بهروز دانشیان

In measuring the efficiency of a set of units over a period of time covering multiple periods, models based on the standard DEA technique ignore the status of each unit in each period that causes misleading results. This paper develops DEA-R models in the presence of multi-periodic data in such a way that the proposed method can evaluate the overall efficiency with respect to the overall and periodic efficiencies of all units. By providing a lower bound on the weights derived from periods, the proposed method prioritizes the units for yielding valuable insights that aid decision makers to better understand the findings from a performance evaluation process. The contribution of this paper is fourfold: (1) the overall efficiency calculated from the proposed method depends on the unit performance of all units in all periods, (2) the proposed method determines the overall efficiency by imposing a lower bound obtained from all periods on the weights, (3) this method endowed with a high discriminatory power in differentiating the units which are evaluated as efficient in the existing multi-period models, (4) To elucidate the details of the proposed method, a comparison is made between the existing models in the literature and the proposed multi-period DEA-R method to measure the efficiency of 22 Taiwanese commercial banks for the period of 2009–2011.

Standard Data Envelopment Analysis (DEA) models measures the efficiency of Decision Making Units (DMUs) in a period of time. In real occasions, multi periods are presented. In presence of a multi-period system, overall efficiency depends on the performance of the DMU in all periods. That is to say, periodic efficiencies must be calculated, also, the overall efficiency is depended to periodic efficiencies. In other words, a DMU cannot be overall efficient, but considered as an efficient unit in each separate period. Hence, the question of pseudo inefficiency is raised?

This paper investigates Ratio-based Data Envelopment Analysis (DEA-R) models to detect pseudo inefficiency in multi-period systems.

The proposed algorithm consists of three steps. As the first step, the average of period-efficiencies is calculated, then the overall efficiency is evaluated as a block-box. For the last step, a ratio of two quantities is estimated. If this ratio is close to unity, there is no significant difference between these two quantities. Otherwise, the estimate claims pseudo inefficiency.

Originality/Value:

 In the literature, pseudo inefficiency has been detected through applying the periodic weights, but this paper proposes a three-step algorithm to investigate pseudo inefficiency. To elucidate the details of the proposed approach, a comparison is made between Kao and Liu [8] and the proposed algorithm to measure the efficiency of 22 Taiwanese commercial banks for the period 2009-2011. The results demonstrate the practicality and superiority of the proposed method in comparison with the existing multi-period models.

The providing a proposed model pair for ranking interval data and their application to evaluate and improve the performance of a service system using results of simulation.

Mathematical techniques (data envelopment analysis) and computer simulation.

By presenting proposed models pair, we were able to improve the performance of a service system by simulating different scenarios for that system. The results show that the introduced scenario could increase the efficiency of system by 22%.

 Introducing new applied methods using mathematical models (Data Envelopment Analysis) and simulations to improve the performance of systems

This paper proposes a DEA-based model for analyze the fuzzy risk in project selection. We used concept semi-variance for measure upper and downside risk and a DEA model for Classification desirable and undesirable risk. Firstly, the proposed model includes new desirable and undesirable risk-return indexes. Thus a novel DEA model is presented for evaluation and Classification desirable and undesirable risks and finally, is extend to fuzzy DEA model for project portfolio selection. An applied example is used to explain the proposed approach and usefulness and applicability of this approach have been illustrated using the 37 available projects.

Some researchers deals to estimation of some of the influences factors in efficiency score in which the DMU, maintains or improves its current efficiency level. This problems are considered in a general framework which is called inverse DEA. This paper studies the inverse data envelopment analysis. The issue of input or output estimation has been examined with improvement in unit efficiency.Therefore, in this paper, by increasing the level of undesirable inputs and the level of desired outputs of decision-making units along with improvements in the efficiency of the decision-maker, the level of changes in the level of desired inputs and the level of undesirable outputs is estimated. To do this, we consider the data as Interval data and then use the inverse DEA method using a multi-objective linear programming model (MOLP), so that the unit performance under evaluation is improved. The following is an applied example of the proposed method.

Trade-off between objective functions in multi-objective optimization is one of the tools for interpreting and studying efficient solutions. Properly efficient solutions are one of the most important theoretical and practical concepts that represent the behavior of the objective functions during a process change. Actually, these solutions are those efficient solutions that filter the anomalies of objective functions at some points, and this will help the manager to decision making to choose more important solutions. One of the most important tools for obtaining solutions with bounded trade-off in multi-objective optimization field is the Sum weighted scalarization method, which many authors have been studying it in interactive optimization field. This paper provides a method for obtaining properly efficient solutions near the ideal point with a theoretical and interactive view and using Sum weighted scalarization method. Since being near to ideal point will be abele to a preference of decision maker; this method examines the preferences of the decision maker without sacrifice the theory. Therefore, this paper presents an approach to finding properly efficient solutions near to the ideal point.

In assessing the relative efficiency of decision-maker units by classical Data Envelopment Analysis (DEA) models, the status of the data is determined from the input or output points of views. In real issues, there are some data whose statuses are debatable. Some decision making units consider them as input to achieve higher efficiency while some other decision making units consider them as output, but these data are known as flexible variables. Thus, these data are known as flexible variables. Several parametric and non-parametric models have been introduced for categorizing such data. In most of the status-oriented models (input or output based) introduced to determine the status of flexible data, different statuses of a model can produce different results in determining the statuses of the flexible variable. In non-status models, the value of M is also used to select the main constraint and to remove the waste constraints. In these models, by choosing different values for M, different results are achieved in determining the status of the flexible variable, the efficiency and return to scale of decision-making units. To solve these problems in DEA, a non-status model is proposed which, in addition to determining the status of the flexible variable, can obviate the computational error, and the problems caused by the presence of M in the model. The advantages of the proposed model are compared with other models with an empirical example.