Deriving the DEA frontier for two-stage processes

Data envelopment analysis (DEA) is a method for measuring the efficiency of peer decision making units (DMUs). Recently DEA has been extended to examine the efficiency of two-stage 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 provides not only an overall efficiency score for the entire process, but as well yields an efficiency score for each of the individual stages. Due to the existence of intermediate measures, the usual procedure of adjusting the inputs or outputs by the efficiency scores, as in the standard DEA approach, does not necessarily yield a frontier projection. The current paper develops an approach for determining the frontier points for inefficient DMUs within the framework of two-stage DEA.     

A geometrical approach for generalizing the production possibility set in DEA

Consider a Data Envelopment Analysis (DEA) study with n Decision Making Units (DMUs) and a model with m inputs plus outputs. The data for this study are a point set, {a¹,…,a ⁿ }, in Open image in new window . A DMU is efficient if its data point is located on the efficient frontier portion of the boundary of an empirical production possibility set, a polyhedral envelopment hull described by the data. From this perspective, DEA efficiency is a purely geometric concept that can be applied to general point sets to identify records with extreme properties. The generalized approach permits new applications for nonparametric frontiers. Examples of such applications are fraud detection, auditing, security, and appraisals. We extend the concept of DEA efficiency to frontier outliers in general envelopment hulls.     

Controlled Envelopment by Face Extension in DEA

Data Envelopment Analysis (DEA) is an approach to assess the relative efficiency of organizations using multiple inputs to produce multiple outputs. This assessment is made from the standpoint most favourable to each organization. If an organization is not well enveloped, in the sense that it is not comparable to a sufficient number of other organizations (called referents), DEA may understate inefficiency. A lower bound on the efficiency measure may be obtained by requiring that the organization being evaluated be compared with at least k non-redundant referents. For any feasible choice of k, the procedure proposed here selects the most favourable set of referents, and guarantees a greatest lower bound on the efficiency measure, thus usefully complementing the information provided by conventional DEA.     

Optimal system design series-network DEA models

There is an urgent need in a wide range of fields such as logistics and supply chain management to develop effective approaches to measure and/or optimally design a network system comprised of a set of units. Data envelopment analysis (DEA) researchers have been developing network DEA models to measure decision making units’ (DMUs’) network systems. However, to our knowledge, there are no previous contributions on the DEA-type models that help DMUs optimally design their network systems. The need to design optimal systems is quite common and is sometimes necessary in practice. This research thus introduces a new type of DEA model termed the optimal system design (OSD) network DEA model to optimally design a DMUs (exogenous and endogenous) input and (endogenous and final) output portfolios in terms of profit maximization given the DMUs total available budget. The resulting optimal network design through the proposed OSD network DEA models is efficient, that is, it lies on the frontier of the corresponding production possibility set.     

The interval efficiency based on the optimistic and pessimistic points of view

Data envelopment analysis (DEA) is a data-oriented approach for evaluating the performances of a set of peer entities called decision-making units (DMUs), whose performance is determined based on multiple measures. The traditional DEA, which is based on the concept of efficiency frontier (output frontier), determines the best efficiency score that can be assigned to each DMU. Based on these scores, DMUs are classified into DEA-efficient (optimistic efficient) or DEA-non-efficient (optimistic non-efficient) units, and the DEA-efficient DMUs determine the efficiency frontier. There is a comparable approach which uses the concept of inefficiency frontier (input frontier) for determining the worst relative efficiency score that can be assigned to each DMU. DMUs on the inefficiency frontier are specified as DEA-inefficient or pessimistic inefficient, and those that do not lie on the inefficient frontier, are declared to be DEA-non-inefficient or pessimistic non-inefficient. In this paper, we argue that both relative efficiencies should be considered simultaneously, and any approach that considers only one of them will be biased. For measuring the overall performance of the DMUs, we propose to integrate both efficiencies in the form of an interval, and we call the proposed DEA models for efficiency measurement the bounded DEA models. In this way, the efficiency interval provides the decision maker with all the possible values of efficiency, which reflect various perspectives. A numerical example is presented to illustrate the application of the proposed DEA models.     

A multi-objective approach to determine alternative targets in data envelopment analysis

The choice for radial projections of classic data envelopment analysis (DEA) models, resulting in a number of projections onto the Pareto-inefficient portion of the frontier, has been seen lately as a disadvantage in DEA. The search for a non-radial projection method resulted in developments such as preference structure models. These models consider a priori preference incorporation, using weights in the search for the most preferred efficient target, although presenting some implementation difficulties. In this paper, we propose a multi-objective approach that determines the bases for a posteriori preference incorporation, through individual projections of each variable (input or output) as an objective function, thus allowing one to obtain a target at every extreme-efficient point on the frontier. This multi-objective approach is shown to be equivalent to the preference structure models, yet presenting some advantages, such as the mapping of the possible weights, assigned to partial efficiencies of an observed unit, in order to reach a specific target.     

A compromise solution approach for finding common weights in DEA: an improvement to Kao and Hung's approach

Data envelopment analysis (DEA) is the leading technique for measuring the relative efficiency of decision-making units (DMUs) on the basis of multiple inputs and multiple outputs. In this technique, the weights for inputs and outputs are estimated in the best advantage for each unit so as to maximize its relative efficiency. But, this flexibility in selecting the weights deters the comparison among DMUs on a common base. For dealing with this difficulty, Kao and Hung (2005) proposed a compromise solution approach for generating common weights under the DEA framework. The proposed multiple criteria decision-making (MCDM) model was derived from the original non-linear DEA model. This paper presents an improvement to Kao and Hung's approach by means of introducing an MCDM model which is derived from a new linear DEA model.     

Joint use of DEA and constrained canonical correlation analysis for efficiency valuations involving categorical variables

The research on efficiency valuations has used two distinct approaches. One is the nonparametric approach known as data envelopment analysis (DEA), the other is the parametric approach based on regression analysis or its extension such as constrained canonical correlation analysis (CCCA). Interestingly, a recent study has employed a hybrid approach that cross-fertilizes DEA and CCCA to compensate for the drawbacks of the two methods and capture their positive aspects. This approach first applies DEA to select efficient units and then utilizes CCCA to identify a smooth efficient frontier with the selected efficient units only. We extend it to incorporate a categorical variable that reflects an environmental effect on efficiency performance. The need for considering a categorical variable arises in practice for an equitable efficiency valuation, as illustrated by managerial performance evaluation of the branches of a fast-food company, where the location of branches such as commercial or noncommercial area significantly affects their performance. We demonstrate various possible ways to handle such a categorical variable in the framework of a hybrid approach and characterize each of the methods. Based on this study, we suggest one method that simultaneously utilizes an extension of DEA, referred to as DEA with categorical variable, and CCCA employing a dummy variable, as in multiple regressions with dummy variables. Through an application to the branches of a fast-food company, we show the efficacy of the suggested method in terms of penalizing the advantageous location effect and compensating for the disadvantageous location effect. We also provide some discussions on the limitations underlying the hybrid approach in order to guide a proper use of this approach to the other potential applications.     

Finding the efficiency score and RTS characteristic of DMUs by means of identifying the efficient frontier in DEA

Data envelopment analysis (DEA) is basically a linear programming based technique used for measuring the relative performance of organizational units, referred to as decision-making units (DMUs), where the presence of multiple inputs and outputs makes comparisons difficult. The ability of identifying frontier DMUs prior to the DEA calculation is of extreme importance to an effective and efficient DEA computation. In this paper, a method for identifying the efficient frontier is introduced. Then, the efficiency score and returns to scale (RTS) characteristic of DMUs will be produced by means of the equation of efficient frontier.     

A DEA two-stage decision processes with shared resources

Data envelopment analysis (DEA) is an approach for measuring the relative efficiency of peer decision making units that have multiple inputs and outputs. In most practical applications of DEA presented in the literature, the presented models assume that outputs are produced perfectly (see Charnes et al. Eur J Oper Res 2:429–444, 1978). However, in many real situations, some outputs are imperfect and they need to be repaired. This paper develops a DEA approach for measuring the efficiency of decision processes which can be divided into two interdependent stages, arranged in series. The novelty of the proposed approach is the existence of perfect and imperfect outputs in a two-stage decision process. This application of two-stage process involves shared resources and the paper gives a best split of these shared resources between two stages. The case of Iranian car representatives is presented.     

Competition strategy and efficiency evaluation for decision making units with fixed-sum outputs

This paper develops a DEA (data envelopment analysis) model to accommodate competition over outputs. In the proposed model, the total output of all decision making units (DMUs) is fixed, and DMUs compete with each other to maximize their self-rated DEA efficiency score. In the presence of competition over outputs, the best-practice frontier deviates from the classical DEA frontier. We also compute the efficiency scores using the proposed fixed sum output DEA (FSODEA) models, and discuss the competition strategy selection rule. The model is illustrated using a hypothetical data set under the constant returns to scale assumption and medal data from the 2000 Sydney Olympics under the variable returns to scale assumption.     

Congestion analysis in DEA inputs under weight restrictions

Data envelopment analysis (DEA), which is used to determine the efficiency of a decision-making unit (DMU), is able to recognize the amount of input congestion. Moreover, the relative importance of inputs and outputs can be incorporated into DEA models by weight restrictions. These restrictions or a priori weights are introduced by the decision maker and lead to changes in models and efficiency interpretation. In this paper, we present an approach to determine the value of congestion in inputs under the weight restrictions. Some discussions show how weight restrictions can affect the congestion amount.     

Gradual technical and scale efficiency improvement in DEA

In data envelopment analysis (DEA) an inefficient unit can be projected onto an efficient target that is far away, i.e. reaching the target may demand large reductions in inputs and increases in outputs. When the inputs and outputs modifications planned are large, it may be troublesome to carry them out all at once. In order to help an inefficient unit reach a distant target, a strategy of gradual improvements with successive, intermediate targets has been proposed. This paper extends such approach to the variable returns to scale (VRS) case. In the VRS scenario we distinguish between units that are technical efficient and those that are not. On the one hand, for those units that are not technical efficient the proposed approach determines successive intermediate targets leading to the technical efficiency frontier, i.e. the priority for those units is to attain technical efficiency. On the other hand, for those units that are technical efficient but not scale efficient the proposed approach computes a sequence of targets ending in the global efficiency frontier, i.e. when technical efficiency is guaranteed the goal is then to attain global efficiency. In both cases, the successive targets are obtained by iteratively solving specific DEA models that take into account given bounds on the rates of change in inputs and outputs that the unit can implement in each step.     

Multiple objective data envelopment analysis as applied to the Indian Pharmaceutical Industry

The change of Intellectual Property Protection (IPP) from a softer process patenting to a stronger product patenting in Indian Pharmaceutical Industry (IPI) is attracting many global drug majors to source their production from India, which is the fourth largest producer of pharmaceuticals in the world. In this paper, the interests of different stake holders like the buyers (multinational enterprises), who are searching for efficient partners and the vendors (Indian drug producers) that are competing for the contracts, are analysed for a suitable efficiency evaluation criterion. The primary objective of this paper is to study how various firms in the IPI with different business strategies, competing for the same opportunities can find suitable benchmarking peer groups to meet the challenges of a dynamic business environment using data envelopment analysis (DEA). A multiple objective DEA model that determines suitable peer groups for inefficient companies is discussed along with more traditional DEA models. The proposed model has the flexibility to include inputs like R&D expenditure and outputs like Exports that are not homogeneously distributed across the firms and address the interests of various stake holders like buyers and vendors simultaneously.     

Scaling units via the canonical correlation analysis in the DEA context

This paper deals with the evaluation of decision making units which have multiple inputs and outputs. A new method (CCA/DEA) is developed where the Canonical Correlation Analysis (CCA) is utilized to provide a full rank scaling for all the units rather than a categorical classification (for efficient and inefficient units) as done by the Data Envelopment Analysis (DEA). The CCA/DEA approach is an attempt to bridge the gap between the frontier approach of DEA and the average tendencies of statistics (econometrics). Nonparametric statistical tests are employed to validate the consistency between the classification from the DEA and the postclassification that was generated by the CCA/DEA.     

A new approach for achievement of the equilibrium efficient frontier with fixed-sum outputs

In a recent paper, Yang et al developed an algorithm based on the extended minimal adjustment strategy and the equilibrium competition strategy to achieve a common equilibrium efficient frontier. However, the computational burden of their algorithm is challenging when a sample contains many inefficient decision-making units (DMUs). In this paper, we propose a linear programming model that can achieve a common equilibrium efficient frontier in a single step, regardless of the number of inefficient DMUs. Furthermore, we demonstrate the existence and the non-uniqueness of the equilibrium efficient frontier and identify its shortcomings through an example. Next, we extend our approach to incorporate weight restrictions to indicate the relative importance of the different inputs and outputs and introduce the secondary goal of minimizing the maximal relative deviation for each fixed-sum output, which can result in a unique equilibrium efficient frontier.     

Studies of some duality properties in the Li and Reeves model

In 1999, Li and Reeves presented the so-called MCDEA (Multiple Criteria Data Envelopment Analysis) model. This model is in fact a three objective linear model. It may be used to improve the discriminatory power of the DEA models, as well as generate a more reasonable distribution of the inputs and outputs weights. Besides the classical optimization of the efficiency index, Li and Reeves introduced two other objective functions, called minisum and minimax. Despite of being an important approach, it does not provide benchmarks or targets for inefficient DMUs. Benchmarks and targets are one of the most important DEA features and in standard DEA are determined using the dual (envelope) model. In this paper, we introduce an approach of the MCDEA dual formulation taking into account only two objective functions at each time. Combining both partial models we suggest benchmarks for each inefficient DMU.     

Measuring the efficiency of forest districts with multiple working circles

Data envelopment analysis (DEA) is a methodology extensively applied to measuring the relative efficiency of decision making units with multiple inputs and multiple outputs. Herein, a DEA model is developed to measure the efficiency of forest districts which are divided into a number of subdistricts called working circles (WCs). The idea is to construct district production frontiers from the WCs of individual districts. Superimposing the district production frontiers of different districts one derives the forest production frontier. The closeness of a district production frontier to the forest production frontier indicates this district's efficiency. As an illustration, the developed model measures the eight districts, with a total of thirty-four WCs, of the national forests of the Republic of China on Taiwan. The results provide the top management with an idea of how far each district can be expected to improve its performance when compared with other districts.     

Resolving a strange case of efficiency

In a recent paper in the Journal of the Operational Research Society, Tone proposes an alternative to the Farrell cost efficiency index to avoid the ‘strange case’ problem in which firms with identical inputs and outputs but with input prices differing by some factor (eg, one has input prices twice another) will have the same Farrell cost efficiency. We provide an alternative cost efficiency indicator that avoids this problem, allows for decomposition into technical and allocative efficiency, and is easily estimated using DEA type models.     

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.