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.

A survey of some small firms in the rural areas of England: their structure and functions, with special reference to factors that affect their development

This study was concerned with the structure, functions and development, especially the performance, of some rural small firms associated with the Council for Small Industries in Rural Areas (C?SIRA) of England. Forty firms were used as the main basis of analysis. For some aspects of the investigation, however, data from another 54 firms, obtained indirectly through nine CoSIRA Organisers, were also used. For performance-analysis, the 40 firms were firstly ranked according to their growth and profitability rates which were calculated from their financial data. Then each of the variables hypothesised to be related to performance was tested to ascertain its relationship with performance, using the Spearman's Rank Correlation technique. The analysis indicated that each of the four factors .. the principal, the firm itself, its management, and the environment - had a bearing upon the performance of the firm. Within the first factor, the owner-manager's background and attitudes were found to be most important; in the second, the firm's size, age and scope of activities were also found to be correlated with performance; with respect to the third, it was revealed that firms which practised some forms of systems in planning, control and costing performed better than those which did not and, finally with respect to the fourth factor, it was found that some of the services provided by CoSIRA, especially credit finance, were facilitative to the firm's performance. Another significant facet of the firms highlighted by the study was their multifarious roles. These, meeting economic, psychological, sociological and political needs, were considered to be most useful to man and his society. Finally, the study has added light to the structural characteristics of the sampled firms, including various aspects of their development, orientation and organisation, as well as their various structural strengths and weakness. ' .

On the boundedness of the SORM DEA models with negative data

Emrouznejad et al. (2010) proposed a Semi-Oriented Radial Measure (SORM) model for assessing the efficiency of Decision Making Units (DMUs) by Data Envelopment Analysis (DEA) with negative data. This paper provides a necessary and sufficient condition for boundedness of the input and output oriented SORM models.

Two-dimensional viscoelastic discrete triangular system with negative-stiffness components

Potential applications of high-damping and high-stiffness composites have motivated extensive research on the effects of negative-stiffness inclusions on the overall properties of composites. Recent theoretical advances have been based on the Hashin-Shtrikman composite models, one-dimensional discrete viscoelastic systems and a two-dimensional nested triangular viscoelastic network. In this paper, we further analyze the two-dimensional triangular structure containing pre-selected negative-stiffness components to study its underlying deformation mechanisms and stability. Major new findings are structure-deformation evolution with respect to the magnitude of negative stiffness under shear loading and the phenomena related to dissipation-induced destabilization and inertia-induced stabilization, according to Lyapunov stability analysis. The evolution shows strong correlations between stiffness anomalies and deformation modes. Our stability results reveal that stable damping peaks, i.e. stably extreme effective damping properties, are achievable under hydrostatic loading when the inertia is greater than a critical value. Moreover, destabilization induced by elemental damping is observed with the critical inertia. Regardless of elemental damping, when the inertia is less than the critical value, a weaker system instability is identified.

A modified semi-oriented radial measure for target setting with negative data

Over the last few years Data Envelopment Analysis (DEA) has been gaining increasing popularity as a tool for measuring efficiency and productivity of Decision Making Units (DMUs). Conventional DEA models assume non-negative inputs and outputs. However, in many real applications, some inputs and/or outputs can take negative values. Recently, Emrouznejad et al. [6] introduced a Semi-Oriented Radial Measure (SORM) for modelling DEA with negative data. This paper points out some issues in target setting with SORM models and introduces a modified SORM approach. An empirical study in bank sector demonstrates the applicability of the proposed model. © 2014 Elsevier Ltd. All rights reserved.

Evaluation efficiency of large-scale data set with negative data:an artificial neural network approach

Data envelopment analysis (DEA) is the most widely used methods for measuring the efficiency and productivity of decision-making units (DMUs). The need for huge computer resources in terms of memory and CPU time in DEA is inevitable for a large-scale data set, especially with negative measures. In recent years, wide ranges of studies have been conducted in the area of artificial neural network and DEA combined methods. In this study, a supervised feed-forward neural network is proposed to evaluate the efficiency and productivity of large-scale data sets with negative values in contrast to the corresponding DEA method. Results indicate that the proposed network has some computational advantages over the corresponding DEA models; therefore, it can be considered as a useful tool for measuring the efficiency of DMUs with (large-scale) negative data.

Null Condition for Semilinear Wave Equation with Variable Coefficients

∗The author was partially supported by M.U.R.S.T. Progr. Nazionale “Problemi Non Lineari...”

On Two Saigo’s Fractional Integral Operators in the Class of Univalent Functions

2000 Mathematics Subject Classification: Primary 26A33, 30C45; Secondary 33A35

Rolle's Theorem for Complex Polynomials with Real Coefficients

Let p(z) be an algebraic polynomial of degree n ¸ 2 with real coefficients and p(i) = p(¡i). According to Grace-Heawood Theorem, at least one zero of the derivative p0(z) is on the disk with center in the origin and radius cot(¼=n). In this paper is found the smallest domain containing at leas one zero of the derivative p0(z).

The Koebe Domain for Concave Univalent Functions

2000 Mathematics Subject Classification: 30C25, 30C45.

Finite Symmetric Functions with Non-Trivial Arity Gap

Given an n-ary k-valued function f, gap(f) denotes the essential arity gap of f which is the minimal number of essential variables in f which become fictive when identifying any two distinct essential variables in f. In the present paper we study the properties of the symmetric function with non-trivial arity gap (2 ≤ gap(f)). We prove several results concerning decomposition of the symmetric functions with non-trivial arity gap with its minors or subfunctions. We show that all non-empty sets of essential variables in symmetric functions with non-trivial arity gap are separable. ACM Computing Classification System (1998): G.2.0.

Operators with Polynomial Coefficients and Generalized Gelfand-Shilov Classes

2010 Mathematics Subject Classification: Primary 35S05, 35J60; Secondary 35A20, 35B08, 35B40.

Fekete-Szegoe problem for certain subclasses of analytic functions with respect to symmetric points

MSC 2010: 30C45

Freak waves and modulational dynamics in plasmas with negative ions

The nonlinear dynamics of modulated electrostatic wavepackets propagating in negativeion plasmas is investigated from first principles. A nonlinear Schrödinger equation is derived by adopting a multiscale technique. The stability of breather- like (bright envelope soliton) structures, considered as a precursor to freak wave (rogue wave) formation, is investigated and then tested via numerical simulations.