Computational strategy for Russell measure in DEA: Second-order cone programming

In aggregation for data envelopment analysis (DEA), a jointly measured efficiency score among inputs and outputs is desirable in performance analysis. A separate treatment between output-oriented efficiency and input-oriented efficiency is often needed in the conventional radial DEA models. Such radial measures usually need to measure both that a current performance attains an efficiency frontier and that all the slacks are zero on optimality. In the analytical framework of the radial measure, Russell measure is proposed to deal with such a difficulty. A major difficulty associated with the Russell measure is that it is modeled by a nonlinear programming formulation. Hence, a conventional linear programming algorithm, usually applied for DEA, cannot solve the Russell measure. This study newly proposes a reformulation of the Russell measure by a second-order cone programming (SOCP) model and applies the primal–dual interior point algorithm to solve the Russell measure.     

Variables reduction in data envelopment analysis

In real applications of data envelopment analysis (DEA), there are a number of pitfalls that could have a major influence on the efficiency. Some of these pitfalls are avoidable and the others remain problematic. One of the most important pitfalls that the researchers confront is the closeness of the number of operational units and the number of inputs and outputs. In performance measurement using DEA, the closeness of these two numbers could yield a large number of efficient units. In this article, some inputs or outputs will be aggregated and the number of inputs and outputs are reduced iteratively. Numerical examples show that in comparison to the single DEA method, our approach has the fewest efficient units. This means that our approach has a superior ability to discriminate the performance of the DMUs.     

Data envelopment analysis vs. principal component analysis: An illustrative study of economic performance of Chinese cities

This article compares two approaches in aggregating multiple inputs and multiple outputs in the evaluation of decision making units (DMUs), data envelopment analysis (DEA) and principal component analysis (PCA). DEA, a non-statistical efficiency technique, employs linear programming to weight the inputs/outputs and rank the performance of DMUs. PCA, a multivariate statistical method, combines new multiple measures defined by the inputs/outputs. Both methods are applied to three real world data sets that characterize the economic performance of Chinese cities and yield consistent and mutually complementary results. Nonparametric statistical tests are employed to validate the consistency between the rankings obtained from DEA and PCA.     

On the quality of the data envelopment analysis model

The user of data envelopment analysis (DEA) has little available guidance on model quality. The technique offers none of the misspecification tests or goodness of fit statistics developed for parametric statistical methods. Yet, if a DEA model is to guide managerial policy, the quality of the model is of crucial importance. This paper suggests four alternative purposes of DEA modelling, and offers four measures of the quality of a DEA model which reflect those purposes. Using Monte Carlo simulation methods, it explores the performance of DEA under a wide variety of assumptions. It notes that four issues will have an important influence on model results: the distribution of true efficiencies in the study sample; the size of the sample; the number of inputs and outputs included in the analysis; and the degree of correlation between inputs and outputs. The paper concludes that any judgement about the reliability of model results must be dependent on the objective of the analysis.     

Modeling undesirable factors in data envelopment analysis

Data envelopment analysis is a mathematical programming technique for identifying efficient frontiers for peer decision making units with multiple inputs and multiple outputs. These performance factors (inputs and outputs) are classified into two groups: desirable and undesirable. Obviously, undesirable factors in production process should be reduced to improve the performance. In the current paper, we present a data envelopment analysis (DEA) model in which can be used to improve the relative performance via increasing undesirable inputs and decreasing undesirable outputs.     

Past-present-future Intertemporal DEA models

It has been well recognized that to thoroughly evaluate a firm’s performance, the evaluator must assess not only its past and present records but also future potential. However, to the best of our knowledge, there are no data envelopment analysis (DEA)-type models proposed in the literature that simultaneously take past, present and, especially, future performance indicators into account. Hence, this research aims at developing a new type of DEA model referred to as Intertemporal DEA models that can be used to fully measure a firm’s efficiency by explicitly considering its key inputs and outputs involving the past-present-future time span. In this research, the proposed Intertemporal DEA models are applied to the performance evaluation of high-tech Integrated Circuit design companies in Taiwan to demonstrate their advantages over other DEA models that ignore intertemporal efficiency.     

Data Envelopment Analysis with Preference Structure

It is important to consider the decision making unit (DMU)'s or decision maker's preference over the potential adjustments of various inputs and outputs when data envelopment analysis (DEA) is employed. On the basis of the so-called Russell measure, this paper develops some weighted non-radial CCR models by specifying a proper set of ‘preference weights’ that reflect the relative degree of desirability of the potential adjustments of current input or output levels. These input or output adjustments can be either less or greater than one; that is, the approach enables certain inputs actually to be increased, or certain outputs actually to be decreased. It is shown that the preference structure prescribes fixed weights (virtual multiplier bounds) or regions that invalidate some virtual multipliers and hence it generates preferred (efficient) input and output targets for each DMU. In addition to providing the preferred target, the approach gives a scalar efficiency score for each DMU to secure comparability. It is also shown how specific cases of our approach handle non-controllable factors in DEA and measure allocative and technical efficiency. Finally, the methodology is applied with the industrial performance of 14 open coastal cities and four special economic zones in 1991 in China. As applied here, the DEA/preference structure model refines the original DEA model's result and eliminates apparently efficient DMUs.     

Returns to scale in dynamic DEA

Two different types of inputs (variable inputs and quasi-fixed inputs) are incorporated into an analytical framework of dynamic data envelopment analysis (DEA). A unique feature of the quasi-inputs is that those are considered as outputs at the current period, while being treated as inputs at the next period. The dynamic DEA can measure interdependency among consecutive periods. This study incorporates the concept of returns to scale into the dynamic DEA.     

A bargaining game model for measuring performance of two-stage network structures

Data envelopment analysis (DEA) is a method for measuring the efficiency of peer decision making units (DMUs), where the internal structures of DMUs are treated as a black-box. Recently DEA has been extended to examine the efficiency of DMUs that have two-stage network structures or processes, where all the outputs from the first stage are intermediate measures that make up the inputs to the second stage. The resulting two-stage DEA model not only provides an overall efficiency score for the entire process, but also yields an efficiency score for each of the individual stages. The current paper develops a Nash bargaining game model to measure the performance of DMUs that have a two-stage structure. Under Nash bargaining theory, the two stages are viewed as players and the DEA efficiency model is a cooperative game model. It is shown that when only one intermediate measure exists between the two stages, our newly developed Nash bargaining game approach yields the same results as applying the standard DEA approach to each stage separately. Two real world data sets are used to demonstrate our bargaining game model.     

A variant of radial measure capable of dealing with negative inputs and outputs in data envelopment analysis

Data envelopment analysis (DEA) is a linear programming methodology to evaluate the relative technical efficiency for each member of a set of peer decision making units (DMUs) with multiple inputs and multiple outputs. It has been widely used to measure performance in many areas. A weakness of the traditional DEA model is that it cannot deal with negative input or output values. There have been many studies exploring this issue, and various approaches have been proposed.     

Theory of integer-valued data envelopment analysis

Conventional data envelopment analysis (DEA) models assume real-valued inputs and outputs. In many occasions, some inputs and/or outputs can only take integer values. In some cases, rounding the DEA solution to the nearest whole number can lead to misleading efficiency assessments and performance targets. This paper develops the axiomatic foundation for DEA in the case of integer-valued data, introducing new axioms of “natural disposability” and “natural divisibility”. We derive a DEA production possibility set that satisfies the minimum extrapolation principle under our refined set of axioms. We also present a mixed integer linear programming formula for computing efficiency scores. An empirical application to Iranian university departments illustrates the approach.     

Relationship between DEA models without explicit inputs and DEA-R models

Data envelopment analysis (DEA) is one of often used modeling tools for efficiency and performance evaluation of decision making units. Ratio DEA (DEA-R) is a group of novel mathematical models that combines standard DEA methodology and ratio analysis. The efficiency score given by standard DEA CCR model is less than or equal to that given by DEA-R model. In case of single input or single output the efficiency scores in CCR and DEA-R models are identical. The paper deals with DEA-R models without explicit inputs, i.e. models where only pure outputs or index data are taken into account. A basic DEA-R model without explicit inputs is formulated and a relation between output-oriented DEA models without explicit inputs and output-oriented DEA-R models is analyzed. Central resource allocation and slack-based measure models within DEA-R framework are examined. Finally they are used for projections of decision making units on the efficient frontier. The results of the proposed models are applied for efficiency evaluation of 15 units (Chinese research institutes) and they are discussed.     

Sensitivity analysis of efficient units in the presence of non-discretionary inputs

Discretionary models of data envelopment analysis (DEA) assume that all inputs and outputs can be varied at the discretion of management or other users. In any realistic situation, however, there may exist “exogenously fixed” or non-discretionary factors that are beyond the control of a DMU’s management, which also need to be considered. This paper discusses and reviews the use of super-efficiency approach in data envelopment analysis (DEA) sensitivity analyses when some inputs are exogenously fixed. Super-efficiency data envelopment analysis (DEA) model is obtained when a decision making unit (DMU) under evaluation is excluded from the reference set. In this paper by means of modified Banker and Morey’s (BM hereafter) model [R.D. Banker, R. Morey, Efficiency analysis for exogenously fixed inputs and outputs, Operations Research 34 (1986) 513–521], in which the test DMU is excluded from the reference set, we are able to determine what perturbations of discretionary data can be tolerated before frontier DMUs become nonfrontier.     

DEA model with shared resources and efficiency decomposition

Data envelopment analysis (DEA) has proved to be an excellent approach for measuring performance of decision making units (DMUs) that use multiple inputs to generate multiple outputs. In many real world scenarios, DMUs have a two-stage network process with shared input resources used in both stages of operations. For example, in hospital operations, some of the input resources such as equipment, personnel, and information technology are used in the first stage to generate medical record to track treatments, tests, drug dosages, and costs. The same set of resources used by first stage activities are used to generate the second-stage patient services. Patient services also use the services generated by the first stage operations of housekeeping, medical records, and laundry. These DMUs have not only inputs and outputs, but also intermediate measures that exist in-between the two-stage operations. The distinguishing characteristic is that some of the inputs to the first stage are shared by both the first and second stage, but some of the shared inputs cannot be conveniently split up and allocated to the operations of the two stages. Recognizing this distinction is critical for these types of DEA applications because measuring the efficiency of the production for first-stage outputs can be misleading and can understate the efficiency if DEA fails to consider that some of the inputs generate other second-stage outputs. The current paper develops a set of DEA models for measuring the performance of two-stage network processes with non splittable shared inputs. An additive efficiency decomposition for the two-stage network process is presented. The models are developed under the assumption of variable returns to scale (VRS), but can be readily applied under the assumption of constant returns to scale (CRS). An application is provided.     

A modified slacks-based measure model for data envelopment analysis with ‘natural’ negative outputs and inputs

This paper is primarily concerned with data envelopment analysis (DEA) of systems where negative outputs and negative inputs arise naturally. Examples of situations in which both negative inputs and negative outputs occur are given. More attention has been paid, in the literature, to the former type of problem. Most available DEA software does not solve this type of problem or copes with negative outputs and possibly negative inputs by assigning zero weights to them. A modified slacks-based measure (MSBM) model is presented, in which both negative outputs and negative inputs occur. The MSBM model overcomes the lack of translation invariance in the slacks-based measure model by drawing on the ideas from the range directional model (RDM). The MSBM model takes into account individual input and output slacks, which provides more precise evaluation of inefficient decision-making units (DMUs). It therefore, generally leads to lower efficiencies for inefficient DMUs than the RDM.     

An application of DEA for comparative analysis and ranking of regions in Serbia with regards to social-economic development

In this paper, we use data envelopment analysis (DEA) to estimate how well regions in Serbia utilize their resources. Based on data for four inputs and four outputs we applied an output-oriented CCR DEA model and it appears that 17 out of 30 regions are efficient. For each inefficient unit, DEA identifies the sources and level of inefficiency for each input and output. An output-oriented set of targets is determined for 13 inefficient regions. In addition, the possibilities of combining DEA and linear discriminant analysis (LDA) in evaluating performance are explored. The efficient regions are ranked using a cross efficiency matrix and an output-oriented version of Andersen–Petersen’s DEA model and the results are analyzed and compared.     

Equivalence in two-stage DEA approaches

Data envelopment analysis (DEA) is a linear programming problem approach for evaluating the relative efficiency of peer decision making units (DMUs) that have multiple inputs and outputs. DMUs can have a two-stage structure where all the outputs from the first stage are the only inputs to the second stage, in addition to the inputs to the first stage and the outputs from the second stage. The outputs from the first stage to the second stage are called intermediate measures. This paper examines relations and equivalence between two existing DEA approaches that address measuring the performance of two-stage processes.     

Prior-Ratio-Analysis procedure to improve data envelopment analysis for performance measurement

This paper proposes the use of a Prior-Ratio-Analysis procedure, analysing output/input ratio indicators, allowing the improvement in efficiency measurement by means of data envelopment analysis (DEA) methodology. This prior analysis is based on the existence of a relationship of individual ratio in the firms to DEA efficiency scores. Use of the proposed procedure allows (i) detection of efficient units whose efficiency could be overestimated and (ii) identification of certain inputs/outputs enhancing particular behaviours. Accordingly, the DEA efficiency analysis could be improved with a major understanding about the factors determining the unit efficiency, and with a measure as a true indicator for discriminating between units, and for ranking them.     

Efficiency decomposition for general multi-stage systems in data envelopment analysis

Conventional data envelopment analysis (DEA) models only consider the inputs supplied to the system and the outputs produced from the system in measuring efficiency, ignoring the operations of the internal processes. The results thus obtained sometimes are misleading. This paper discusses the efficiency measurement and decomposition of general multi-stage systems, where each stage consumes exogenous inputs and intermediate products (produced from the preceding stage) to produce exogenous outputs and intermediate products (for the succeeding stage to use). A relational model is developed to measure the system and stage efficiencies at the same time. By transforming the system into a series of parallel structures, the system efficiency is decomposed into the product of a modification of the stage efficiencies. Efficiency decomposition enables decision makers to identify the stages that cause the inefficiency of the system, and to effectively improve the performance of the system. An example of an electricity service system is used to explain the idea of efficiency decomposition.