Comparing and Combining Two Approaches for Chance Constrained DEA

This paper presents a comparison of two different models (Land et al (1993) and Olesen and Petersen (1995)), both designed to extend DEA to the case of stochastic inputs and outputs. The two models constitute two approaches within this area, that share certain characteristics. However, the two models behave very differently, and the choice between these two models can be confusing. This paper presents a systematic attempt to point out differences as well as similarities. It is demonstrated that the two models under some assumptions do have Lagrangian duals expressed in closed form. Similarities and differences are discussed based on a comparison of these dual structures. Weaknesses of the each of the two models are discussed and a merged model that combines attractive features of each of the two models is proposed.

Reverse efficiency measures for environmental assessment in data envelopment analysis

Environmental issues are becoming more and more important in our everyday life. Data Envelopment Analysis (DEA) is a tool developed for measuring relative operational efficiency. DEA can also be employed to estimate environmental efficiency where undesirable outputs like greenhouse gases exist. The classical DEA method identifies best practices among a given empirical data set. In many situations, however, it is advantageous to determine the worst practices and perform efficiency evaluation by comparing DMUs with the full-inefficient frontier. This strategy requires that the conventional production possibility set is defined from a reverse perspective. In this paper, presence of both desirable and undesirable outputs is assumed and a methodological framework for performing an unbiased efficiency analysis is proposed. The reverse production possibility set is defined and new models are presented regarding the full-inefficient frontier. The operational, environmental and overall reverse efficiencies are studied. The important notion of weak disposability is discussed and the effects of this assumption on the proposed models are investigated. The capability of the proposed method is examined using data from a real-world application about paper production.     

Measuring residential energy efficiency improvements with DEA

This paper measures energy efficiency improvements of US single-family homes between 1997 and 2001 using a two-stage procedure. In the first stage, an indicator of energy efficiency is derived by means of Data Envelopment Analysis (DEA), and the analogy between the DEA estimator and traditional measures of energy efficiency is demonstrated. The second stage employs a bootstrapped truncated regression technique to decompose the variation in the obtained efficiency estimates into a climatic component and factors attributed to efficiency improvements. Results indicate a small but significant improvement of energy efficiency over the studied time interval, mainly accounted for by fuel oil and natural gas users.     

Metafrontier efficiency analysis for hospital pharmacy services using dynamic network DEA framework

Medication management is a complex but critical process within the healthcare delivery system. The pharmacy department in healthcare facilities is responsible for acquisition, distribution and dispensing of medication to patients that involves a series of network process. This process can be categorized into two main subprocesses: i) pharmacy store and ii) patient services (i.e., ambulatory and inpatient pharmacy). The objective of this study was to investigate the relative efficiency level of the two subprocesses of pharmacy services in Malaysia's public hospitals. We used a nonconvex metafrontier technology to estimate technical efficiency of hospital pharmacies between specialist and nonspecialist hospital categories under the dynamic network data envelopment analysis (DNDEA) framework. For overall efficiency, both specialist and nonspecialist categories had similar mean efficiency scores. However, when measuring the efficiency level according to pharmacy store and patient services separately, the nonspecialist category had a higher mean efficiency score in pharmacy store, whereas for patient service efficiency, both categories had similar results. The patient service efficiency level was lower consistently over time, suggesting that the overall inefficiency of hospital pharmacy is greatly influenced by the inefficiency of the patient service. This suggests that systematic improvements in patient service efficiency should be a higher priority than pharmacy store efficiency to further increase the overall efficiency level. We believe that our findings will provide valuable information to policymakers towards achieving an efficient public healthcare service.     

DEA efficiency in agriculture: Measurement unit issues

The selection of inputs and outputs in DEA models represents a vibrant methodological topic. At the same time; however, the problem of the impact of different measurement units of selected inputs is understated in empirical literature. Using the example of Czech farms, we show that the DEA method does not provide consistent score estimates, neither a stable ranking for different popular measurements of labour and capital factors of production. For this reason, studies based on DEA efficiency results for differently measured inputs should be compared only with great caution.     

Research efficiency analysis of China's university faculty members: A modified meta-frontier DEA approach

Traditionally, data envelopment analysis (DEA) requires all decision-making units (DMUs) to have similar characteristics and experiences within the same external conditions. In many cases, this assumption fails to hold, and thus, difficulties will be encountered to some extent when measuring efficiency with a standard DEA model. Ideally, the performance of DMUs with different characteristics could be examined using the DEA meta-frontier framework. However, some of these DMUs are mixed-type DMUs that may affiliate with more than one group. Furthermore, the total number of observations of these mixed-type DMUs is limited. This is one of the common problems when studies focus on faculty research performance in higher education institutions. In general, a faculty member is affiliated with a certain department, and if the departmental assessment policy is not suitable for faculty members who are involved in interdisciplinary research, their performance could be underestimated. Therefore, the proposed model is an extension of the DEA meta-frontier framework that can assess the performance of mixed-type DMUs by constructing the reference set without the same type of DMUs. In this paper, the scientific research efficiency of faculty members at the Inner Mongolia University is used as an example to provide a better understanding of the proposed model. The proposed model is intended to provide a fair and balanced performance assessment method that reflects actual performance, especially for mixed-type DMUs.     

Target and technical efficiency in DEA: controlling for environmental characteristics

In this paper we propose a target efficiency DEA model that allows for the inclusion of environmental variables in a one stage model while maintaining a high degree of discrimination power. The model estimates the impact of managerial and environmental factors on efficiency simultaneously. A decomposition of the overall technical efficiency into two components, target efficiency and environmental efficiency, is derived. Estimation of target efficiency scores requires the solution of a single large non-linear optimization problem and provides both a joint estimation of target efficiency scores from all DMUs and an estimation of a common scalar expressing the environmental impact on efficiency for each environmental factor. We argue that if the indices on environmental conditions are constructed as the percentage of output with certain attributes present, then it is reasonable to let all reference DMUs characterized by a composed fraction lower than the fraction of output possessing the attribute of the evaluated DMU enter as potential dominators. It is shown that this requirement transforms the cone-ratio constraints on intensity variables in the BM-model (Banker and Morey 1986) into endogenous handicap functions on outputs. Furthermore, a priori information or general agreements on allowable handicap values can be incorporated into the model along the same lines as specifications of assurance regions in standard DEA.

Efficiency analysis of social protection expenditure in the Italian Regions

The attention and demand for greater social protection is increasing among the populations of all European countries. It is difficult to identify which of the structures and infrastructures, sectors and regional budgets are inefficient and/or negligent in respect of providing more social protection. In the political sphere the problem is examined from a qualitative point of view, because it is essential to have a valid decisional support system that provides useful information for structural and economic intervention programs devised to improve social protection. Regional spending on social protection is a fundamental component of individual well-being. This work is precisely aimed at assessing individual well-being in terms of technical expenses efficiency in the Italian Regions. Stochastic frontier analysis and a nonparametric deterministic model structure are the tools used to investigate the social protection determinants in the paper.     

A combined machine learning algorithms and DEA method for measuring and predicting the efficiency of Chinese manufacturing listed companies

Data Envelopment Analysis (DEA) is a linear programming methodology for measuring the efficiency of Decision Making Units (DMUs) to improve organizational performance in the private and public sectors. However, if a new DMU needs to be known its efficiency score, the DEA analysis would have to be re-conducted, especially nowadays, datasets from many fields have been growing rapidly in the real world, which will need a huge amount of computation. Following the previous studies, this paper aims to establish a linkage between the DEA method and machine learning (ML) algorithms, and proposes an alternative way that combines DEA with ML (ML-DEA) algorithms to measure and predict the DEA efficiency of DMUs. Four ML-DEA algorithms are discussed, namely DEA-CCR model combined with back-propagation neural network (BPNN-DEA), with genetic algorithm (GA) integrated with back-propagation neural network (GANN-DEA), with support vector machines (SVM-DEA), and with improved support vector machines (ISVM-DEA), respectively. To illustrate the applicability of above models, the performance of Chinese manufacturing listed companies in 2016 is measured, predicted and compared with the DEA efficiency scores obtained by the DEA-CCR model. The empirical results show that the average accuracy of the predicted efficiency of DMUs is about 94%, and the comprehensive performance order of four ML-DEA algorithms ranked from good to poor is GANN-DEA, BPNN-DEA, ISVM-DEA, and SVM-DEA.     

Changes in hospital efficiency and size: An integrated propensity score matching with data envelopment analysis

Turkey has made huge investments in city hospitals. The distinguishing feature of these hospitals is that they are physically large. Although many studies have investigated the efficiency of public hospitals, there are a few studies on the effect of hospital size on efficiency. This study examines the effect of hospital size on changes in public hospital efficiencies. The analysis is made up of three steps. First, using a bootstrap data envelopment analysis (DEA), the pure efficiency scores of each hospital were calculated. Second, propensity score matching (PSM) was used to ensure that any differences could be attributed to a particular class of hospital size, and not be due to differences in sample characteristics between the intervention and control groups. To highlight a potential time difference between small and large hospitals, the efficiencies of hospitals were examined from 2014 to 2017. Third, the Mann–Whitney U test was used to conduct a robustness check of the DEA and PSM results. Fourth, logistic regression was used on balanced data to examine the determinants of the efficiency of public hospitals. There are remarkable differences in the results obtained before and after matching the groups based on the bed-occupancy rate. Additionally, urban location is a key predictor of efficient and inefficient hospitals. This study also highlights that integrating DEA and PSM is a useful strategy in accurately identifying predictors of efficiencies of hospitals by creating balanced groups. Health policymakers should consider the efficiency advantages of high workload and service burden in the planning of public hospitals.     

The role of spatial interdependence in local government cost efficiency: An application to waste Italian sector

The paper aims to study the effect of spatial interdependence, among nearby municipalities, on public services efficiency. An empirical analysis on the waste disposal service in 4250 Italian municipalities was carried out to evaluate the efficiency of waste management expenditure, once the impact of positive/negative externalities, of neighbouring local governments, on efficiency levels is isolated. From a methodological point of view, our study extends the spatial stochastic frontier methodology proposed in Fusco & Vidoli (2013) usable only for production analysis, allowing to admit into a cost frontier the spatial autocorrelation among residuals. Ignoring spatial autocorrelation leads to inferential problems violating one of the most important assumption of classical regression models: the non-correlation of the residuals. We found a significant spatial interdependence among neighbouring municipalities in term of cost efficiency, that, thanks to the methodology proposed, has been isolated allowing a discussion on the specific efficiency of municipalities. These results may suggest the need to consider proximity effects in future investigations about the efficiency of waste management and, more generally, of public services.     

Methodological Advances in DEA: A survey and an application for the Dutch electricity sector

We survey the methodological advances in DEA over the last 25 years and discuss the necessary conditions for a sound empirical application. We hope this survey will contribute to the further dissemination of DEA, the knowledge of its relative strengths and weaknesses, and the tools currently available for exploiting its full potential. Our main points are illustrated by the case of the DEA study used by the regulatory office of the Dutch electricity sector (Dienst Toezicht Elektriciteitswet; Dte) for setting price caps.     

Aggregating the DEA prospect cross-efficiency with an application to state key laboratories in China

With growing investments in the state key laboratories (SKLs) of China, it is essential to assess the efficiency of the administrative departments regarding managing the SKLs of China. However, few studies have been conducted about the evaluation of the performance of Chinese administrative departments in managing SKLs. To fill this gap, this paper investigates the performance within 22 SKL administrative departments in China, based on a data envelopment analysis cross-efficiency prospect aggregation approach incorporating the risk preference of decision maker. The empirical results show the major findings: (a) serious imbalance exists regarding the investment of 22 SKL administrative departments; (b) there are great differences among the performance of 22 SKL administrative departments; (c) some SKL administrative departments face an insufficient situation regarding the outputs; (d) different risk attitudes of decision maker have the significant impact on the evaluation results of the 22 SKL administrative departments. Based on these findings, we provide several policy suggestions for the development of SKLs in China.     

Operating efficiency in Chinese universities: An extended two-stage network DEA approach

The result shows that it accepts the null hypothesis. Namely, there is no significant difference in the operating efficiency of universities in different regions. That is to say, although the efficiency of the central and western universities is slightly better than that of the eastern universities in terms of the average efficiency, there is no significant efficiency difference among the eastern, central, and western regions statistically. Therefore, it shows a balanced development trend for the efficiency of universities in different regions.     

Combining common-weights DEA window with the Malmquist index: A case of China’s iron and steel industry

In the conventional data envelopment analysis (DEA) window analysis, a decision-making unit (DMU) in each window is treated as different units in each period so that the evaluation for one unit is performed on different scales over time. This paper proposes a novel window analysis based on common weight across time (CWAT), which evaluates each unit in each window by its common scale independent of time. The model for obtaining common weights is described as linear programming. And the paper suggests the Malmquist productivity index (MPI) on CWAT, CWAT MPI, to analyze productivity change by inheriting the result of window analysis. The numerical experiments are illustrated to examine the validity of CWAT and MPI, and the result shows that the proposed method provides a new evaluation scale compared to previous studies. The proposed model is applied to evaluate the performance of China 45 iron and steel enterprises during 2009–2017. The energy and environmental efficiency are calculated using CWAT, and CWAT MPI analyzes the productivity change.     

A cautionary note on methods of comparing programmatic efficiency between two or more groups of DMUs in data envelopment analysis

In some applications of data envelopment analysis (DEA) there may be doubt as to whether all the DMUs form a single group with a common efficiency distribution. The Mann–Whitney rank statistic has been used to evaluate if two groups of DMUs come from a common efficiency distribution under the assumption of them sharing a common frontier and to test if the two groups have a common frontier. These procedures have subsequently been extended using the Kruskal–Wallis rank statistic to consider more than two groups. This technical note identifies problems with the second of these applications of both the Mann–Whitney and Kruskal–Wallis rank statistics. It also considers possible alternative methods of testing if groups have a common frontier, and the difficulties of disaggregating managerial and programmatic efficiency within a non-parametric framework.      

Adjusting for the environment in DEA: A comparison of alternative models based on empirical data

Due to the existence of free software and pedagogical guides, the use of Data Envelopment Analysis (DEA) has been further democratized in recent years. Nowadays, it is quite usual for practitioners and decision makers with no or little knowledge in operational research to run their own efficiency analysis. Within DEA, several alternative models allow for an environmental adjustment. Four alternative models, each user-friendly and easily accessible to practitioners and decision makers, are performed using empirical data of 90 primary schools in the State of Geneva, Switzerland. Results show that the majority of alternative models deliver divergent results. From a political and a managerial standpoint, these diverging results could lead to potentially ineffective decisions. As no consensus emerges on the best model to use, practitioners and decision makers may be tempted to select the model that is right for them, in other words, the model that best reflects their own preferences. Further studies should investigate how an appropriate multi-criteria decision analysis method could help decision makers to select the right model.     

A new method for measuring congestion in data envelopment analysis

In data envelopment analysis (DEA), there are two principal methods for identifying and measuring congestion: Those of Färe et al. [Färe R, Grosskopf S. When can slacks be used to identify congestion. An answer to W. W. Cooper, L. Seiford, J. Zhu. Socio-Economic Planning Sciences 2001;35:1–10] and Cooper et al. [Cooper WW, Deng H, Huang ZM, Li SX. A one-model approach to congestion in data envelopment analysis. Socio-Economic Planning Sciences 2002;36:231–8]. In the present paper, we focus on the latter work in proposing a new method that requires considerably less computation. Then, by proving a selected theorem, we show that our proposed methodology is indeed equivalent to that of Cooper et al.     

Decision making framework for tender evaluation and contractor selection in public organizations with risk considerations

Selecting the best construction contractor plays a critical role in the success of any construction project. Moreover, in the public sector, the traditional lowest bid method is still broadly used and contracts are often awarded based on the lowest price. However, this method has been criticized by many researchers because even if it might guarantee the lowest cost for a project, it does not guarantee the maximum value in terms of time and quality. More particularly, the risk exposure during the tendering process is usually very high and the success of the construction project is strongly related to managing this risk in an appropriate way. Therefore, the selection of the most appropriate contractor should be based on a set of criteria such as technical capability, financial stability, risk, safety, etc., in addition to cost in order to avoid problems that may happen after the contract is awarded. This study aims therefore to develop a decision making framework (DMF) to assist the public organizations in selecting the most appropriate construction contractor(s). The proposed DMF uses a combination of multi-criteria decision making (MCDM) tools and fuzzy logic theory and consists of three stages. In the first stage, data envelopment analysis (DEA) is used to reduce the number of contractors, based on multiple criteria, such that only efficient contractors are considered. In the second stage, the risk factors that are related to each efficient contractor are identified and assessed using a fuzzy logic based approach. Finally, in the third stage, a bi-objective mixed integer linear programming (MILP) model is developed to select the best contractor(s) based on cost and risk and to determine the optimal quantity of work to be assigned to each selected contractor. Indeed, the proposed approach considers the multiple award contract case in which more than one contractor can be selected to share the amount of work to be performed. We assume that prior to using the proposed DMF, a pre-qualification study is conducted using multiple criteria chosen by the public organization, and only pre-qualified contractors are included in the first stage of the proposed DMF. Moreover, a case study inspired from the contractor selection process in a public organization in the United Arab Emirates (UAE) is used to show the effectiveness of the proposed approach.     

A combination of QFD and imprecise DEA with enhanced Russell graph measure: A case study in healthcare

Quality function deployment (QFD) is a proven tool for process and product development, which translates the voice of customer (VoC) into engineering characteristics (EC), and prioritizes the ECs, in terms of customer's requirements. Traditionally, QFD rates the design requirements (DRs) with respect to customer needs, and aggregates the ratings to get relative importance scores of DRs. An increasing number of studies stress on the need to incorporate additional factors, such as cost and environmental impact, while calculating the relative importance of DRs. However, there is a paucity of methodologies for deriving the relative importance of DRs when several additional factors are considered. Ramanathan and Yunfeng [43] proved that the relative importance values computed by data envelopment analysis (DEA) coincide with traditional QFD calculations when only the ratings of DRs with respect to customer needs are considered, and only one additional factor, namely cost, is considered. Also, Kamvysi et al. [27] discussed the combination of QFD with analytic hierarchy process–analytic network process (AHP–ANP) and DEAHP–DEANP methodologies to prioritize selection criteria in a service context. The objective of this paper is to propose a QFD–imprecise enhanced Russell graph measure (QFD–IERGM) for incorporating the criteria such as cost of services and implementation easiness in QFD. Proposed model is applied in an Iranian hospital.