected support costs over a random planning horizon. We show that under some mild conditions the customer's optimal coverage policy has a threshold structure. We also show through an analytical study and through numerical examples how flexible warranties can result in higher profits and higher attach rates. Chapter 4 examines the designing and pricing of residual value warranty that refunds customers at the end of warranty period based on customers' claim history. Traditional extended warranties for IT products do not differentiate customers according to their usage rates or operating environment. These warranties are priced to cover the costs of high-usage customers who tend to experience more failures and are therefore more costly to support. This makes traditional warranties economically unattractive to low-usage customers. In this chapter, we introduce, design and price residual value warranties. These warranties refund a part of the upfront price to customers who have zero or few claims according to a pre-determined refund schedule. By design, the net cost of these warranties is lower for light users than for heavy users. As a result, a residual value warranty can enable the provider to price-discriminate based on usage rates or operating conditions without the need to monitor individual customers' usage. Theoretic results and numerical experiments demonstrate how residual value warranties can appeal to a broader range of customers and significantly increase the provider's profits.Operations research, Industrial engineeringrw2267Industrial Engineering and Operations ResearchDissertationsDevelopment of Construction Projects Scheduling with Evolutionary Algorithms
http://academiccommons.columbia.edu/catalog/ac:140087
Tavakolan, Mehdihttp://hdl.handle.net/10022/AC:P:11408Mon, 10 Oct 2011 00:00:00 +0000Evolutionary Algorithms (EAs) as appropriate tools to optimize multi-objective problems have been applied to optimize construction projects in the last two decades. However, studies on improving the convergence ratio and processing time in the most applied algorithms such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO) and Ant Colony Optimization (ACO) in construction engineering and management domains remain poorly understood. Furthermore, hybrid algorithms such as Hybrid Genetic Algorithm-Particle Swarm Optimization (HGAPSO) and Shuffled Frog Leaping Algorithm (SFLA) have been presented in computational optimization and water resource management domains during recent years to prevent pitfalls of the aforementioned algorithms. In this dissertation, I present three studies on hybrid algorithms to show that our proposed hybrid approaches are superior than existing optimization algorithms in finding better project schedule solutions with less total project cost, shorter total project duration, and less total resources allocation moments. In the first, I present a HGAPSO approach to solve complex, TCRO problems in construction project planning. Our proposed approach uses the fuzzy set theory to characterize uncertainty about the input data (i.e., time, cost, and resources required to perform an activity). In the second, I present the SFLA algorithm to solve TCRO problems using splitting allowed during activities execution. The third study involves the evaluation of the inflation impact on resources unit price during execution of construction projects. This research presents the comprehensive TCRO model by comparing two hybrid algorithms, HGAPSO and SFLA, with the three most capable algorithms -- GA, PSO and ACO -- in six different examples in terms of the structure of projects, construction assumptions and kinds of Time-Cost functions. Each of the three studies helps overcome parts of EAs problems and contributes to obtaining optimal project schedule solutions of total project duration, total project cost and total resources allocation moments of construction projects in the planning stage. The findings have significant implications in improving the scheduling of construction projects.Civil engineering, Industrial engineeringmt2568Civil Engineering and Engineering MechanicsDissertationsSqueezing the most out of ATM
http://academiccommons.columbia.edu/catalog/ac:125355
Choudhury, Gagan L.; Whitt, Wardhttp://hdl.handle.net/10022/AC:P:8585Fri, 02 Apr 2010 00:00:00 +0000Although ATM seems to be the wave of the future, one analysis requires that the utilization of the network be quite low. That analysis is based on asymptotic decay rates of steady-state distributions used to develop a concept of effective bandwidths for connection admission control. The present authors have developed an exact numerical algorithm that shows that the effective-bandwidth approximation can overestimate the target small blocking probabilities by several orders of magnitude when there are many sources that are more bursty than Poisson. The bad news is that the appealing simple connection admission control algorithm using effective bandwidths based solely on tail-probability asymptotic decay rates may actually not be as effective as many have hoped. The good news is that the statistical multiplexing gain on ATM networks may actually be higher than some have feared. For one example, thought to be realistic, the analysis indicates that the network actually can support twice as many sources as predicted by the effective-bandwidth approximation. The authors also show that the effective bandwidth approximation is not always conservative. Specifically, for sources less bursty than Poisson, the asymptotic constant grows exponentially in the number of sources (when they are scaled as above) and the effective-bandwidth approximation can greatly underestimate the target blocking probabilities. Finally, they develop new approximations that work much better than the pure effective-bandwidth approximation.Industrial engineeringww2040ArticlesContinuity of a queueing integral representation in the M1 topology
http://academiccommons.columbia.edu/catalog/ac:125349
Pang, Guodong; Whitt, Wardhttp://hdl.handle.net/10022/AC:P:8584Fri, 02 Apr 2010 00:00:00 +0000We establish continuity of the integral representation y(t)=x(t)+∫0th(y(s)) ds, t≥0, mapping a function x into a function y when the underlying function space D is endowed with the Skorohod M1 topology. We apply this integral representation with the continuous mapping theorem to establish heavy-traffic stochastic-process limits for many-server queueing models when the limit process has jumps unmatched in the converging processes as can occur with bursty arrival processes or service interruptions. The proof of M1-continuity is based on a new characterization of the M1 convergence, in which the time portions of the parametric representations are absolutely continuous with respect to Lebesgue measure, and the derivatives are uniformly bounded and converge in L1.many-server queues, heavy-traffic limits, Skorohod M1 topology, continuous mapping theorem, bursty arrival processes, Industrial engineeringgp2224, ww2040Industrial Engineering and Operations ResearchArticlesThe N-k Problem in Power Grids: New Models, Formulations and Numerical Experiments (Extended Version)
http://academiccommons.columbia.edu/catalog/ac:125318
Bienstock, Daniel; Verma, Abhinavhttp://hdl.handle.net/10022/AC:P:8574Wed, 17 Mar 2010 00:00:00 +0000Given a power grid modeled by a network together with equations describing the power flows, power generation and consumption, and the laws of physics, the so-called N-k problem asks whether there exists a set of k or fewer arcs whose removal will cause the system to fail. The case where k is small is of practical interest. We present theoretical and computational results involving a mixed-integer model and a continuous nonlinear model related to this question.Industrial engineeringdb17Applied Physics and Applied Mathematics, Industrial Engineering and Operations ResearchArticles