Dynamic data envelopment analysis: A relational analysis

This paper proposes a dynamic data envelopment analysis (DEA) model to measure the system and period efficiencies at the same time for multi-period systems, where quasi-fixed inputs or intermediate products are the source of inter-temporal dependence between consecutive periods. A mathematical relationship is derived in which the complement of the system efficiency is a linear combination of those of the period efficiencies. The proposed model is also more discriminative than the existing ones in identifying the systems with better performance. Taiwanese forests, where the forest stock plays the role of quasi-fixed input, are used to illustrate this approach. The results show that the method for calculating the system efficiency in the literature produces over-estimated scores when the dynamic nature is ignored. This makes it necessary to conduct a dynamic analysis whenever data is available.     

A study on the persistence of Farrell’s efficiency measure under a dynamic framework

This article introduces a sequence of four systematic methods to examine the extent to which the economic efficiency of Taiwan’s commercial banks persists and to uncover the potential dynamic link between bank performance and various financial indicators. Quasi-fixed inputs are explicitly incorporated in the DEA model to account for possible adjustment costs, regulation, or indivisibilities. Among the four methods, the dynamic panel data model and the Markov model appear to be exploited for the first time in the area of the DEA approach. Evidence is found that bank efficiency exhibits moderate persistence over the sample period, implying that the given sample banks fail to adjust their production techniques in a timely manner. Regulatory authorities and bank managers are suggested to be aware of the level of undesirable non-performing loans due to their close relationship with bank performance.     

Optimal Paths And Costs Of Adjustment In Dynamic DEA Models: With Application To Chilean Department Stores

In this paper we propose a range of dynamic data envelopment analysis (DEA) models which allow information on costs of adjustment to be incorporated into the DEA framework. We first specify a basic dynamic DEA model predicated on a number of simplifying assumptions. We then outline a number of extensions to this model to accommodate asymmetric adjustment costs, non-static output quantities, non-static input prices, and non-static costs of adjustment, technological change, quasi-fixed inputs and investment budget constraints. The new dynamic DEA models provide valuable extra information relative to the standard static DEA models—they identify an optimal path of adjustment for the input quantities, and provide a measure of the potential cost savings that result from recognising the costs of adjusting input quantities towards the optimal point. The new models are illustrated using data relating to a chain of 35 retail department stores in Chile. The empirical results illustrate the wealth of information that can be derived from these models, and clearly show that static models overstate potential cost savings when adjustment costs are non-zero. This paper arises out the senior author's PhD thesis at the University of New England, Australia. The authors gratefully acknowledge Dr. George E. Battese for his comments on earlier drafts of this work.     

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.     

Do mergers improve hospital productivity?

This paper complements the existing literature on hospital mergers by using data envelopment analysis (DEA) to generate both efficiency and productivity measures to ascertain whether hospital mergers, at least in the short run, result in performance gains. Using data over the period 1996–1998, we apply DEA, both pre-merger and post-merger, to set of hospitals that merged in 1997 as well as to a matching control group of non-merging hospitals over the same timeframe. A comparison of DEA efficiency scores and the Malmquist index values across the case and control hospitals allow us to assess whether any increase in productivity is the result of a merger rather than simply and randomly adding two hospitals' inputs and outputs together.     

A new proposed model of restricted data envelopment analysis by correlation coefficients

The concept of efficiency in data envelopment analysis (DEA) is defined as weighted sum of outputs/weighted sum of inputs. In order to calculate the maximum efficiency score, each decision making unit (DMU)’s inputs and outputs are assigned to different weights. Hence, the classical DEA allows the weight flexibility. Therefore, even if they are important, the inputs or outputs of some DMUs can be assigned zero (0) weights. Thus, these inputs or outputs are neglected in the evaluation. Also, some DMUs may be defined as efficient even if they are inefficient. This situation leads to unrealistic results. Also to eliminate the problem of weight flexibility, weight restrictions are made in DEA. In our study, we proposed a new model which has not been published in the literature. We describe it as the restricted data envelopment analysis ((ARIII(COR))) model with correlation coefficients. The aim for developing this new model, is to take into account the relations between variables using correlation coefficients. Also, these relations were added as constraints to the CCR and BCC models. For this purpose, the correlation coefficients were used in the restrictions of input–output each one alone and their combination together. Inputs and outputs are related to the degree of correlation between each other in the production. Previous studies did not take into account the relationship between inputs/outputs variables. So, only with expert opinions or an objective method, weight restrictions have been made. In our study, the weights for input and output variables were determined, according to the correlations between input and output variables. The proposed new method is different from other methods in the literature, because the efficiency scores were calculated at the level of correlations between the input and/or output variables.     

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.     

Generalizing cross redundancy in data envelopment analysis

Lee and Choi (2010) proved that a cross redundant output in a CCR or BCC DEA study is unnecessary and can be eliminated from the model without affecting the results of the study. A cross redundant output, as characterized by Lee and Choi, can be expressed as a specially constrained linear combination of both some outputs and some inputs. This article extends the contributions of Lee and Choi (2010) in at least three ways: (i) by adding precision and clarity to some of their definitions; (ii) by introducing specific definitions that complement the ones in their paper; and (iii) by conducting some additional analysis on the impact of the presence of other types of linear dependencies among the inputs and outputs of a DEA model. One reason that it is important to identify and remove cross redundant inputs or outputs from DEA models is that the computational burden of the DEA study is decreased, especially in large applications.     

Measuring the performance of manufacturing firms with super slacks based model of data envelopment analysis: An application of 500 major industrial enterprises in Turkey

Data envelopment analysis (DEA) is a mathematical programming technique which has a wide application area. There are many applications of DEA to measure firms’ performance. Balance sheet data is frequently used in order to measure performance of firms through DEA. So it is the characteristic of balance sheets that assets and liabilities amount to the same value. When the data for inputs and outputs are selected from both assets and liabilities sections of the balance sheet, it is important that more attention be paid to the analysis since values assigned to inputs and outputs could be included in assets and liabilities at the same time. Such a situation could create problems concerning the conclusions drawn as a result of analysis.     

Classifying and characterizing efficiencies and inefficiencies in data development analysis

DEA (Data Envelopment Analysis) attempts to identify sources and estimate amounts of inefficiencies contained in the outputs and inputs generated by managed entities called DMUs (=Decision Making Units). Explicit formulation of underlying functional relations with specified parametric forms relating inputs to outputs is not required. An overall (scalar) measure of efficiency is also obtained for each DMU from the observed values of its multiple inputs and outputs without requiring uses of a priori weights. There are many different ways of specifying DEA reference sets. A partition into 6 classes is provided for such observations in which 3 are scale inefficient and 3 are scale efficient with the latter containing substs of DMUs that are also technically (=zero waste) efficient.     

Network DEA: Additive efficiency decomposition

In conventional DEA analysis, DMUs are generally treated as a black-box in the sense that internal structures are ignored, and the performance of a DMU is assumed to be a function of a set of chosen inputs and outputs. A significant body of work has been directed at problem settings where the DMU is characterized by a multistage process; supply chains and many manufacturing processes take this form. Recent DEA literature on serial processes has tended to concentrate on closed systems, that is, where the outputs from one stage become the inputs to the next stage, and where no other inputs enter the process at any intermediate stage. The current paper examines the more general problem of an open multistage process. Here, some outputs from a given stage may leave the system while others become inputs to the next stage. As well, new inputs can enter at any stage. We then extend the methodology to examine general network structures. We represent the overall efficiency of such a structure as an additive weighted average of the efficiencies of the individual components or stages that make up that structure. The model therefore allows one to evaluate not only the overall performance of the network, but as well represent how that performance decomposes into measures for the individual components of the network. We illustrate the model using two data sets.     

Cone dominance and efficiency in DEA

This paper incorporates cones on virtual multipliers of inputs and outputs into DEA analysis. Cone DEA models are developed to generalize the dual of the BCC models as well as congestion models. Input-output data and/or numbers of DMUs for BCC models are inadequate to capture many aspects where judgments, expert opinions, and other external information should be taken into analysis. Cone DEA models, on the other hand, offer improved definitions of efficiency over general cone and polyhedral cone structures. The relationships between cone models and BCC models as well as those between cone models and congestion models are discussed in the development. Two numerical examples are provided to illustrate our findings.     

Experimental evidence on robustness of data envelopment analysis

There is an on-going debate about variable selection in data envelopment analysis (DEA) as there are no diagnostic checks for model misspecification. This paper contributes to this debate by investigating the sensitivity of DEA efficiency estimates to including inappropriate and/or omitting several important variables in a large-sample DEA model. Data are simulated from constant, increasing and decreasing returns-to-scale (RS) Cobb–Douglas production processes. For constant and decreasing RS processes with irrelevant inputs, DEA tends to overestimate efficiency in almost all production units. When relevant variables are omitted, variable RS appears to be a safer option. The correct RS specification is vital when the DEA model includes irrelevant variables. The effect of omission of relevant inputs on individual production unit efficiency is more adverse compared to the inclusion of irrelevant ones.     

Improving data envelopment analysis by the use of production trade-offs

Production technologies in data envelopment analysis (DEA) are described in terms of inputs and outputs. Production trade-offs represent simultaneous changes to the inputs and outputs that are possible in the technology under consideration. Recently, a method for their incorporation in DEA models has been developed. It was shown that the use of production trade-offs not only improves the discrimination of DEA models but also preserves the traditional meaning of efficiency as a radial improvement factor for inputs and outputs. This new paper follows the above development and provides an example of its use in the assessment of efficiency of university departments. The paper avoids excessive technical detail which can be found in the previous publication and instead focuses on the implementation of this new technique.     

Pesticide use,environmental spillovers and efficiency: A DEA risk-adjusted efficiency approach applied to Dutch arable farming

Pesticides are widely used by crop producers in developed countries to combat risk associated with pests and diseases. However, their indiscriminate use can lead to various environmental spillovers that may alter the agricultural production environment thus contributing to production risk. This study utilises a data envelopment analysis (DEA) approach to measure performance of arable farms, incorporating pesticides’ environmental spillovers and output variance as undesirable outputs in the efficiency analysis and taking explicitly into account the effect of pesticides and other inputs on production risk. The application focuses on panel data from Dutch arable farms over the period 2003–2007. A moment approach is used to compute output variance, providing empirical representations of the risk-increasing or -decreasing nature of the used inputs. Finally, shadow values of risk-adjusted inputs are computed. We find that pesticides are overused in Dutch arable farming and there is a considerable evidence of the need for decreasing pesticides’ environmental spillovers.     

Measuring technical efficiency in the presence of pesticide spillovers and production uncertainty: The case of Dutch arable farms

Pesticides’ dynamic effects and production uncertainty play an important role in farmers’ production decisions. Pesticides have a current production impact through reducing crop damage in the current period and a future impact through impacting the farm biodiversity which alters the future production environment. This study presents the difference in inefficiency arising from models that ignore the dynamic effects of pesticides in production decisions and the impact of production uncertainty. A dynamic data envelopment analysis (DEA) model is applied to outputs, inputs, and undesirables of Dutch arable farms over the period 2003–2007. A bootstrap approach is used to explain farmers’ performance, providing empirical representations of the impact of stochastic elements on production. These empirical representations are used to adjust firms’ inefficiency scores to incorporate production uncertainty in efficiency evaluation. We find that efficiency increased dramatically when a production technology representation that considers both pesticides’ dynamic impacts, and production uncertainty is adopted.     

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.     

The LeChatelier principle in a DEA model

This paper aims to relate the LeChatelier principle, first introduced into economics by Samuelson (1947), with the DEA approach through two propositions. These propositions allow for bridging the principle over a DEA model with and without the presence of non-discretionary inputs and enable one to make comparisons for the various efficiency measures under different conditions. The quasi-fixity of some inputs hinders a firm’s capacity from instantly and freely adjusting its input combination in order to minimize its production costs. The assumption that all inputs are discretionary tends to exaggerate managers’ ability to dispense resources and renders invalid information on the adjustment of the current input mix.     

Weight-restricted DEA in action: from expert opinions to mathematical models

A common problem in real-world DEA applications is that all inputs and outputs may not be equally relevant to the organizations analysed and their stakeholders. In many cases, one is also faced with a data set where the decision-making units do not clearly outnumber the quantity of inputs and outputs. This study reports an application where DEA embellished with weight restrictions is used to analyse the efficiency of public organizations to overcome the above-mentioned problems. Whereas there are numerous documented applications of weight-restricted DEA in the literature, the process of defining the actual weight restrictions is seldom described. However, that part — defining the actual weights restrictions based on price, preference or value information — is the most difficult step involved in using the weight-restricted DEA. Comparing various weight restriction schemes with real data suggests that the ability to consider and include preference information in DEA adds important insights into the analysis.     

Identifying the efficiency status in network DEA

Data envelopment analysis (DEA) is commonly employed to evaluate the efficiency performance of a decision making unit (DMU) that transforms exogenous inputs into final outputs. In such a black-box DEA approach, details of an internal production process of the DMU are typically ignored and hence the locations of inefficiency are not adequately provided. In view of this, DEA researchers have recently developed various network approaches by looking into the black box, where the inputs that enter the box and the outputs that come out of it are only considered. However, most of these network approaches evaluate divisional efficiency by using an optimal solution of their respective optimization problem. If such an optimal solution is used in the case when there are multiple optima, then managerial guidance based on this solution alone may be inappropriate because more appropriate targets from the viewpoint of management may be ignored. Taking this fact into account, therefore, we propose a network approach for identifying the efficiency status of each DMU and its divisions. This approach provides a practical computational procedure.