Negative data in DEA:a directional distance approach applied to bank branches

This paper is drawn from the use of data envelopment analysis (DEA) in helping a Portuguese bank to manage the performance of its branches. The bank wanted to set targets for the branches on such variables as growth in number of clients, growth in funds deposited and so on. Such variables can take positive and negative values but apart from some exceptions, traditional DEA models have hitherto been restricted to non-negative data. We report on the development of a model to handle unrestricted data in a DEA framework and illustrate the use of this model on data from the bank concerned.

School outcomes:sharing the responsibility between pupil and school

This paper uses a Data Envelopment Analysis based approach to decompose pupil under-attainment into that attributable to the school the pupil attends and that attributable to the pupil. The approach measures pupil attainment in terms of value added. Data on over 6700 A-level pupils from 122 English schools have been analysed. The results suggest that at current levels of school effectiveness a pupil's own application accounts for the major part of any under-attainment, though schools also have scope to improve their effectiveness.The approach also makes it possible to identify target attainment levels a pupil could be set and the extent to which the attainment of those targets necessitates an improvement in the effectiveness of the school the pupil attends and in the pupil's own efforts.

A DEA model for units with negative data

In this paper we propose an alternative method for measuring efficiency of Decision making Units, which allows the presence of variables with both negative and positive values. The model is applied to data on the notional effluent processing system to compare the results with recent developed methods; Modified Slacks Based Model as suggested by Sharp et al (2007) and Range Directional Measures developed by Silva Portela et al (2004). A further example explores advantages of using the new model.

A circular Malmquist-type index for measuring productivity

This paper develops two new indices for measuring productivity in multi-input multi-output situations. One index enables the measure of productivity change of a unit over time while the second index makes it possible to compare two units on productivity at the same or different points in time. Productivity in a single input single output context is defined as the ratio of output to input. In multi-input multi-output contexts this ratio is not defined. Instead, one of the methods traditionally used is the Malmquist Index of productivity change over time. This is computed by reference to the distances of the input-output bundles of a production unit at two different points in time from the efficient boundaries corresponding to those two points in time. The indices developed in this paper depart form the use of two different reference boundaries and instead they use a single reference boundary which in a sense is the most efficient boundary observed over two or more successive time periods. We discuss the assumptions which make possible the definition of such a single reference boundary and proceed to develop the two Malmquist-type indices for measuring productivity. One key advantage of using a single reference boundary is that the resulting index values are circular. That is it is possible to use the index values of successive time periods to derive an index value of productivity change over a time period of any length covered by successive index values or vice versa. Further, the use of a single reference boundary makes it possible to construct an index for comparing the productivities of two units either at the same or at two different points in time. This was not possible with the traditional Malmquist Index. We decompose both new indices into components which isolate production unit from industry or comparator unit effects. The components themselves like the indices developed are also circular. The components of the indices drill down to reveal more clearly the performance of each unit over time relative either to itself or to other units. The indices developed and their components are aimed at managers of production units to enable them to diagnose the performance of their units with a view to guiding them to improved performance.

A semi-oriented radial measure for measuring the efficiency of decision making units with negative data, using DEA

Data Envelopment Analysis (DEA) is a nonparametric method for measuring the efficiency of a set of decision making units such as firms or public sector agencies, first introduced into the operational research and management science literature by Charnes, Cooper, and Rhodes (CCR) [Charnes, A., Cooper, W.W., Rhodes, E., 1978. Measuring the efficiency of decision making units. European Journal of Operational Research 2, 429–444]. The original DEA models were applicable only to technologies characterized by positive inputs/outputs. In subsequent literature there have been various approaches to enable DEA to deal with negative data. In this paper, we propose a semi-oriented radial measure, which permits the presence of variables which can take both negative and positive values. The model is applied to data on a notional effluent processing system to compare the results with those yielded by two alternative methods for dealing with negative data in DEA: The modified slacks-based model suggested by Sharp et al. [Sharp, J.A., Liu, W.B., Meng, W., 2006. A modified slacks-based measure model for data envelopment analysis with ‘natural’ negative outputs and inputs. Journal of Operational Research Society 57 (11) 1–6] and the range directional model developed by Portela et al. [Portela, M.C.A.S., Thanassoulis, E., Simpson, G., 2004. A directional distance approach to deal with negative data in DEA: An application to bank branches. Journal of Operational Research Society 55 (10) 1111–1121]. A further example explores the advantages of using the new model.

Malmquist-type indices in the presence of negative data:an application to bank branches

In this paper we develop an index and an indicator of productivity change that can be used with negative data. For that purpose the range directional model (RDM), a particular case of the directional distance function, is used for computing efficiency in the presence of negative data. We use RDM efficiency measures to arrive at a Malmquist-type index, which can reflect productivity change, and we use RDM inefficiency measures to arrive at a Luenberger productivity indicator, and relate the two. The productivity index and indicator are developed relative to a fixed meta-technology and so they are referred to as a meta-Malmquist index and meta-Luenberger indicator. We also address the fact that VRS technologies are used for computing the productivity index and indicator (a requirement under negative data), which raises issues relating to the interpretability of the index. We illustrate how the meta-Malmquist index can be used, not only for comparing the performance of a unit in two time periods, but also for comparing the performance of two different units at the same or different time periods. The proposed approach is then applied to a sample of bank branches where negative data were involved. The paper shows how the approach yields information from a variety of perspectives on performance which management can use.

Productivity change in the water industry in England and Wales:application of the meta-Malmquist Index

This paper uses a meta-Malmquist index for measuring productivity change of the water industry in England and Wales and compares this to the traditional Malmquist index. The meta-Malmquist index computes productivity change with reference to a meta-frontier, it is computationally simpler and it is circular. The analysis covers all 22 UK water companies in existence in 2007, using data over the period 1993–2007. We focus on operating expenditure in line with assessments in this field, which treat operating and capital expenditure as lacking substitutability. We find important improvements in productivity between 1993 and 2005, most of which were due to frontier shifts rather than catch up to the frontier by companies. After 2005, the productivity shows a declining trend. We further use the meta-Malmquist index to compare the productivities of companies at the same and at different points in time. This shows some interesting results relating to the productivity of each company relative to that of other companies over time, and also how the performance of each company relative to itself over 1993–2007 has evolved. The paper is grounded in the broad theory of methods for measuring productivity change, and more specifically on the use of circular Malmquist indices for that purpose. In this context, the contribution of the paper is methodological and applied. From the methodology perspective, the paper demonstrates the use of circular meta-Malmquist indices in a comparative context not only across companies but also within company across time. This type of within-company assessment using Malmquist indices has not been applied extensively and to the authors’ knowledge not to the UK water industry. From the application perspective, the paper throws light on the performance of UK water companies and assesses the potential impact of regulation on their performance. In this context, it updates the relevant literature using more recent data.

New insights on measuring bank branches efficiency through DEA:transactional, operational, and profit assessments

This thesis presents a number of methodological developments that were raised by a real life application to measuring the efficiency of bank branches. The advent of internet banking and phone banking is changing the role of bank branches from a predominantly transaction-based one to a sales-oriented role. This fact requires the development of new forms of assessing and comparing branches of a bank. In addition, performance assessment models must also take into account the fact that bank branches are service and for-profit organisations to which providing adequate service quality as well as being profitable are crucial objectives. This study analyses bank branches performance in their new roles in three different areas: their effectiveness in fostering the use of new transaction channels such as the internet and the telephone (transactional efficiency); their effectiveness in increasing sales and their customer base (operational efficiency); and their effectiveness in generating profits without compromising the quality of service (profit efficiency). The chosen methodology for the overall analysis is Data Envelopment Analysis (DEA). The application attempted here required some adaptations to existing DEA models and indeed some new models so that some specialities of our data could be handled. These concern the development of models that can account for negative data, the development of models to measure profit efficiency, and the development of models that yield production units with targets that are nearer to their observed levels than targets yielded by traditional DEA models. The application of the developed models to a sample of Portuguese bank branches allowed their classification according to the three performance dimensions (transactional, operational and profit efficiency). It also provided useful insights to bank managers regarding how bank branches compare between themselves in terms of their performance, and how, in general, the three performance dimensions are connected between themselves.

Estimating the scope for savings in referrals and drug prescription costs in the general Practice units of a UK primary care trust

This paper explores the potential for cost savings in the general Practice units of a Primary Care Trust (PCT) in the UK. We have used Data Envelopment Analysis (DEA) to identify benchmark Practices, which offer the lowest aggregate referral and drugs costs controlling for the number, age, gender, and deprivation level of the patients registered with each Practice. For the remaining, non-benchmark Practices, estimates of the potential for savings on referral and drug costs were obtained. Such savings could be delivered through a combination of the following actions: (i) reducing the levels of referrals and prescriptions without affecting their mix (£15.74 m savings were identified, representing 6.4% of total expenditure); (ii) switching between inpatient and outpatient referrals and/or drug treatment to exploit differences in their unit costs (£10.61 m savings were identified, representing 4.3% of total expenditure); (iii) seeking a different profile of referral and drug unit costs (£11.81 m savings were identified, representing 4.8% of total expenditure). © 2012 Elsevier B.V. All rights reserved.

Using DEA to estimate potential savings at GP units at medical specialty level

The aim of this paper is to identify benchmark cost-efficient General Practitioner (GP) units at delivering health care in the Geriatric and General Medicine (GMG) specialty and estimate potential cost savings. The use of a single medical specialty makes it possible to reflect more accurately the medical condition of the List population of the Practice so as to contextualize its expenditure on care for patients. We use Data Envelopment Analysis (DEA) to estimate the potential for cost savings at GP units and to decompose these savings into those attributable to the reduction of resource use, to altering the mix of resources used and to those attributable to securing better resource 'prices'. The results reveal a considerable potential for savings of varying composition across GP units. © 2013 Elsevier Ltd.

Economic efficiency when prices are not fixed:disentangling quantity and price efficiency

This paper proposes an approach to compute cost efficiency in contexts where units can adjust input quantities and to some degree prices so that through their joint determination they can minimise the aggregate cost of the outputs they secure. The model developed is based on the data envelopment analysis (DEA) framework and can accommodate situations where the degree of influence over prices ranges from minimal to considerable. When units cannot influence prices at all the model proposed reduces to the standard cost efficiency DEA model for the case where prices are taken as exogenous. In addition to the cost efficiency model, we introduce an additive decomposition of potential cost savings into a quantity and a price component, based on Bennet indicators. © 2014 Elsevier Ltd.

Applications of data envelopment analysis in education

Non-parametric methods for efficiency evaluation were designed to analyse industries comprising multi-input multi-output producers and lacking data on market prices. Education is a typical example. In this chapter, we review applications of DEA in secondary and tertiary education, focusing on the opportunities that this offers for benchmarking at institutional level. At secondary level, we investigate also the disaggregation of efficiency measures into pupil-level and school-level effects. For higher education, while many analyses concern overall institutional efficiency, we examine also studies that take a more disaggregated approach, centred either around the performance of specific functional areas or that of individual employees.

Identifying the scope for savings at inpatient episode level:an illustration applying DEA to chronic obstructive pulmonary disease

Chronic obstructive pulmonary disease (COPD) is characterized by a largely irreversible obstruction of the airways, and is one of the leading causes of chronic morbidity and mortality worldwide. This paper illustrates the use of Data Envelopment Analysis (DEA) to assess the potential for cost savings at COPD inpatient episode level. The analysis uses the length of stay of each episode as a surrogate for expenditure on that episode while allowing for the medical condition of the patient and the quality of care received. We find substantial possible reductions in length of stay which would translate to cost savings. The paper also explores differences both between hospitals and between care teams within hospitals so that cost efficient protocols of treatment can be identified and disseminated.

Simulação de desempenho luminoso para salas de aula em Natal-RN

The city of Natal has a significant daylight availability, although it use isn’t systematically explored in schools architecture. In this context, this research aims to determine procedures for the analysis of the daylight performance in school design in Natal-RN. The method of analysis is divided in Visible Sky Factor (VSF), simulating and analyzing the results. The annual variation of the daylight behavior requires the adoption of dynamic simulation as data procedure. The classrooms were modelled in SketchUp, simulated in Daysim program and the results were assessed by means of spreadsheets in Microsoft Excel. The classrooms dimensions are 7.20mx 7.20m, with windows-to-wall-ratio (WWR) of 20%, 40% and 50%, and with different shading devices, such as standard horizontal overhang, sloped overhang, standard horizontal overhang with side view protection, standard horizontal overhang with a dropped edge, standard horizontal overhang with three horizontal louvers, double standard horizontal overhang, double standard horizontal overhang with three horizontal louvers, plus the use of shelf light in half the models with WWR of 40% and 50%. The data was organized in spreadsheets, with two intervals of UDI: between 300lux and 2000 lux and between 300lux and 3000lux. The simulation was performed with the weather file of 2009 to the city of NatalRN. The graphical outputs are illuminance curves, isolines of UDI among 300lux and 2000 lux and tables with index of occurrences of glare and to an UDI among 300lux 3000lux. The best UDI300-2000lux performance was evidenced to: Phase 1 (models with WWR of 20%), Phase 2 (models with WWR of 40% and 50% with light shelf). The best UDI300-3000lux performance was evidenced to: Phase 1 (models with WWR of 20% and 40% with light shelf) and Phase 2 (models with WWR of 40% and 50% with light shelf). The outputs prove that the daylight quality mainly depends on the shading system efficacy to avoid the glare occurrence, which determines the daylight discomfort. The bioclimatic recommendations of big openings with partial shading (with an opening with direct sunlight) resulted in illuminances level higher than the acceptable upper threshold. The improvement of the shading system percentage (from 73% to 91%) in medium-size of openings (WWR 40% and 50%) reduced or eliminate the glare occurrence without compromising the daylight zone depth (7.20m). The passive zone was determined for classrooms with satisfactory daylight performance, it was calculated the daylight zone depth rule-of-thumb with the ratio between daylight zone depth and the height of the window for different size of openings. The ratio ranged from 1.54 to 2.57 for WWR of 20%, 40% and 50% respectively. There was a reduction or elimination of glare in the passive area with light shelf, or with awning window shading.

Síntese de ferritas de cobalto e níquel dopadas com zinco e caracterização de suas propriedades eletromagnéticas

This work shows that the synthesis by combustion is a prominent alternative to obtain ceramic powders of higher oxides, nanostructured and of high purity, as the ferrites of formulas Co(1-x)Zn(x)Fe2O4 e Ni(1-x)Zn(x)Fe2O4 with x ranging from 0.2 mols, in a range from 0.2 ≤ x ≥ 1.0 mol, that presents magnetic properties in coexistence of ferroelectric and ferrimagnetic states, which can be used in antennas of micro tapes and selective surfaces of low frequency in a range of miniaturized microwaves, without performance loss. The obtainment occurred through the combustion process, followed by appropriate physical processes and ordered to the utilization of the substrate sinterization process, it gave us a ceramic material, of high purity degree in a nanometric scale. The Vibrating Sample Magnetometer (VSM) analysis showed that those ferritic materials presents parameters, as materials hysteresis, that have own behavior of magnetic materials of good quality, in which the magnetization states can be suddenly changed with a relatively small variation of the field intensity, having large applications on the electronics field. The X-ray Diffraction (XRD) analysis of the ceramic powders synthesized at 900 °C, characterize its structural and geometrical properties, the crystallite size and the interplanar spacing. Other analysis were developed, as Scanning Electron Microscopy (SEM), X-ray Fluorescence (XRF), electric permittivity and the tangent loss, in high frequencies, through the equipment ZVB - 14 Vector Network Analyzer 10 MHz-14 GHz, of ROHDE & SCHWART.