Evaluating the efficiency of a two-stage production process using data envelopment analysis

Data envelopment analysis (DEA) has been widely used to evaluate the comparative efficiencies of production processes. Most of the DEA applications assume that production processes consist of one stage. However, many production processes such as IT investments have more than one stage. In a two‐stage production process, the first stage inputs produce intermediate outputs, which are used as inputs to the second stage to produce the final outputs. In such cases, using single‐stage DEA may result in inaccurate efficiency evaluation. To address such problems, DEA models assuming two‐stage production processes have been developed. In this paper, we extend two‐stage DEA models by considering input and output slacks. We apply our model to the data from the banking industry and compare the results with those of the previous two‐stage DEA models. Our model can identify weakly efficient units of evaluation that could not be identified by the previous models.     

Two-stage inference using data envelopment analysis efficiency measurements in univariate production models

This article addresses the problem of modeling data envelopment analysis (DEA) inefficiencies as dependent on contextual variables. For this purpose we use a statistical model similar in appearance to inefficiency component specifications in stochastic frontier models. The underlying production response is univariate. The approach is asymptotic and is based on a two‐stage statistical inference procedure. In the first stage inefficiencies are estimated using DEA. In the second stage these estimates are modeled as if they were the true inefficiencies by means of a statistical model dependent on the contextual variables. To define this data generating process one could use a flexible family of distributions like the truncated normal. Theoretical inefficiencies are assumed to be independent but not identically distributed. Some of the asymptotic results implied by the two‐stage inference procedure are inspected in finite samples by means of Monte Carlo simulations. The procedure is illustrated with an example where a deterministic production model is fitted to research data generated by the major state company responsible for agricultural research in Brazil.     

Slacks-based measures of efficiency in imprecise data envelopment analysis: An approach based on data envelopment analysis with double frontiers

Data envelopment analysis (DEA) is a mathematical approach for evaluating the efficiency of decision-making units (DMUs) that convert multiple inputs into multiple outputs. Traditional DEA models assume that all input and output data are known exactly. In many situations, however, some inputs and/or outputs take imprecise data. In this paper, we present optimistic and pessimistic perspectives for obtaining an efficiency evaluation for the DMU under consideration with imprecise data. Additionally, slacks-based measures of efficiency are used for direct assessment of efficiency in the presence of imprecise data with slack values. Finally, the geometric average of the two efficiency values is used to determine the DMU with the best performance. A ranking approach based on degree of preference is used for ranking the efficiency intervals of the DMUs. Two numerical examples are used to show the application of the proposed DEA approach.     

Evaluation of information technology investment: a data envelopment analysis approach

The increasing use of information technology (IT) has resulted in a need for evaluating the productivity impacts of IT. The contemporary IT evaluation approach has focused on return on investment and return on management. IT investment has impacts on different stages of business operations. For example, in the banking industry, IT plays a key role in effectively generating (i) funds from the customer in the forms of deposits and then (ii) profits by using deposits as investment funds. Existing approaches based upon data envelopment analysis (DEA) only measure the IT efficiency or impact on one specific stage when a multi-stage business process is present. A detailed model is needed to characterize the impact of IT on each stage of the business operation. The current paper develops a DEA non-linear programming model to evaluate the impact of IT on multiple stages along with information on how to distribute the IT-related resources so that the efficiency is maximized. It is shown that this non-linear program can be treated as a parametric linear program. It is also shown that if there is only one intermediate measure, then the non-linear DEA model becomes a linear program. Our approach is illustrated with an example taken from previous studies.     

数据包络分析研究热点综述

数据包络分析是面向多输入多输出决策单元的有效性评估方法。在介绍数据包络分析的基本思想和模型基础之上,总结了近年来国内外的研究热点,包括两阶段DEA、效率排序DEA、随机DEA和相关扩展问题,旨在围绕以上研究热点,对DEA近年来的理论研究及其扩展模型进行梳理和分类。最后对数据包络分析进一步研究提出展望。     

Indian thermal power plant challenges and remedies via application of modified data envelopment analysis

This paper evaluates the performance of coal‐fired thermal power plants in India for the year 2008–2009 using data envelopment analysis (DEA); subdividing the power plants into three categories depending on their scale—small, medium, and large. The classical DEA model is analyzed to identify the efficient ones from the whole gamut of plants run by various organizations of the central government, state government, and private sector. Slack analysis is carried out to explore the specific areas that need to be focused on, in quantitative terms, for the overall efficiency improvement. Further efficiency evaluation is extended from a single criterion‐based conventional approach to a multiple criteria oriented approach, and the resulting DEA models are more efficient and flexible in many aspects, particularly in discriminant and weight analysis. Results of multicriteria DEA (MCDEA) are substantiated with cross‐efficiency analysis by deploying the weights obtained by the MCDEA in the cross‐efficiency analysis. On the basis of the insights provided by the outcome of the analysis, both qualitative and quantitative measures are proposed for improvement of the plant performances. The result of this analysis may assist the management of the power plants to introspect and review their systems and processes for optimal use of resources. The methodology adopted in the present work can also be employed for deeper understanding of power plants in other parts of India as well as in other countries.     

Evaluating ecommerce websites cognitive efficiency: An integrative framework based on data envelopment analysis

This paper presents an integrative framework to evaluate ecommerce website efficiency from the user viewpoint using Data Envelopment Analysis (DEA). This framework is inspired by concepts driven from theories of information processing and cognition and considers the website efficiency as a measure of its quality and performance. When the users interact with the website interfaces to perform a task, they are involved in a cognitive effort, sustaining a cognitive cost to search, interpret and process information, and experiencing either a sense of satisfaction or dissatisfaction for that. The amount of ambiguity and uncertainty, and the search (over-)time during navigation that they perceive determine the effort size – and, as a consequence, the cognitive cost amount – they have to bear to perform their task. On the contrary, task performing and result achievement provide the users with cognitive benefits, making interaction with the website potentially attractive, satisfying, and useful. In total, 9 variables are measured, classified in a set of 3 website macro-dimensions (user experience, site navigability and structure). The framework is implemented to compare 52 ecommerce websites that sell products in the information technology and media market. A stepwise regression is performed to assess the influence of cognitive costs and benefits that mostly affect website efficiency.     

A new data envelopment analysis method for ranking decision making units: an application in industrial parks

Relative efficiency of decision‐making units (DMUs) is assessed by classical data envelopment analysis (DEA) models. DEA is a popular technique for efficiency evaluation. There might be a couple of efficient DMUs. Classical DEA models cannot fully rank efficient DMUs. In this paper, a novel technique for fully ranking all DMUs based on changing reference set using a single virtual inefficient DMU is proposed. To this end, the first concept of virtual DMU is defined as average of all inefficient DMUs. Virtual DMU is a proxy of all inefficient DMUs. This new method proposes a new ranking method that takes into account impact of efficient DMUs on virtual DMU and impact of efficient DMUs on influences of other efficient DMUs. A case study is given to show applicability of the proposed approach.     

An interactive application of data envelopment analysis in microcomputers

This article describes a general-purpose microcomputer code for data envelopment analysis (DEA) that incorporates four different DEA models in the form of a user-friendly, menu-driven structure.Research financially supported by Dean's Professorship, College of Business, the Ohio State University.     

Allocating natural resource reduction amounts: A data envelopment analysis based‐approach considering production technology heterogeneity

Previous studies resource allocation methods based on data envelopment analysis assume that all the assessed decision‐making units share a common production technology, and all decision‐making units become efficient after the resources are allocated. However, in the real world, production technology tends to be heterogeneous among the decision‐making units because of the differences in economic development, geographic location, and market conditions. Correspondingly, when some decision‐making units are far away from the efficient frontier, they may not become efficient easily using the resources allocated to them. In this paper, we propose a data envelopment analysis‐based approach which considers production technology heterogeneity among decision‐making units when allocating resource reduction amounts to each. In our model, the decision‐making units are divided into subgroups based on their economic development level, an important indicator directly reflecting each decision‐making unit's production technology level. Each subgroup has its specific production technology, and the decision‐making units in the same subgroup have a similar technology level, which allows better identification of how the production of those decision‐making units can change when their resource inputs change. We present an empirical example using China's mainland provinces as decision‐making units to demonstrate the practicability and applicability of our proposed model.     

Negative data in data envelopment analysis: Efficiency analysis and estimating returns to scale

The classic Data Envelopment Analysis (DEA) models developed with the assumption that all inputs and outputs are non-negative, whereas, we may face a case with negative data in the actual business world. So, the need to adapt the DEA models so that they are applicable to cases includes inputs and outputs which can take both negative and non-negative values has been an issue. It can be readily demonstrated that the assumption of constant returns to scale (CRS) is not possible in technologies under negative data. So, one of the interesting and challenge questions is how to determine the state of RTS in the presence of negative data under variable returns to scale (VRS) technology. Accordingly, in this contribution, we first address the efficiency measure and then suggest a method to discover the state of returns to scale (RTS) in the presence of negative input and output values which has not been discussed much enough so far in DEA literature. Finally, the main results are elaborated by some illustrative examples.     

Cross efficiency evaluation method based on weight-balanced data envelopment analysis model

In this paper, the cross efficiency evaluation method, regarded as a DEA extension tool, is firstly reviewed for its utilization in identifying the Decision Making Unit (DMU) with the best practice and ranking the DMUs by their respective cross-efficiency scores. However, we then point out that the main drawback of the method lies in non-uniqueness of cross-efficiency scores resulted from the presence of alternate optima in traditional DEA models, obviously making it become less effective. Aiming at the research gap, a weight-balanced DEA model is proposed to lessen large differences in weighted data (weighted inputs and weighted outputs) and to effectively reduce the number of zero weights for inputs and outputs. Finally, we use two examples of the literature to illustrate the performance of this approach and discuss some issues of interest regarding the choosing of weights in cross-efficiency evaluations.     

A stochastic cross‐efficiency data envelopment analysis approach for supplier selection under uncertainty

This paper addresses one of the key objectives of the supply chain strategic design phase, that is, the optimal selection of suppliers. A methodology for supplier selection under uncertainty is proposed, integrating the cross‐efficiency data envelopment analysis (DEA) and Monte Carlo approach. The combination of these two techniques allows overcoming the deterministic feature of the classical cross‐efficiency DEA approach. Moreover, we define an indicator of the robustness of the determined supplier ranking. The technique is able to manage the supplier selection problem considering nondeterministic input and output data. It allows the evaluation of suppliers under uncertainty, a particularly significant circumstance for the assessment of potential suppliers. The novel approach helps buyers in choosing the right partners under uncertainty and ranking suppliers upon a multiple sourcing strategy, even when considering complex evaluations with a high number of suppliers and many input and output criteria.     

Impacts of distributors and group purchasing organizations on hospital efficiency and profitability: a bilateral data envelopment analysis model

Total health care expenses have risen significantly in the United States. There are many factors and variables that can impact hospital operating efficiencies. Among them, engaging a distributor or group purchasing organization (GPO) is one method to influence efficiency throughout the entire supply chain. This research investigates the impact of distributors and GPOs on hospital efficiency and profitability. The data from the 2015 American Hospital Association (AHA) Annual Hospital Survey of which 6251 hospitals participated are used. These hospitals were separated by those who purchased supplies through a distributor and those who did not. Likewise, the same was performed for those hospitals that used GPO and those that did not. This study employs DEA-Solver software to develop four types of bilateral DEA models. The results of the DEA model use a ranking variable (rank sum) to rank the variables within the two groups (distributor and no distributor) to determine if there is a significant difference between distributor and nondistributor. The same is performed for GPO and non-GPO. We examined the impact of the several control variables on hospital efficiency for distributors and GPOs. Results indicate that the control variables (region, education, profit/nonprofit, government/nongovernment, and system/nonsystem) made a significant difference for hospitals that used a distributor and a GPO. Lessons and implications are discussed for future research issues, such as quality of patient care and a frontier production function.     

Trade‐offs in integer data envelopment analysis

If production trade‐offs—which represent simultaneously feasible exchanges in the inputs and outputs of decision‐making units (DMUs)—are added to an integer production possibility set (IPPS), a new IPPS is produced; conventional axioms of production do not generate a new IPPS, however. This paper develops the axiomatic foundation for data envelopment analysis (DEA) for integer‐value inputs and outputs in the presence of production trade‐offs by introducing a new axiom of “natural trade‐offs.” First, a mixed‐integer linear programming formula called an integer DEA trade‐off (IDEA‐TO) is presented for computing efficiency scores and reference points. The numeration algorithm (NA) method presented in this concept is improved, and an improved numeration algorithm (INA) method for solving integer DEA (IDEA) models is developed. Finally, comparison between the two methods and a generalized INA method for solving the IDEA‐TO model are presented.     

数据包络分析模型的化工试验设计方法评价

数据包络分析(DEA)是以“相对效率评价”基于化工试验中反应物、生成物之间的投入、产出关系,探讨了化工试验设计,主要探讨了在化工试验设计中DEA作为评价正交试验设计方法的一种有效的分析工具的理论和应用。实例分析表明,将DEA方法运用于化工试验设计的评价具有计算简单,意义清楚的特点,是对正交试验设计的有益补充。     

Common set of weights in data envelopment analysis under prospect theory

Data envelopment analysis (DEA) is a data‐driven tool for performance evaluation, measuring decision‐making units (DMUs) and designating them with specific weightings. The standard DEA model typically sets up that decision‐makers (DMs) are wholly rational to select the most favourable weights to obtain the maximum performance score, but does not take into account their attitude toward risk during the assessment. The prospect theory generally matches humans' psychological behaviours. Thus, our study captures the non‐rational behaviours of DMs, performing under risk scenarios, in order to construct a novel common‐weights DEA model that maximizes the total prospect value, which can vary more steeply for losses than for gains, hence obtaining a more realistic common weight scheme. Our proposed model not only generates DMUs, with higher total prospect values, but also greater degrees of satisfaction. The current study shows that the prospect theory can be aptly extended to the DEA research area, supplying a proper guideline for future DEA research.     

A robust optimization approach for imprecise data envelopment analysis

Crisp input and output data are fundamentally indispensable in traditional data envelopment analysis (DEA). However, the input and output data in real-world problems are often imprecise or ambiguous. Some researchers have proposed interval DEA (IDEA) and fuzzy DEA (FDEA) to deal with imprecise and ambiguous data in DEA. Nevertheless, many real-life problems use linguistic data that cannot be used as interval data and a large number of input variables in fuzzy logic could result in a significant number of rules that are needed to specify a dynamic model. In this paper, we propose an adaptation of the standard DEA under conditions of uncertainty. The proposed approach is based on a robust optimization model in which the input and output parameters are constrained to be within an uncertainty set with additional constraints based on the worst case solution with respect to the uncertainty set. Our robust DEA (RDEA) model seeks to maximize efficiency (similar to standard DEA) but under the assumption of a worst case efficiency defied by the uncertainty set and it’s supporting constraint. A Monte-Carlo simulation is used to compute the conformity of the rankings in the RDEA model. The contribution of this paper is fourfold: (1) we consider ambiguous, uncertain and imprecise input and output data in DEA; (2) we address the gap in the imprecise DEA literature for problems not suitable or difficult to model with interval or fuzzy representations; (3) we propose a robust optimization model in which the input and output parameters are constrained to be within an uncertainty set with additional constraints based on the worst case solution with respect to the uncertainty set; and (4) we use Monte-Carlo simulation to specify a range of Gamma in which the rankings of the DMUs occur with high probability.     

Measuring environmental sustainability performance of freight transportation seaports in China: A data envelopment analysis approach based on the closest targets

Because of China's rapid economic development, its freight transportation system has grown to become one of China's high-pollution-emission sectors. However, there are few studies that pay close attention to measuring and improving the environmental performance of China's freight transportation system, especially in regard to seaports. In this paper, data envelopment analysis (DEA) is applied to measure the environmental performance of freight transportation seaports. In addition, we also provide benchmarking information to point the way to improving environmental performance effectively. Our proposed DEA model is based on the closest targets, which satisfies the strong monotonicity and can yield the most relevant solution for the inefficient seaports. An empirical study of 21 of China's primary freight transportation seaports shows that most of them have relatively good environmental performance. Among the five coastal port groups, the Bohai-rim port group had the best environmental performance, whereas the Pearl River port group had the worst. Our data show significant differences between the best and worst performances, indicating that more measures should be taken to balance and coordinate the development between the five coastal port groups.     

Improving the discrimination of data envelopment analysis models in multiple time periods

The trade‐offs approach is an advanced tool for the improvement of the discrimination of data envelopment analysis (DEA) models; this can improve the traditional meaning of efficiency as a radial improvement factor for inputs or outputs. Therefore, the Malmquist index – the prominent index for measuring the productivity change of decision making units (DMUs) in multiple time periods that use DEA models with variable returns to scale and constant returns to scale technologies – can be improved by using the trade‐offs technology. Hence, an expanded Malmquist index can be defined as an improved method of a traditional Malmquist index that uses the production possibility set, which could present more discrimination of DMUs, in the presence of the trade‐offs technology. In addition, similar to a traditional Malmquist index, it breaks down into different components. An illustrative example is presented to show the ability of the suggested method of presenting the Malmquist index from a computational point of view.