Data envelopment scenario analysis with imprecise data

In the existing DEA models, we have a centralized decision maker (DM) who supervises all the operating units. In this paper, we solve a problem in which the centralized DM encounters limited or constant resources for total inputs or total outputs. We establish a DEA target model that solves and deals with such a situation. In our model, we consider the decrease of total input consumption and the increase of total output production; however, in the existing DEA models, total output production is guaranteed not to decrease. Considering the importance of imprecise data in organizations, we define our model so as to deal with interval and ordinal data. A numerical illustration is provided to show the application of our model and the advantages of our approach over the previous one.     

Ranking DMUs by ideal points with interval data in DEA

An original DEA model is to evaluate each DMU optimistically, but the interval DEA model proposed in this paper has been formulated to obtain an efficiency interval consisting of evaluations from both the optimistic and the pessimistic viewpoints.     

Target setting in data envelopment analysis using MOLP

Data envelopment analysis (DEA) and multiple objective linear programming (MOLP) can be used as tools in management control and planning. The existing models have been established during the investigation of the relations between the output-oriented dual DEA model and the minimax reference point formulations, namely the super-ideal point model, the ideal point model and the shortest distance model. Through these models, the decision makers’ preferences are considered by interactive trade-off analysis procedures in multiple objective linear programming. These models only consider the output-oriented dual DEA model, which is a radial model that focuses more on output increase. In this paper, we improve those models to obtain models that address both inputs and outputs. Our main aim is to decrease total input consumption and increase total output production which results in solving one mathematical programming model instead of n models. Numerical illustration is provided to show some advantages of our method over the previous methods.     

Optical properties of frustrated cholesteric liquid crystals in planar cell

ABSTRACT

We investigated the alignment director of a frustrated cholesteric liquid crystal (CLC) confined in a planar cell. Three cells with different confinement ratio (c?=?d/p) (where p is the pitch and d is the cell thickness) are prepared. Under an electric field, the CLC planar texture is transformed into a cholesteric fingerprint (CF). The results showed that CF contrast depends on c. When c?≈?2, CLC stripes are formed by a periodic CF, with a period equal to the CLC pitch. The CF is developed and slowly extended to the whole cell surface along the rubbing direction and the contrast of the grating stripes keeps unchangeable. Yet, the CLC finger borders have a different light intensity. However, when c?≈?1, the CF contrast increases with time. When c?θ between the polarizer and the CFs.     

Sensitivity and stability analysis on the first and second levels of efficiency score relative to data error

In data envelopment analysis (DEA), efficient decision making units (DMUs) are of primary importance as they define the efficient frontier. The current paper develops a new sensitivity analysis approach for a category DMUs and finds the stability radius for all efficient DMUs. By means of combining some classic DEA models and with the condition that the efficiency scores of efficient DMUs remain unchanged, we are able to determine what perturbations of the data can be tolerated before efficient DMUs become inefficient. Our approach generalizes the conventional sensitivity analysis approach in which the inputs of efficient DMUs increase and their outputs decrease, while the inputs of inefficient DMUs decrease and their outputs increase. We find the maximum quantity of perturbations of data so that all first level efficient DMUs remain at the same level.     

A posteriori analysis: error estimation for the eighth order boundary value problems in reproducing Kernel space

In the previous work (Akram and Rehman Numer. Algor. 62 527–540 2013), Akram and Rehman presented the reproducing kernel method (RKM) for solving various eighth order boundary value problems. However, an effective error estimation for this method has not yet been discussed. This work is devoted to deal with this problem. Some other aspects of the RKM will be considered such as convergence analysis and numerical implementations.     

A linear programming approach to test efficiency in multi-objective linear fractional programming problems

In a multi-objective linear fractional programming problem (MOLFPP), it is often useful to check the efficiency of a given feasible solution, and if the solution is efficient, it is useful to check strong or weak efficiency. In this paper, by applying a geometrical interpretation, a linear programming approach is achieved to test weak efficiency. Also, in order to test strong efficiency for a given weakly efficient point, a linear programming approach is constructed.     

Isoperimetric Inequalities for a Wedge-Like Membrane

For a wedge-like membrane, Payne and Weinberger proved in 1960 an isoperimetric inequality for the fundamental eigenvalue which in some cases improves the classical isoperimetric inequality of Faber–Krahn. In this work, we introduce “relative torsional rigidity” for this type of membrane and prove new isoperimetric inequalities in the spirit of Saint-Venant, Pólya–Szeg?, Payne, Payne–Rayner, Chiti, and Talenti, which link the eigenvalue problem with the boundary value problem in a fundamental way.     

Green Function Bounds and Parabolic Potentials on a Half-Space

By proving a lower and an upper bound for Green's function of certain parabolic operators with Lipschitz coefficients in 0\} {\text{ and }}0 < T < + \infty $$ " align="middle" border="0"> , we give a characterization of the associated parabolic potentials and we study in a last part the boundary behaviour of these potentials for n=1.