With a brief review of the studies on the industry in Data Envelopment Analysis (DEA) framework, the present paper proposes inner and outer technologies when only some basic information is available about the technology. Furthermore, applying Linear Programming techniques, it also determines lower and upper bounds for directional distance function (DDF) measure, overall and allocative efficiency in industry level. Finally, the results are illustrated using a Cobb-Douglas function.

In production theory, it is necessary to be capable of predicting the production func- tion’s long-run behaviors. Hereof, returns to scale is a helpful concept. Returns to scale describes the reaction of a production function to the proportionally scaling all its input variables. In this regard, Data envelopment analysis (DEA) provides a com- prehensive framework for returns to scale evaluation. A sequence of attempts has been made on the subject of returns to scale in DEA literature which cause DEA to be ex- panded to widespread applications. Centralization of carried out studies in firm level, on one hand, and the importance of economical inter-operation in performance analysis in industry level, on the other hand, were the main motivation to start a new range of studies around identifying the return to scale in industry level. This paper collaborates interesting relations between firms and industry technology with performance analysis techniques to extract a relation between returns to scale status of firms and system-wide unit based on the reference set method.

In recent years, the notion of scale elasticity—the relative changes of outputs with respect to relative changes of inputs—has received a lot of ink in the literature. However, all prior studies, except a few of them, assume that changes are equi-proportional. This simplifying assumption makes scale elasticity measure to preserve the throughput mix and implicitly ignores both input independencies and decision-maker preferences. This paper seeks to investigate two main objectives. It initially proposes the notion of directional scale elasticity to allow evaluation of elasticity in any direction which may naturally alter the mix. Subsequently, by providing a tangible geometric interpretation, it attempts to clarify the measure. Relevant computations are used to construct cross sections of frontier in a given direction by enlisting the advantages of parametric optimization algorithm.

In this paper, the notion of scale elasticity is initially developed for models with non-discretionary inputs. A new unified formulation, resembling those for classic developments is proposed for computation of scale elasticity in presence of exogenously fixed inputs in the framework of date envelopment analysis.

In order to remove the harshness of fixed inputs, we invoke regression of fixed inputs over efficiency measures and therefore units with more favorable environment indices are discounted for pioneers set. This naturally implies that different production possibility sets are induced according to environmental affect. Scale elasticity is then computed using indirect approach for both differentiable and non-differentiable cases.

Also, the approach is illustrated with numerical examples and proved its benefit over selective approach, proposed by Podinovski and Førsund, by comparing and contrasting with numerical data. Moreover, the geometry and rationale behind the notion are described.

Multiple attribute decision making forms an important part of the decision process for both small (individual) and large (organization) problems. When available information is precise, many methods exist to solve this problem. But the uncertainty and fuzziness inherent in the structure of information make rigorous mathematical models inappropriate for solving this type of problems. This paper incorporates the fuzzy set theory and the basic nature of subjectivity due to the ambiguity to achieve a flexible decision approach suitable for uncertain and fuzzy environment. The proposed method can take both real and fuzzy inputs. An outranking intensity is introduced to determine the degree of overall outranking between competing alternatives, which are represented by fuzzy numbers. Numerical examples finally illustrate the approach.

This paper incorporates the basic concepts of subjectivity with the objective of decision theory to develop a method which intellectualizes ambiguity into multiple-criteria decision-making (MCDM) problems. An outranking intensity is introduced to determine the degree of overall outranking between competing alternatives, which are represented by fuzzy numbers. The comparison of these degrees is made through the concept of overall existence ranking index. Comparative examples, as well as a case study, are given to illustrate the approach.