In recent years, fair allocation of resources or fixed costs in DEA have been noticed by researches, in which the main objective is unchanging efficiency of decision making units, In which the main purpose is to not change the efficiency of decision-making units before and after the allocation of costs. On the other hand, all studies have been due to the fraction-scale data, and any special attention have not been paid to an interval-scale data so far, because of the ratio of the measurement on such a scale are meaningless. Therefore, the structure of this paper is to study the use of an interval-scale and fractional data in a fair allocation of costs between the units such that the principle of unchanging efficiency remains in the presence of such data.

Many models in DEA have been proposed to estimate returns to scale. Determining the nature of returns to scale has considerable of importance in the theory of production.Knowing the fact that returns to scale is a constant, ascending or descending decision making unit, proper actions can be performed to develop the decision making units. In this study, the efficiency of parallel production systems with shared resources is evaluated such that the data is inexact and interval, so the function of these systems is interval too.Then a model is proposed to estimate returns to scale of interval data on these systems; when the data is inexact, the nature of returns to scale of these units is inexact too, so returns to scale is estimated as multiple in best and worst conditions.

Data Envelopment Analysis (DEA) models with interval inputs and outputs have been rarely discussed in DEA literature. This paper, using the enhanced Russell measurement proposes an extended model which permits the presence of interval scale variables which can take both negative and positive values. The model is compared with most well-known DEA models of which include the CCR model, the BCC model and the additive model. An empirical data set is used to illustrate the model.

Unemployment is one of the most important economic problems in Iran, so that many of its managers plan to increase employment rates. Increasing the employment rate needs to increase economic productivity which DEA is one of the most appropriate evaluation methods for estimating the productivity of similar organizations. Employment in the amount of data input and output can be just interval. In this study by solving two models, using one of which the upper bound for efficiency and using the other, the lower bound for decision making units efficiency is acquired, we provide a new model for Most productive scale size with interval data. The main purpose of this study is to determine the productivity of Iran and sensitive indicators to provide a fundamental solution to exit from unemployment. The economic sector managers can do more exact planning for economic growth.

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.