A distance-based measure of super efficiency in data envelopment analysis: an application to gas companies

Conventional data envelopment analysis (DEA) assists decision makers in distinguishing between efficient and inefficient decision making units (DMUs) in a homogeneous group. Standard DEA models can not provide more information about efficient units. Super-efficiency DEA models can be used in ranking the performance of efficient DMUs and overcome this obstacle. Because of the possible infeasibility, the use of super efficiency models has been restricted. This research proposes a methodology to determine a distance-based measure of super-efficiency. The proposed methodology overcomes the infeasibility problem of the existing ranking methodologies. The applicability of the proposed model is illustrated in the context of the analysis of gas companies?? performance.     

The Fermat rule for multifunctions for super efficiency

Using variational analysis, we study the vector optimization problems with objectives being closed multifunctions on Banach spaces or in Asplund spaces. In terms of the coderivatives and normal cones, we present Fermat’s rules as necessary or sufficient conditions for a super efficient solution of the above problems.     

The N=4 super Landau models

We briefly describe a new superextended Landau model with a worldline N=4 supersymmetry and an internal target space ISU (2|2) supersymmetry. It shares many features with the previously studied N=2 supersymmetric Landau model, which is also briefly described.     

The weighted Russell measure of technical efficiency

Theoretical consideration of technical efficiency has existed since Koopmans [10] defined it for production possibilities for which it is not possible to increase any output without simultaneously increasing any input, ceteris paribus. The nonparametric approach to efficiency measurement known as Data Envelopment Analysis is based on the index of Farrell [9], which measures radial reduction in all inputs consistent with observed output. Even after Farrell efficiency is achieved, however, there may exist additional slack in individual inputs, suggesting that the Farrell index does not necessarily measure Koopmans inefficiency. To solve this problem, the non-radial Russell measure was introduced. This paper shows that problems may arise with the Russell measure due to restrictive assumptions on the implicit weighting of inputs and outputs. This paper develops a new measure, the Weighted Russell measure, that relaxes this assumption. Using simulated data, the new measure is shown to be preferred to existing methods. In addition, the new method is applied to analyze the performance of New York State school districts.     

Packing measure of super separated iterated function systems

Let J be the limit set of an iterated function system in \(\mathbb {R}^d\) satisfying the open set condition. It is well known that the h-dimensional packing measure of J is positive and finite when h is given by Hutchinson’s formula. However, it may be hard to find a formula for the h-dimensional packing measure of J. We introduce the super separation condition and use it to reduce the problem of computing the packing measure to checking densities of a finite number of balls around each point in the limit set. We then use this fact to find formulas for the packing measure of a class of Cantor sets in \(\mathbb {R}\), a class of fractals based on regular convex polygons in \(\mathbb {R}^2\), and a class of fractals based on regular simplexes in \(\mathbb {R}^d\) for \(d \ge 3\).     

The Lagrange multiplier rule for super efficiency in vector optimization

In this paper, we study constrained multiobjective optimization problems with objectives being closed-graph multifunctions in Banach spaces. In terms of the coderivatives and Clarke's normal cones, we establish Lagrange multiplier rules for super efficiency as necessary or sufficient optimality conditions of the above problems.     

Using a nonparametric technique to measure the cost efficiency of postal delivery branches

A multiple-input and multiple-output model for measuring the cost efficiency of postal delivery branches is proposed. We analyze the complete postal network of the Serbian post delivery offices, which includes 1,194 post office branches. To compare the branches that operate under the same or similar conditions, the branches are grouped into 18 clusters by implementing the appropriate clustering algorithm. This enables a three-level analysis: branches–clusters–network. The cost efficiency of the branches is measured using data envelopment analysis. The efficiency of a particular cluster is calculated as an average cost efficiency score of the branches that belong to this cluster, and finally, the efficiency of the postal delivery network is assessed. The distribution of cost efficiency scores per clusters takes values from 15 to 92 %. At the level of the total network, the cost efficiency is 40 %, which indicates that there are possibilities for improvement. To obtain more specific guidelines, that is, the decomposition of cost efficiency into pure technical efficiency, the scale efficiency and allocative efficiency were assessed for each cluster and for the total delivery network. This research is beneficial to policy makers defining the scope of universal service obligation and to company managers who want to optimize the postal network. For example, the results of this study indicate that, at a minimum, 794 delivery branches could improve their efficiency by resource reallocation.     

Developing a decomposable measure of profit efficiency using DEA

In for-profit organizations efficiency measurement with reference to the potential for profit augmentation is particularly important as is its decomposition into technical, and allocative components. Different profit efficiency approaches can be found in the literature to measure and decompose overall profit efficiency. In this paper, we highlight some problems within existing approaches and propose a new measure of profit efficiency based on a geometric mean of input/output adjustments needed for maximizing profits. Overall profit efficiency is calculated through this efficiency measure and is decomposed into its technical and allocative components. Technical efficiency is calculated based on a non-oriented geometric distance function (GDF) that is able to incorporate all the sources of inefficiency, while allocative efficiency is retrieved residually. We also define a measure of profitability efficiency which complements profit efficiency in that it makes it possible to retrieve the scale efficiency of a unit as a component of its profitability efficiency. In addition, the measure of profitability efficiency allows for a dual profitability interpretation of the GDF measure of technical efficiency. The concepts introduced in the paper are illustrated using a numerical example.     

The finite-dimensional super integrable system of a super NLS-mKdV equation

Based on the constructed Lie superalgebra, the super Hamiltonian structure of a NLS-mKdV hierarchy is obtained by making use of super-trace identity. Moreover, an explicit super Bargmann symmetry constraint and its associated binary nonlinearization of Lax pairs are carried out for the super NLS-mKdV system.     

The expected value models on Sugeno measure space

Uncertain programming is a theoretical tool to handle optimization problems under uncertain environment. The research reported so far is mainly concerned with probability, possibility, or credibility measure spaces. Up to now, uncertain programming realized in Sugeno measure space has not been investigated. The first type of uncertain programming considered in this study and referred to as an expected value model optimizes a given expected objective function subject to some expected constraints. We start with a concept of the Sugeno measure space. We revisit some main properties of the Sugeno measure and elaborate on the g_λ random variable and its characterization. Furthermore, the laws of the large numbers are discussed based on this space. In the sequel we introduce a Sugeno expected value model (SEVM). In order to construct an approximate solution to the complex SEVM, the ideas of a Sugeno random number generation and a Sugeno simulation are presented along with a hybrid approach.     

The average virtual waiting time as a measure of performance

Under weak conditions the average virtual waiting time converges exponentially fast to its limit. For this reason this quantity has been suggested as a measure of performance for queueing systems. We consider theM/G/1 queue and provide estimation and limiting behaviour of the index of exponential decay.     

The spanning bound as a measure of range query complexity

The subject matter of this paper concerns the complexity of data structures which permit insertions and deletions of records, and range queries of the form Query (Region); Return Σ_{key(r) ? region} value(r) (Region ? Γ), where value(r) (the value associated with a record r) lies in a commutative semigroup S, and Γ denotes a set of regions of the space of possible keys. A combinatorially defined quantity called the spanning bound is defined and is shown to provide a lower bound for the inherent worst case complexity of a sequence of n interminxed insertions, deletions, and range queries. Moreover, the strength of the spanning bound is demonstrated by proving the existence of data structures which come close to achieving it.     

Some properties of the exit measure for super Brownian motion

 We consider the exit measure of super Brownian motion with a stable branching mechanism of a smooth domain D of ℝ ^d . We derive lower bounds for the hitting probability of small balls for the exit measure and upper bounds in the critical dimension. This completes results given by Sheu [22] and generalizes the results of Abraham and Le Gall [2]. Because of the links between exits measure and partial differential equations, those results imply bounds on solutions of elliptic semi-linear PDE. We also give the Hausdorff dimension of the support of the exit measure and show it is totally disconnected in high dimension. Eventually we prove the exit measure is singular with respect to the surface measure on ∂D in the critical dimension. Our main tool is the subordinated Brownian snake introduced by Bertoin, Le Gall and Le Jan [4]. Received: 6 December 1999 / Revised version: 9 June 2000 / Published online: 11 December 2001     

A network efficiency measure with application to critical infrastructure networks

In this paper, we demonstrate how a new network performance/efficiency measure, which captures demands, flows, costs, and behavior on networks, can be used to assess the importance of network components and their rankings. We provide new results regarding the measure, which we refer to as the Nagurney–Qiang measure, or, simply, the N–Q measure, and a previously proposed one, which did not explicitly consider demands and flows. We apply both measures to such critical infrastructure networks as transportation networks and the Internet and further explore the new measure through an application to an electric power generation and distribution network in the form of a supply chain. The Nagurney and Qiang network performance/efficiency measure that captures flows and behavior can identify which network components, that is, nodes and links, have the greatest impact in terms of their removal and, hence, are important from both vulnerability as well as security standpoints.     

The overall efficiency of the dynamic DEA models

Central European Journal of Operations Research - This paper deals with the dynamic efficiency analysis based on Data Envelopment Analysis (DEA) models. Our aim is to formulate new dynamic DEA...     

向量均衡问题的超有效性的对偶形式

在局部凸空间中引进了向量均衡问题的强超有效解、C-强超有效解、弱超有效解, C-弱超有效解、齐次超有效解、 C-齐次超有效解的概念,并在局部凸空间中用极理论为工具讨论了向量均衡问题的 C-弱超有效解, C-超有效解, C-齐次超有效解,以及C-强超有效解的对偶形式. 又在赋范线性空间中讨论了向量均衡问题的以上各种超有效解之间的等价性,并且在赋范线性空间具正规锥的条件下讨论了向量均衡问题的以上各种超有效解的对偶形式. 作为它的应用,给出了向量优化问题各种超有效解的对偶形式.     

A characterization of super efficiency in vector equilibrium problems

In this paper, by using the Baire category theorem we give a characterization of superefficient solution for vector equilibrium problems in Banach space without the ordering cone having a bounded base.     

A dynamic non-parametric measure of output efficiency

A non-parametric programming model for measuring output efficiency that allows for input allocation over finitely many time periods is introduced in this paper. The model thus generalizes the standard non-parametric efficiency measuring models by adding a dynamic aspect to efficiency gauging.     

Encroaching lists as a measure of presortedness

Encroaching lists are a generalization of monotone sequences in permutations. Since ordered permutations contain fewer encroaching lists than random ones, the number of such listsm provides a measure of presortedness with advantages over others in the literature. Experimental and analytic results are presented to cast light on the properties of encroaching lists. Also, we describe a new sorting algorithm,melsort, with complexityO(nlogm). Thus it is linear for well ordered sets and reduces to mergesort andO(nlogn) in the worst case.This work was partially supported by National Science Foundation Grant CCSR-8714565.     

Two-dimensional efficiency decomposition to measure the demand effect in productivity analysis

This paper proposes a two-dimensional efficiency decomposition (2DED) of profitability for a production system to account for the demand effect observed in productivity analysis. The first dimension identifies four components of efficiency: capacity design, demand generation, operations, and demand consumption, using Network Data Envelopment Analysis (Network DEA). The second dimension decomposes the efficiency measures and integrates them into a profitability efficiency framework. Thus, each component’s profitability change can be analyzed based on technical efficiency change, scale efficiency change and allocative efficiency change. An empirical study based on data from 2006 to 2008 for the US airline industry finds that the regress of productivity is mainly caused by a demand fluctuation in 2007-2008 rather than technical regression in production capabilities.