Chapter 7 DEA multiplier analytic center sensitivity with an illustrative application to independent oil companies

The setE of extreme points which are also efficient are of basic importance in defining the efficiency frontier, from which the observations for all other DMUs are evaluated in DEA. A significant question which we address is “What variations in the data can be tolerated before the membership inE is changed?” This topic is explored using (1) a simple illustrative example, and (2) production data for 30 independent oil companies during the period 1983–1985. Data were allowed to vary simultaneously for all observations and in different subsets determined by random drawings of data for points both inE and not inE. The results were found to be robust in this study, thereby lending further support to earlier studies which also found these classifications into efficient and inefficient performers to be robust in DEA. Technical developments for these new methods of sensitivity analysis are supplied. These developments feature an application of analytic center (interior point) algorithms which ensure that the Strong Complementary Slackness Condition (SCSC) is fulfilled. The solutions satisfy a mathematical condition called “centrality”. Generally, the solutions are at interior points calledanalytic centers. At these interior points, continuity of the input-output ratios ensures that DMUs inE remain inE for at least small relative variations in the data, while empirically these properties have been found to extend to much larger variations in the data sets.     

A pulsed, optically-pumped rubidium laser at high pump intensity

A rubidium laser operating at 795 nm is optically pumped by a pulsed titanium sapphire laser to investigate the dynamics of Diode Pumped Alkali Lasers (DPALs). Linear scaling of output intensity for longitudinal excitation at intensities of 1.3-43 kW/cm² and as much as 32 times threshold is observed. The slope efficiency depends directly on the number of absorbed photons for alkali concentrations of 0.8-2.0 × 10¹³ atoms/cm³ with no evidence for second order kinetics. The effective absorption cross section is reduced in part by the broad spectral width of the pump source relative to the pressure broadened lineshape. Spin orbit relaxation between the pumped and upper laser levels is sufficiently fast at 550 Torr of methane to prevent bottlenecking at all but the highest intensities. Comparison of laser characteristics with a quasi-two level analytic model suggests performance near the ideal steady-state limit, with the exception of modest mode matching.     

Efficiency and equity in private and public education: A nonparametric comparison

We present a nonparametric approach for (1) efficiency and (2) equity evaluation in education. Firstly, we use a nonparametric (Data Envelopment Analysis) model that is specially tailored to assess educational efficiency at the pupil level. The model accounts for the fact that typically minimal prior structure is available for the behavior (objectives and feasibility set) under evaluation. It allows for uncertainty in the data, while it corrects for exogenous ‘environmental’ characteristics that are specific to each pupil. Secondly, we propose two multidimensional stochastic dominance criteria as naturally complementary aggregation criteria for comparing the performance of different school types (private and public schools). While the first criterion only accounts for efficiency, the second criterion also takes equity into consideration. The model is applied for comparing private (but publicly funded) and public primary schools in Flanders. Our application finds that no school type robustly dominates another type when controlling for the school environment and taking equity into account. More generally, it demonstrates the usefulness of our nonparametric approach, which includes environmental and equity considerations, for obtaining ‘fair’ performance comparisons in the public sector context.     

Eighth-order methods with high efficiency index for solving nonlinear equations

In this paper, we derive a new family of eighth-order methods for solving simple roots of nonlinear equations by using weight function methods. Per iteration these methods require three evaluations of the function and one evaluation of its first derivative, which implies that the efficiency indexes are 1.682. Numerical comparisons are made to show the performance of the derived methods, as shown in the illustration examples.     

Bayesian estimation of the product of two proportions

Suppose that for i = 1,2, a Bernoulli random variable with success probability θ_i is observable from population i. The problem is to estimate θ = θ₁θ₂ using a Bayesian approach with squared error estimation loss in θ. For estimating θ, the best nonrandom sampling scheme, the two-stage sampling scheme, and the optimal sampling scheme are discussed. It is shown that the two-stage sampling scheme is typically asymptotically optimal, and can improve the Bayes risk (over the best nonrandom allocation) up to fifty percent     

Investigation on electrochemical analysis of ZnO nanoparticles and its performance for dye-sensitized solar cells using various natural dyes

The dye-sensitized solar cells were fabricated using five different dyes extracted from the Ixora flower, Pongame leaves, Neem leaves, Pongame leaves, and Almond fruit. ZnO nanoparticle has been prepared via the solvothermal method. The prepared samples were characterized by structural properties of XRD, FE-SEM EDAX, and HR-TEM, Optical properties of UV–Visible and FTIR studies, and Conductivity studies of EIS spectra. The effect of natural dye extract from chlorophyll and anthocyanin pigment group was investigated for the performance of J-V characterization. The efficiency of almond extract of solar cells is found to be better than that of the other four solar cells.     

基于模糊ANP的系统系的效能评估算法及其应用

针对系统系效能的综合评估问题,基于模糊ANP提出了一种新算法.考虑到效能之间的关联性,建立起分级式网络化效能评价指标系统系,实现了系统系(SoS)到子系统,再到系统功能之间的逐级映射,进而得到系统系效能评估的层次模型.采用改进模糊指数标度的网络分析法定量计算系统功能对系统系效能的权重,得到系统功能对系统系效能的贡献度.最后以微电网构成的电力系统为例验证分析,证明所提算法的有效性.     

On the measurement of technical efficiency in the public sector

Existing measures of technical inefficiency obtained through linear programming models in the public sector do not properly control for environmental variables that affect production. It will be shown that the consequences of not controlling for these fixed factors are biased estimates of technical efficiency. This paper extends the mathematical programming approach to frontier estimation known as Data Envelopment Analysis to allow for environmental variables. This modified model will be then contrasted with the existing model that purportedly controls for exogeneous factors to measure public sector efficiency with simulated data. The results provide evidence that the existing Data Envelopment Analysis model will overestimate the level of technical inefficiency and that the modified model developed in this paper does a better job controlling for exogenous factors. The modified model is also applied to analyze the technical efficiency of school districts.     

Effect of mobile phase anionic additives on selectivity,efficiency, and sample loading capacity of cationic drugs in reversed-phase liquid chromatography

In the present work, we study the effect of mobile phase anionic additive type and concentration on the selectivity, efficiency, and sample loading capacity of cationic drugs in reversed-phase liquid chromatography (RPLC). The type and concentration of an anionic additive are known to have a strong effect on the absolute retention of cations in RPLC; in contrast they have only a small effect on the selectivity of one cation relative to a second as seen here. This is mainly due to the similarity of the ion pair formation constants between the selected cations. The limiting retention factors of cations (i.e. the retention factor of the fully ion-paired analyte at very high additive concentration) are roughly proportional to their inherent hydrophobicities (i.e. the retention factor of the analyte in the absence of the anionic additive). With a given anion, differences in ion pairing strength between the solutes are required for effective selectivity adjustment. Based on the Wade–Lucy–Carr (W–L–C) kinetic model of overload peaks, the approach we developed in our previous work was used to study the effect of mobile phase anionic additives type and concentration on the limiting plate count (N₀) and sample loading capacity (ω_0.5) of various cationic drugs. Under linear chromatographic conditions, where the analyte exhibits its smallest peak width and thus maximum apparent plate count, the type and concentration of anionic additives have almost no effect on peak width. In comparison to neutral analytes the sorption isotherms of cationic species are very easily overloaded even when many fewer moles of cations as compared to neutrals are injected. We showed that different anionic additives profoundly affect the cations’ “overload profiles” (i.e. plots of plate count versus amount injected) by changing the sample loading capacities. The increase in sample loading capacities with different anions show the same order as the extent of ion pairing between the anions and the basic analytes. The detrimental effect of sample overloading on peak width can be greatly diminished by using either a stronger ion pairing agent or a higher concentration of a given ion pairing agent. Both effects operate by increasing the sample loading capacity, thereby allowing more solute to be injected. We believe that the increase in sample loading capacity described above is due in part to the increase in the number of ion-exchange sites as more anions sorb to the stationary phase. At the same time, the formation of a neutral ion-paired analyte also increases the amount of cation which can be loaded onto the stationary phase by allowing a greater fraction of the analyte to be present in the stationary phase as an electrically neutral (i.e. ion-paired) species.