83 research outputs found
Capacity expansion and cost efficiency improvement in the warehouse problem
The warehouse problem with deterministic production cost, selling prices, and demand was introduced in the 1950s and there is a renewed interest recently due to its applications in energy storage and arbitrage. In this paper, we consider two extensions of the warehouse problem and develop efficient computational algorithms for finding their optimal solutions. First, we consider a model where the firm can invest in capacity expansion projects for the warehouse while simultaneously making production and sales decisions in each period. We show that this problem can be solved with a computational complexity that is linear in the product of the length of the planning horizon and the number of capacity expansion projects. We then consider a problem in which the firm can invest to improve production cost efficiency while simultaneously making production and sales decisions in each period. The resulting optimization problem is nonĂą convex with integer decision variables. We show that, under some mild conditions on the cost data, the problem can be solved in linear computational time. Ă© 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 367Ăą 373, 2016Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/134190/1/nav21703_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/134190/2/nav21703.pd
Supply Function Competition in Electricity Markets with Flexible, Inflexible, and Variable Generation
In this paper we study the supply function competition between power-generation firms with different levels of flexibility. Inflexible firms produce power at a constant rate over an operating horizon, while flexible firms can adjust their output to meet the fluctuations in electricity demand. Both types of firms compete in an electricity market by submitting supply functions to a system operator, who solves an optimal dispatch problem to determine the production level for each firm and the corresponding market price. We study how firmsâ (in)flexibility affects their equilibrium behavior and the market price. We also analyze the impact of variable generation (such as wind and solar power) on the equilibrium, with the focus on the effects of the amount of variable generation, its priority in dispatch, and the production- based subsidies. We find that the classic supply function equilibrium model overestimates the intensity of the market competition, and even more so as more variable generation is introduced into the system. The policy of economically curtailing variable generation intensifies the market competition, reduces price volatility, and improves the systemâs overall efficiency. Moreover, we show that these benefits are most significant in the absence of the production-based subsidies.http://deepblue.lib.umich.edu/bitstream/2027.42/102571/1/2014Jan28OWu.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/102571/4/1218_Wu_Apr14.pd
Competition and Optimization in Electricity Systems
Electricity prices are characterized by high volatility and severe price spikes. At the root of these phenomena is the strategic behavior of market participants. A good understanding of the market competition is key to making better regulation, contract, and investment decisions. The goal of this thesis is to study the following market competition problems: (1) the competition between flexible generators with fast ramping rates and inflexible generators with constant production rates, (2) the effect of the renewable generation penetration and production based subsidies on the competition and operating efficiency, (3) generation competition in transmission constrained networks, and (4) competition in the capacity expansion of electricity networks.
We first consider a centralized electricity model and find that reducing the production based subsidies to renewable plants dampens their intermittency effect through controlled curtailment, cuts operational cost, and improves the system's balance. We then consider an oligopoly in which generators submit supply function bids and analyze a supply function equilibrium (SFE) model with generators that have different ramping rates. We find that the controlled curtailment of renewables has an additional benefit in oligopolistic markets as it can reduce generator market power, which has favorable operational efficiency and electricity price ramifications. We also find that the classical SFE model is inadequate for modeling renewables and inflexible generators, and can grossly overestimate the competition intensity. We modify the SFE model to account for these issues. Afterwards, a Bertrand model is used to study the duopoly competition in a transmission constrained network. We find that adding transmission constraints in this model does not change the bidding policy, instead it changes the critical demand levels at which firms revise their position from competitive to aggressive bidding. We also solve the symmetric mixed strategy Nash equilibrium problem for multiple generators in a Bertrand electricity auction. Finally, we study several transmission expansion schemes and devise two investment mechanisms that achieve near social optimality.PhDIndustrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/107307/1/mmgwaiz_1.pd
Totally real surfaces in C
It has been shown that a totally real surface in CP2 with parallel mean curvature vector and constant Gaussian curvature is either flat or totally geodesic
Convergence of expansions in Schr\"odinger and Dirac eigenfunctions, with an application to the R-matrix theory
Expansion of a wave function in a basis of eigenfunctions of a differential
eigenvalue problem lies at the heart of the R-matrix methods for both the
Schr\"odinger and Dirac particles. A central issue that should be carefully
analyzed when functional series are applied is their convergence. In the
present paper, we study the properties of the eigenfunction expansions
appearing in nonrelativistic and relativistic -matrix theories. In
particular, we confirm the findings of Rosenthal [J. Phys. G: Nucl. Phys. 13,
491 (1987)] and Szmytkowski and Hinze [J. Phys. B: At. Mol. Opt. Phys. 29, 761
(1996); J. Phys. A: Math. Gen. 29, 6125 (1996)] that in the most popular
formulation of the R-matrix theory for Dirac particles, the functional series
fails to converge to a claimed limit.Comment: Revised version, accepted for publication in Journal of Mathematical
Physics, 21 pages, 1 figur
Time-Changed Fast Mean-Reverting Stochastic Volatility Models
We introduce a class of randomly time-changed fast mean-reverting stochastic
volatility models and, using spectral theory and singular perturbation
techniques, we derive an approximation for the prices of European options in
this setting. Three examples of random time-changes are provided and the
implied volatility surfaces induced by these time-changes are examined as a
function of the model parameters. Three key features of our framework are that
we are able to incorporate jumps into the price process of the underlying
asset, allow for the leverage effect, and accommodate multiple factors of
volatility, which operate on different time-scales
On the Implementation of Constraints through Projection Operators
Quantum constraints of the type Q \psi = 0 can be straightforwardly
implemented in cases where Q is a self-adjoint operator for which zero is an
eigenvalue. In that case, the physical Hilbert space is obtained by projecting
onto the kernel of Q, i.e. H_phys = ker(Q) = ker(Q*). It is, however,
nontrivial to identify and project onto H_phys when zero is not in the point
spectrum but instead is in the continuous spectrum of Q, because in this case
the kernel of Q is empty.
Here, we observe that the topology of the underlying Hilbert space can be
harmlessly modified in the direction perpendicular to the constraint surface in
such a way that Q becomes non-self-adjoint. This procedure then allows us to
conveniently obtain H_phys as the proper Hilbert subspace H_phys = ker(Q*), on
which one can project as usual. In the simplest case, the necessary change of
topology amounts to passing from an L^2 Hilbert space to a Sobolev space.Comment: 22 pages, LaTe
Modeling ophthalmic surfaces using Zernike, Bessel and Chebyshev type functions
The visual system of the human eye is a part of the central nervous system by which the human body sees and interprets the information provided by the visible light in order to build a representation of the world around. During the propagations of the light through the eye, the retinal image can be deteriorated by diseases and disorders. For retinal images, the most important sources of images quality degradation are diffraction and optical aberrations. In order to measure and correct aberrations, there is a number of surfaces related to the anatomy and physiology of the eye. It is important to measure and mathematically model these surfaces to study their properties.publishe
Clinical outcomes of ED patients with bandemia
BackgroundAlthough an elevated white blood cell count is a widely utilized measure for evidence of infection and an important criterion for evaluation of systemic inflammatory response syndrome, its component band count occupies a more contested position within clinical emergency medicine. Recent studies indicate that bandemia is highly predictive of a serious infection, suggesting that clinicians who do not appreciate the value of band counts may delay diagnosis or overlook severe infections.ObjectivesWhereas previous studies focused on determining the quantitative value of the band count (ie, determining sensitivity, threshold for bandemia, etc.), this study directs attention to patient-centered outcomes, hypothesizing that the degree of bandemia predisposes patients to subsequent negative clinical outcomes associated with underappreciated severe infections.MethodsThis retrospective study of electronic medical records includes patients who initially presented to the emergency department (ED) with bandemia and were subsequently discharged from the ED. These patients were screened for repeat ED visits within 7 days and death within 30 days.ResultsIn patients with severe bandemia who were discharged from the ED, there was a 20.9% revisit rate at 7 days and a 4.9% mortality rate at 30 days, placing severely bandemic patients at 5 times significantly greater mortality compared to nonbandemic patients (P = .032).ConclusionOur review of patient outcomes suggests that the degree of bandemia, especially in the setting of concurrent tachycardia or fever, is associated with greater likelihood of negative clinical outcomes
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