An extended slacks-based measure model for data envelopment analysis with negative data

Data envelopment analysis (DEA) is a non-parametric approach based on linear programming that has been widely applied for evaluating the relative efficiency of a set of homogeneous decision-making units (DMUs) with multiple inputs and outputs. The original DEA models use positive input and output variables that are measured on a ratio scale, but these models do not apply to the variables in which negative data can appear. However, with the widespread use of interval scale data and undesirable data, the emphasis has been directed towards the simultaneous consideration of the positive and negative data in DEA models. In this paper, using the slacks-based measure, we propose an extended model to evaluate the efficiency of DMUs, even if some variables are measured on an interval scale and some on a ratio scale. Moreover, the extended model allows for the presence of all interval-scale variables, which are capable of taking both negative and positive values.     

A simplified version of the DEA cost efficiency model

This short paper deals with a current cost efficiency model and decreases the number of its constraints as well as its variables, which leads to a strong reduction in the computational requirements.     

Finding the efficiency score and RTS characteristic of DMUs by means of identifying the efficient frontier in DEA

Data envelopment analysis (DEA) is basically a linear programming based technique used for measuring the relative performance of organizational units, referred to as decision-making units (DMUs), where the presence of multiple inputs and outputs makes comparisons difficult. The ability of identifying frontier DMUs prior to the DEA calculation is of extreme importance to an effective and efficient DEA computation. In this paper, a method for identifying the efficient frontier is introduced. Then, the efficiency score and returns to scale (RTS) characteristic of DMUs will be produced by means of the equation of efficient frontier.     

The diffraction of elastic waves by an imperfect fusion bond

We consider diffraction by a semi-infinite crack located alonga fusion interface between two differing elastic media. Twotypes of crack, namely open and partially closed cracks, areinvestigated. An open crack is modelled by a stress-free contactboundary condition and a partially closed crack is modelledby a spring contact boundary condition. For the latter, thejump in the stress across the crack is assumed to be proportionalto the jump in the displacement across the crack. This situationarises in, for example, a K-weld where the fine grain of theparent material (for example, ferritic or forged austeniticsteel) is in stark contrast with the coarse-grained weld metal(for example, austenitic weld metal). In the metal weld thedirection of the grain axis varies through the metal. However,diffraction is a local phenomenon and so the austenitic steelis assumed to have a zonal axis so that it may be modelled bya transversely isotropic composite. The ferritic or forged austeniticsteel will be modelled as an isotropic material.     

Selecting symmetric weights as a secondary goal in DEA cross-efficiency evaluation

In data envelopment analysis (DEA), the cross-efficiency evaluation method introduces a cross-efficiency matrix, in which the units are self and peer evaluated. A problem that possibly reduces the usefulness of the cross-efficiency evaluation method is that the cross-efficiency scores may not be unique due to the presence of alternate optima. So, it is recommended that secondary goals be introduced in cross-efficiency evaluation. In this paper we propose the symmetric weight assignment technique (SWAT) that does not affect feasibility and rewards decision making units (DMUs) that make a symmetric selection of weights. A numerical example is solved by our proposed method and its solution is compared with those of alternative approaches.     

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.     

Nonsmooth multiobjective optimization using limiting subdifferentials

In this study, using the properties of limiting subdifferentials in nonsmooth analysis and regarding a separation theorem, some weak Pareto-optimality (necessary and sufficient) conditions for nonsmooth multiobjective optimization problems are proved.     

Inverse DEA under inter-temporal dependence using multiple-objective programming

This paper deals with the inverse Data Envelopment Analysis (DEA) under inter-temporal dependence assumption. Both problems, input-estimation and output-estimation, are investigated. Necessary and sufficient conditions for input/output estimation are established utilizing Pareto and weak Pareto solutions of linear multiple-objective programming problems. Furthermore, in this paper we introduce a new optimality notion for multiple-objective programming problems, periodic weak Pareto optimality. These solutions are used in inverse DEA, and it is shown that these can be characterized by a simple modification in weighted sum scalarization tool.     

Efficiency Analysis and Ranking of DMUs with Fuzzy Data

In this paper, a fuzzy version of CCR model (Charnes, Cooper and Rhodes (1978)) with asymmetrical triangular fuzzy number is presented and a procedure is suggested for its solution. The basic idea is to transform the fuzzy CCR model into a crisp linear programming problem by applying an alternative -cut approach. Thereby, the problem is converted to an interval programming. In this method, instead of comparing the equality (or inequality) of two intervals, a variable is defined in the interval, not only satisfies the set of constraints, but also maximizes the efficiency value. We also propose a ranking method for fuzzy DMUs using presented fuzzy DEA approach. To demonstrate the concept, numerical examples are solved and solutions are compared with Guo and Tanaka (2001).