Finding weak defining hyperplanes of PPS of the BCC model

Production possibility set (PPS) is intersection of the several halfspaces. Every halfspace corresponds with one strong or weak defining hyperplane (facet). This research proposes a method to find weak defining hyperplanes of PPS of BCC model. We state and prove some properties relative to our method. Numerical examples are provided for illustration.     

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.     

Improving discrimination in data envelopment analysis: PCA–DEA or variable reduction

Within the data envelopment analysis context, problems of discrimination between efficient and inefficient decision-making units often arise, particularly if there are a relatively large number of variables with respect to observations. This paper applies Monte Carlo simulation to generalize and compare two discrimination improving methods; principal component analysis applied to data envelopment analysis (PCA–DEA) and variable reduction based on partial covariance (VR). Performance criteria are based on the percentage of observations incorrectly classified; efficient decision-making units mistakenly defined as inefficient and inefficient units defined as efficient. A trade-off was observed with both methods improving discrimination by reducing the probability of the latter error at the expense of a small increase in the probability of the former error. A comparison of the methodologies demonstrates that PCA–DEA provides a more powerful tool than VR with consistently more accurate results. PCA–DEA is applied to all basic DEA models and guidelines for its application are presented in order to minimize misclassification and prove particularly useful when analyzing relatively small datasets, removing the need for additional preference information.     

Sorting with networks of data structures

We consider the problem of sorting a permutation using a network of data structures as introduced by Knuth and Tarjan. In general the model as considered previously was restricted to networks that are directed acyclic graphs (DAGs) of stacks and/or queues. In this paper we study the question of which are the smallest general graphs that can sort an arbitrary permutation and what is their efficiency. We show that certain two-node graphs can sort in time Θ(n²) and no simpler graph can sort all permutations. We then show that certain three-node graphs sort in time Ω(n^3/2), and that there exist graphs of k nodes which can sort in time Θ(nlog_kn), which is optimal.     

Input/output selection in DEA under expert information,with application to financial markets

Data envelopment analysis (DEA), as generally used, assumes precise knowledge regarding which variables are inputs and outputs; however, in many applications, there exists only partial knowledge. This paper presents a new methodology for selecting input/output variables endogenously to the DEA model in the presence of partial (or expert’s) knowledge by employing a reward variable observed exogenous to the operation of the DMUs. The reward is an allocation of a limited resource by an external agency, e.g. capital allocation by a market, based on the perceived internal managerial efficiencies. We present an iterative two-stage optimization model which addresses the benefit of possibly violating the expert information to determine an optimal internal performance evaluation of the DMUs for maximizing its correlation with the reward metric. Theoretical properties of the model are analyzed and statistical significance tests are developed for the marginal value of expert violation. The methodology is applied in Fundamental Analysis of publicly-traded firms, using quarterly financial data, to determine an optimized DEA-based fundamental strength indicator. More than 800 firms covering all major sectors of the US stock market are used in the empirical evaluation of the model. The firms so-screened by the model are used within out-of-sample mean-variance long-portfolio allocation to demonstrate the superiority of the methodology as an investment decision tool.     

Stochastic DEA with ordinal data applied to a multi-attribute pricing problem

Multiple attribute pricing problems are highly challenging due to the dynamic and uncertain features in the associated market. In this paper, we address the condominium multiple attribute pricing problem using data envelopment analysis (DEA). In this study, we simultaneously consider stochastic variables, non-discretionary variables, and ordinal data, and present a new type of DEA model. Based on our proposed DEA, an effective performance measurement tool is developed to provide a basis for understanding the condominium pricing problem, to direct and monitor the implementation of pricing strategy, and to provide information regarding the results of pricing efforts for units sold as well as insights for future building design. A case study is executed on a leading Canadian condominium developer.     

An epsilon-based measure of efficiency in DEA – A third pole of technical efficiency

In DEA, we have two measures of technical efficiency with different characteristics: radial and non-radial. In this paper we compile them into a composite model called “epsilon-based measure (EBM).” For this purpose we introduce two parameters which connect radial and non-radial models. These two parameters are obtained from the newly defined affinity index between inputs or outputs along with principal component analysis on the affinity matrix. Thus, EBM takes into account diversity of input/output data and their relative importance for measuring technical efficiency.     

Ranking decision-making units using common weights in DEA

Data envelopment analysis (DEA) is a linear programming technique that is used to measure the relative efficiency of decision-making units (DMUs). Liu et al. (2008) [13] used common weights analysis (CWA) methodology to generate a CSW using linear programming. They classified the DMUs as CWA-efficient and CWA-inefficient DMUs and ranked the DMUs using CWA-ranking rules. The aim of this study is to show that the criteria used by Liu et al. are not theoretically strong enough to discriminate among the CWA-efficient DMUs with equal efficiency. Moreover, there is no guarantee that their proposed model can select one optimal solution from the alternative components. The optimal solution is considered to be the only unique optimal solution. This study shows that the proposal by Liu et al. is not generally correct. The claims made by the authors against the theorem proposed by Liu et al. are fully supported using two counter examples.     

General and multiplicative non-parametric corporate performance models with interval ratio data

The increasing intensity of global competition has led organizations to utilize various types of performance measurement tools for improving the quality of their products and services. Data envelopment analysis (DEA) is a methodology for evaluating and measuring the relative efficiencies of a set of decision making units (DMUs) that use multiple inputs to produce multiple outputs. All the data in the conventional DEA with input and/or output ratios assumes the form of crisp numbers. However, the observed values of data in real-world problems are sometimes expressed as interval ratios. In this paper, we propose two new models: general and multiplicative non-parametric ratio models for DEA problems with interval data. The contributions of this paper are fourfold: (1) we consider input and output data expressed as interval ratios in DEA; (2) we address the gap in DEA literature for problems not suitable or difficult to model with crisp values; (3) we propose two new DEA models for evaluating the relative efficiencies of DMUs with interval ratios, and (4) we present a case study involving 20 banks with three interval ratios to demonstrate the applicability and efficacy of the proposed models where the traditional indicators are mostly financial ratios.     

3D HYBRID DEPTH MIGRATION AND FOUR-WAY SPLITTING SCHEMES

The alternately directional implicit （ADI） scheme is usually used in 3D depth migration. It splits the 3D square-root operator along crossline and inline directions alternately. In this paper, based on the ideal of data line, the four-way splitting schemes and their splitting errors for the finite-difference （FD） method and the hybrid method are investigated. The wavefield extrapolation of four-way splitting scheme is accomplished on a data line and is stable unconditionally. Numerical analysis of splitting errors show that the two-way FD migration have visible numerical anisotropic errors, and that four-way FD migration has much less splitting errors than two-way FD migration has. For the hybrid method, the differences of numerical anisotropic errors between two-way scheme and four-way scheme are small in the case of lower lateral velocity variations. The schemes presented in this paper can be used in 3D post-stack or prestack depth migration. Two numerical calculations of 3D depth migration are completed. One is the four-way FD and hybrid 3D post-stack depth migration for an impulse response, which shows that the anisotropic errors can be eliminated effectively in the cases of constant and variable velocity variations. The other is the 3D shot-profile prestack depth migration for SEG/EAEG benchmark model with two-way hybrid splitting scheme, which presents good imaging results. The Message Passing Interface （MPI） programme based on shot number is adopted.