Data envelopment analysis is a method for evaluating the relative efficiency of a collection of decision making units. The DEA classic MODELs calculate each unit’ s efficiency in the best condition, meaning that finds a weight that the DMU is at its maximum efficiency. In this paper, utilizing the directional distance function MODEL in the presence of undesirable outputs, the efficiency of each unit has been calculated in the best and worst condition and an efficiency INTERVAL for each DMU is designated and then with aid from these efficiency INTERVAL, we present an INTERVAL for each unit with a proportionate Malmquist productivity index, that these INTERVALs indicate the progression or regression of each DMU.

Recently the concept of facility efficiency, which defined by data envelopment analysis (DEA), introduced as a location MODELing objective, that provides facilities location’s effect on their performance in serving demands. By combining the DEA MODELs with the location problem, two types of “efficiencies” are optimized: spatial efficiency which measured by finding the least cost location and allocation patterns for facilities, and the facility efficiency in serving demands which measured by DEA efficiency score. In this paper, location-allocation MODELs with DEA in INTERVAL inputs and outputs environments are combined. A new pair of INTERVAL DEA/location MODELs are constructed and run.

This paper proposes an alternative approach for efficiency analysis when a set of DMUs uses INTERVAL scale variables in the productive process. To test the influence of these variables, we present a general approach of deriving DEA MODELs to DEAl with the variables. We investigate a number of performance measures with unrestricted-in-sign INTERVAL and/or INTERVAL scale variables.

In this article, we investigate the measurement of performance in DMUs in which input and/or output values are given as imprecise data. By imprecise data, we mean that in some cases, we only know that the actual values are inside certain INTERVALs, and in other cases, data are specified only as ordinal preference information. In this article, we present two distinct perspectives for determining the upper and lower bounds of the efficiency the DMU under evaluation can have with imprecise data: (1) The optimistic perspective, which uses DEA-efficient production frontier, and seeks the best score among various values of the efficiency score; the measured efficiency in this perspective is called the best relative efficiency or the optimistic efficiency. (2) The pessimistic perspective, which uses inefficiency frontier, also called input frontier, and seeks the lowest score among various values of the efficiency score; the measured efficiency in this perspective is called the worst relative efficiency or the pessimistic efficiency. For this reason and contrary to some DEA-related studies, we do not restrict our attention only to precise data. We will investigate a more general case of DEAling with imprecise data, providing a method for obtaining the upper and lower bounds of efficiency. Two numerical examples will be presented to illustrate the application of the proposed DEA approach.‎‎

In this paper we extend the concept of "cost minimizing industry structure" and develop two DEA MODELs for DEAling with imprecise data. The main aim of this study is to propose an approach to compute the industry cost efficiency measure in the presence of INTERVAL data. We will see that the value obtained by the proposed approach is an INTERVAL value. The lower bound and upper bound of the INTERVAL industry cost efficiency measure are computed and then decomposed into three components to examine the relationship between them and the lower and upper bounds of the individual INTERVAL cost efficiency measures. We also define the cost efficient organization of the industry as a set of DMUs, which minimizes the total cost of producing the INTERVAL industry output vector. In fact, this paper determines the optimal number of DMUs and the reallocation of the industry observed outputs among them. We hereby determine the effects of the optimal number of DMUs and the reallocation of outputs among them on the INTERVAL industry cost efficiency measure. Finally, a numerical example will be presented to illustrate the proposed approach.

In the classical data envelopment analysis (DEA) MODELs, inputs and outputs are assumed as known variables, and these MODELs cannot DEAl with unknown amounts of variables directly. In recent years, there are few researches on handling missing data. This paper suggests a new INTERVAL based approach to apply missing data, which is the modified version of Kousmanen (2009) approach. First, the proposed approach suggests using an acceptable range for missing inputs and outputs, which is determined by the decision maker (DM). Then, applying the least favourable bounds of missing data along with using the proposed range is suggested in estimating the production frontier. A data set is used to illustrate the approach.

Data envelope analysis (DEA) is an approach to estimate the relative efficiency of decision making units (DMUs). Several studies were conducted in order to prioritize efficient units and some useful MODELs such as cross-efficiency matrix (CEM) were presented. Besides, a number of DEA MODELs with INTERVAL data have been developed and ranking DMUs with such data was solved. However, presenting an obtained crisp data derived INTERVAL data is a critical problem, so that many researches were implemented so as to compute weights and averaging the INTERVAL data. In this paper we propose the new algorithm to find more suitable weight applying a data mining approach of DMU’s data. For this purpose, we employed clustering and pair-wise comparison matrix on given relative efficiency from CEM. Results indicate there is meaningful different between efficiency of DMUs with lower bound and that of DMUs with upper bound.

In this paper, the difference between multiplicative and envelopment MODELs of network DEA is examined, in which network DEA multiplicative MODEL is able to calculate efficiency and the envelopment MODEL can calculate the projection on the frontier. Here, a MODEL is presented that can calculate both frontier projection and efficiency in network DEA. Since in real world, many data are INTERVAL data, we present a MODEL in this article that calculates the efficiency of the units being evaluated by such these INTERVAL data. Since data are as INTERVALs, the resulting efficiencies are calculated as INTERVALs. We present two MODELs for calculating the lower and upper bounds for any DMU and prove that these MODELs giveupper and lower bounds of efficiency.

The data envelopment analysis MODEL (DEA) is the appropriate approach in measuring the efficiency of corporation, while in this MODEL the decision maker is unable to enter the risk condition and the time factors in the results. On the order hand, in the agricultural investigations, the decision maker faces the risk condition and productivity problem. Basically the INTERVAL data envelopment analysis (IDEA) is a useful instrument in measuring the efficiency of several corporations with attention to risk condition and imprecise data, when also Window DEA prepares feasibility calculation of productivity. In this study, with taking advantage from IDEA and Window DEA techniques, the technical efficiency of important provinces in production of wheat crop is determined. The results show that among the selected provinces during period 1999-2004 Khoozestan has the highest ranking in productivity whereas Hamadan and East Azarbaijan have the lowest in their agricultural sectors. Also with attention to risk factor, Fars has the highest ranking in efficiency while Kordestan has the lowest in farming wheat.