Abstract

     This study integrated multiple objective decision-making approaches including data envelopment analysis (DEA), rough set theory and TOPSIS method for exploring the competitiveness of pharmaceutical multinational enterprises. Firstly, this study applied an advanced two-stage network DEA to measure the R&D efficiency and business performance of pharmaceutical multinational enterprises (PMNEs) listed in the Forbes Global 2000 and ranked these PMNEs by using rough set theory, DEA and TOPSIS method. In addition, differences in environmental, social, and governance (ESG) performance across three continents were investigated. Findings show that North America is significantly the best (worst) region in terms of business performance (R&D efficiency) while Europe is significantly the best (worst) region in terms of R&D efficiency (business performance). Alfresa Holdings Corporation, a PMNE from Japan, is the only PMNE that is efficient from both an R&D and business performance perspective. European PMNEs have significantly better environmental and social performance than other regions, however, they have the worst governance performance. Overall, this study provides insights to managers and investors into the application of various methods for accurately measuring performance and ranking multinational enterprises.

Introduction

     The pharmaceutical industry is one of the most important and competitive industries in the world, it not only has a critical role in the health maintenance of individuals but also in economic growth (Sharma & Modgil, 2019). Pharmaceutical firms have spent a substantial proportion of their time and investment in research and development (R&D) (Rao, 2020). In 2018, R&D expenditure in the pharmaceutical industry was 179 billion U.S. dollars globally (Mikulic, 2020). A correct grasp of the R&D efficiency of the industry is required to improve resource allocation and thereby prevent either excess or shortage of resource inputs (Liu & Lyu, 2020). According to Lu et al. (2019), evaluating multiple indicators simultaneously is useful for appropriate decision-making. An overall efficiency can be decomposed into two stages of efficiencies (Kao & Hwang, 2008), suggesting that we should also evaluate the sub-processes of a firm (Kao & Hwang, 2011). That is, managers should evaluate their firm performance not only from a multidimensional perspective but also from those of its internal processes. As mentioned in the research of Sharma and Modgil (2019), business performance additionally depends on cost reduction of manufacturing operations and improving the firm’s innovative ability. Recently, Hsieh et al. (2020) have applied two-stage data envelopment analysis (DEA) to investigate organizations’ innovation and business performance by investigating the network structures of decision-making units (DMUs).

Conclusion

     This study measures the firm performance of 41 PMNEs from a two-stage perspective, namely R&D efficiency and business performance, by integrating a two-stage network DEA and SOCP technique. Moreover, this study integrates the DEA approach and rough set theory to rank PMNEs. The findings of this research can serve as a reference for managers of PMNEs in their decision-making process. Besides, we examine differences in the ESG scores of the PMNEs among different geographic regions (America, Asia, and Europe). This acts as a guide for investors, managers, and other stakeholders when attempting to move their ESG initiatives further.

     R&D performances in the operation of the observed PMNEs are not attracting enough attention. Alfresa Holdings Corporation is the only efficient PMNE for both R&D efficiency and business performance. North America is significantly the best (worst) region in terms of business performance (R&D efficiency) while Europe is significantly the best (worst) region in terms of R&D efficiency (business performance). From the perspective of ESG performance, European PMNEs significantly have better environmental and social performance than other regions whereas they are the worst concerning governance performance.

1. Introduction

2. Related studies and research questions

3. Research design

4. Results

5. Conclusion

Appendix: Variable Definitions

Reference

This paper examines the association between the managerial ability of acquiring firms and their long-term performance after mergers and acquisitions (M&As). Based on M&A data for U.S. firms from 2000 to 2012, we find that acquiring firms with higher managerial ability achieve better longterm operating performance and stock returns. We also find that the positive effect of managerial ability on long-term performance is more pronounced when acquirers and target firms belong to the same industry. The result suggests that managers who have higher ability to manage their firms, i.e., to generate higher revenues for given resources, are more capable of achieving higher synergy benefits and better post-acquisition performance in same-industry acquisitions than in cross-industry acquisitions.

Introduction

Pursuing mergers and acquisitions (M&As) is a highly popular investment strategy among firms seeking to boost their corporate growth or strengthen their competitive advantage over rivals. The global volume of M&A deals in 2018 and 2017 reached US$4.1 trillion and US$3.7 trillion, respectively (J.P. Morgan, 2019). The common reason for engaging in M&As is to achieve synergy and efficiency effects, and ultimately to increase the shareholder wealth of acquiring firms (Tuch and O’Sullivan, 2007; Vaara, 2002). Prior M&A studies generally indicate positive short-term returns for target firms (e.g., Martynova and Renneboog, 2008). However, empirical research into acquirer post-acquisition performance has failed to find consistent evidence of improved performance after acquisitions. Agrawal and Jaffe (2000) show that the abnormal returns to acquiring firms in the years following an acquisition are negative, or at best not statistically different from zero. In the meta-analyses of empirical research on post-acquisition performance, King et al. (2004), Tuch and O’Sullivan (2007) and Dutta and Jog (2009) conclude that, on average, M&A activity does not lead to superior financial performance. These studies highlight great variations in acquisition performance, with about 40% of acquiring firms achieving positive returns in the twoto three-year period after acquisitions, and about 50% suffering negative returns.

1- Introduction

2- Literature review

3- Research methodology

4- Results

5- Discussion and conclusion

References

Abstract

Various approaches are used to measure the firms’ performance. Grey relational analysis is one of the multiple attribute decision-making methods and data envelopment analysis is used to calculate the efficiency. Regarding the importance of water and wastewater companies’ services, the present study, evaluates the performance and rank these companies by using grey relational analysis and data envelopment analysis approaches based on balanced scorecard criteria. Besides, balanced scorecard considers all levels of organization. In this research, statistical population includes thirty-five municipal water and wastewater companies in Iran for the year 2017. In order to ascertain grey relational grade, fuzzy normalization method was used then by subtracting normalized numbers from one, reference sequences obtained and in the next step, grey relational coefficient was calculated and finally, grey relational grade was determined by multiplying relative weight from Shannon entropy to relational coefficients. In order to assess companies’ efficiency in data envelopment analysis, after ascertaining input and output indices, with the assumption of constant returns to scale and output-oriented viewpoint, the efficiency scores were calculated. Also, to rank efficient units Anderson-Petersen model implemented. Results demonstrated that, grey relational analysis is a more accurate method to measure the performance of water and wastewater companies.

Introduction

Performance measurement defined as the process of quantifying the efficiency and effectiveness of a past action (Neely, Adams, & Kennerley, 2002). It has been used extensively in public sector in the last two decades (Speklé & Verbeeten, 2014). In many countries, Public sector is responsible for the major part of water and sewage services (Consciência Silvestre, 2012). Moreover, efficient management of water firms is necessary for sustainable municipal water processes (Molinos-Senante, Porcher, & Maziotis, 2018). So, assessing the performance of water industry is needed broadly due to its environmental, economic and social benefits (Nogueira Vilanova, Magalhães Filho, & Perrella Balestieri, 2015). One of the performance measurement methods that have been considered extensively in the recent years is balanced scorecard (BSC). BSC is a strategic planning tool developed by Kaplan and Norton in 1992. It is a promising approach for providing a deep and precise understanding of the past and current status of companies. BSC consists both financial and non-financial aspects (Glykas, Valiris, & Chytas, 2011; Dehghanbaghi, Varmazyar, & Afkhami, 2016). In order to measure the performance of an organization, various criteria are used: such as effectiveness, efficiency, productivity, profitability, etc. In many complicated systems, many parameters affect the system simultaneously. Therefore, in decision-making process we encounter multiple criteria. Various methods used in solving multi criteria tasks such as analytic hierarchy process, the technique for order of preference by similarity to ideal solution (TOPSIS), data envelopment analysis and so on (Yoon & Hwang, 1995). However, sometimes the grey relationships between indicators, lack of sufficient and clear information or difficulty of collecting experimental and practical data are the problems researchers face in some systems. Thus, to avoid data aggregation and wasting resources, grey relational analysis is an appropriate approach in these conditions (Lin, Chen, & Liu, 2004).

1- Introduction

2- Methods and data

3- Analysis of empirical results

4- Conclusions and policy implications

References

Abstract

China has implemented its carbon emission trading system (ETS) in seven pilots since 2013. Many methods have been used to evaluate the effect and efficiency of the ETS in reducing carbon emissions. Evaluating the carbon ETS to determine whether it has co-benefited the economy and environment in the seven pilots is crucial for the development of China. Moreover, different methods of measurement reveal different results on how efficient the seven carbon emission trading markets (ETMs) are. We use the difference-in-differences (DID) method to evaluate the impact of carbon emissions and economic growth following ETS implementation. Based on the data of industrial carbon emissions in 30 provinces of China from 2008 to 2016, the impact of ETS on the carbon emission reduction and economic growth of enterprises is empirically tested. Data envelopment analysis (DEA) evaluates the operating efficiency of the carbon ETMs. Based on the seven carbon emission trading pilots conducted in China in 2014–2016, the carbon ETMs differentiation system in the pilot area is taken as the input index and the ETS implementation effect is used as the output index to construct the full DEA evaluation model for gauging the operation efficiency of the carbon ETMs. The results show that the implementation of the carbon trading policy increases the economic dividend (13.6%) generated by the gross industrial output value, but significantly reduces the emission (24.2%) of industrial CO2 in all seven carbon emission trading pilots. The average DEA efficiency of the seven carbon ETMs operations in China have increased annually.

Introduction

To realize the international carbon emission reduction target, the National Development and Reform Commission promulgated the Notice on Carbon Emission Rights Pilot Work in October 2011. Seven provinces and cities, including Beijing, Tianjin, Shanghai, Guangdong, Shenzhen, Hubei, and Chongqing, were selected to conduct the pilot work of the carbon ETS. Each pilot had covered more than 20 industries and nearly 3000 key emission enterprises by the end of September 2017. The market operation has been generally stable, with an accumulated turnover of 200 Mt of CO2. The industrial sector is the main carbon emitter. Therefore, the industrial CO2 emissions and gross industrial output value are the key data to evaluate the effect of the carbon ETS. In addition, exploring the operating efficiency of the seven carbon ETMs is a powerful illustration of the ETS. The effect of carbon ETS implementation and its operating efficiency at home and abroad in recent years are reported in this study. A large corpus of literature has explored the impact of the carbon ETS on economic growth and environment. P. et al. [1] used the energy-saving and emission-reduction investment data of 29 provinces and cities in China from 1996 to 2005, based on the allocation of five regional emission reduction targets, such as carbon emissions, energy consumption, population, GDP, and per capita GDP. The study found that emission reduction targets based on carbon emissions and populations are more equitable in terms of abatement cost savings across regions. Hübler et al. [2] used the computable general equilibrium model to evaluate the carbon trading policy in China. Model simulations reveal that climate policy can result in a GDP loss of around 1% in 2020 and a welfare loss of around 2% by 2030. Wang et al.

1- Introduction

2- Hierarchical evaluation index system of investment strategies in distribution networks

3- Dynamic yardstick evaluation method for investment strategies in distribution networks

4- Case study

5- Conclusions

References

Abstract

The traditional investment for distribution networks is mainly evaluated and conducted from the static perspective. A dynamic comprehensive evaluation method is essential to obtain an efficient investment strategy. Firstly, a hierarchical evaluation index system is constructed to describe the overall performance of the distribution network, which includes six types of criteria such as information level, power supply capacity, asset utilization efficiency and economy, power supply quality and loss, power supply reliability, and sustainable development level. Each criterion is composed of input and output indicators. Then, using projection pursuit method considering subjective weight constraints, a combined weight optimization model is proposed to calculate the weight vector of each criterion. Furthermore, the data envelopment analysis (DEA) based dynamic evaluation approach is set up to compute the investment efficiency defined as ratio of output and input. The time degree theory is also introduced to realize dynamic evaluation. Via yardstick competition among multiple regions and “reward and punishment” rule, a precise investment planning strategy can be achieved while minimizing construction cost and maximizing efficiency of the resource allocation. The numerical results on a practical 10-region distribution system in four planning cycles verify the effectiveness of the proposed method.

Introduction

With the accelerating growth of electricity usage in modern times, the distribution network, playing a significant role in guaranteeing high quality and reliability of power supply for customers, has faced serious challenges. It is a sophisticated and enormous project for distribution networks to achieve precise investment planning [1]. Currently, it is a fact that automation reform of the distribution network is still in its infancy. Meanwhile, the investment scale of the distribution network is gigantic and shows an increasing trend year by year in China. Such being the case, there is no doubt that evaluating the overall investment efficiency comprehensively and scientifically is beneficial to efficaciously avoid deficiency of construction, to strike a balance between technology and economy in the distribution network [2]. In recent years, significant research efforts have been devoted to the optimal investment of modern power distribution systems. A multiobjective optimization considering reliability and costs as two objective functions has been presented in Ref. [3] to make investment strategy for multi-stage smart distribution network expansion planning. Although applying of the proposed model has shown a significant improvement in the area of distribution network planning, contemporary expansion of power system and information infrastructures weren’t considered. Mokryani. G [4] proposed a probabilistic method for active distribution networks (ADN) investment planning with integration of demand response (DR), aiming at simultaneously minimizing the total investment cost and total energy losses of the lines from the point of view of distribution system operators (DSOs). In Ref. [5], regarding DR as virtual distributed resources to cover the effect of uncertain parameters, an aggregated model for planning and reconfiguration of ADN has been proposed, where a bi-level optimization procedure is developed to solve the proposed model. Zeng and Feng [6] presented an optimal integrated investment strategy for supporting growing penetration of electric vehicles in distribution systems. In Ref. [7], by minimizing the total investment and operational costs, a multi-stage expansion planning is proposed to consider dynamic behavior of the system parameters asset management and geographical constraints.

1- Introduction

2- Cross-efficiency evaluation

3- Prospect theory

4- Prospect cross-efficiency model for cross-efficiency evaluation

5- An illustrative example

6- Conclusions and discussions

References

Abstract

Cross-efficiency evaluation in data envelopment analysis (DEA) is a useful tool in evaluating the performance of decision-making units (DMUs). It is generally assumed that decision makers (DMs) are completely rational in common cross-efficiency evaluation models, which fail to consider the DM’s risk attitude that plays an important role in the evaluation process. To fill this gap, we investigate the cross-efficiency evaluation in DEA based on prospect theory. First, we introduce a prospect value of the DMU to capture the non-rational psychological aspects of a DM under risk. Second, based on the prospect value, we propose a new cross-efficiency model termed the prospect cross-efficiency (PCE) model. Particularly, some existing cross-efficiency evaluation models can be deemed as the special cases of the PCE model with suitable adjustments of the parameters. Furthermore, this paper provides an empirical example to evaluate cross-efficiency with several selected universities directly managed by the Ministry of Education of China to illustrate the effectiveness of the PCE model in ranking DMUs.

Introduction

Cross-efficiency evaluation, developed by Sexton, Silkman, and Hogan (1986), has been widely accepted as a discriminative assessment tool for data envelopment analysis (DEA). It is generally used for distinguishing efficient decision-making units (DMUs) from one another (Despotis, 2002). Each DMU in cross-efficiency evaluation has a self-evaluated efficiency derived by its own set of optimal weights and n 1 peer-evaluated efficiencies obtained by the optimal weights of other DMUs. Consequently, a final efficiency for ranking DMUs is aggregated based on n efficiencies. The major characteristics of cross-efficiency evaluation are the following: (1) ranking the DMUs in a unique order (Doyle & Green, 1995), (2) eliminating unrealistic weight schemes without predetermining any weight restrictions (Anderson, Hollingsworth, & Inman, 2002), and (3) effectively differentiating between good and poor performers among the DMUs (Boussofiane, Dyson, & Thanassoulis, 1991). Due to these advantages, cross-efficiency evaluation has been used in a variety of applications, including project ranking (Green, Doyle, & Cook, 1996), the measurement of the labour assignment in a cellular manufacturing system (Ertay & Ruan, 2005), sports rankings (Wu, Liang, & Chen, 2009), corporate philanthropic selection (Partovi, 2011), the supplier selection problem in public procurement (Falagario, Sciancalepore, Costantino, & Pietroforte, 2012), and portfolio selection (Lim, Oh, & Zhu, 2014; Mashayekhi & Omrani, 2016). Despite the many advantages and wide applications of cross-efficiency, its usefulness is possibly reduced by the non-uniqueness of the optimal weights (Doyle & Green, 1994). Specifically, the possible existence of multiple optimal weights in the evaluation leads to different sets of cross-efficiency scores for each DMU.

Data envelopment analysis (DEA) is a technique for identifying the best practices of a given set of decision-making units (DMUs) whose performance is categorized by multiple performance metrics that are classified as inputs and outputs. Although DEA is regarded as non-parametric, the sample size can be an issue of great importance in determining the efficiency scores for the evaluated units, empirically, when the use of too many inputs and outputs may result in a significant number of DMUs being rated as efficient. In the DEA literature, empirical rules have been established to avoid too many DMUs being rated as efficient. These empirical thresholds relate the number of variables with the number of observations. When the number of DMUs is below the empirical threshold levels, the discriminatory power among the DMUs may weaken, which leads to the data set not being suitable to apply traditional DEA models. In the literature, the lack of discrimination is often referred to as the “curse of dimensionality”. To overcome this drawback, we provide a simple approach to increase the discriminatory power between efficient and inefficient DMUs using the well-known pure DEA model, which considers either inputs only or outputs only. Three real cases, namely printed circuit boards, Greek banks, and quality of life in Fortune’s best cities, have been discussed to illustrate the proposed approach.

Introduction

Data envelopment analysis (DEA) is an excellent management science tool that measures the relative performance of a set of entities or decision-making units (DMUs) with multiple performance measures that are classified as inputs and outputs. Nevertheless, problems of discrimination between efficient and inefficient DMUs often arise when there is a relatively large number of performance measures (variables) when compared to the number of DMUs; this may lead to efficient units being incorrectly classified as inefficient and inefficient units being misclassified as efficient. As Adler and Yazhemsky (2010, p. 283) showed, “the latter occurs particularly frequently with small data sets under the assumption of variable returns-to-scale”. In the literature, the lack of discrimination is often referred to as the “curse of dimensionality” (e.g., Adler & Golany, 2007; Daraio & Simar, 2007). The lack of discriminating power has important implications, as in practice it can limit the managerial insights that can be drawn (Ghasemi, Ignatius, & Rezaee, 2019). In this sense, regarding the number of DMUs (sample size), it is quite clear that there are advantages to having larger data sets, as at a given number of DMUs, the efficiency score of each DMU can rely heavily on the number of variables (inputs and outputs) (Cinca & Molinero, 2004) – as such, the greater the number of variables, the less discerning the DEA analysis is (Jenkins & Anderson, 2003). Nevertheless, the literature indicates some empirical rules regarding the number of DMUs versus the number of inputs and outputs.

This study proposes a decomposition approach based upon data envelopment analysis that identifies various sources of CO2 emission. In addition to the previously identified seven sources, we propose three new ones. As an empirical application, this study applies the proposed approach to examine ten sources of CO2 emission across Chinese provinces from 2008 to 2015. In the empirical study, we overcome methodological difficulties related to (a) what methodological merits of technology change indexes are and how to measure them in a separated manner and (b) how to separate effects of various sources and how to identify the annual shift of those sources of CO2 emission changes. This study finds three empirical implications. First, three sources may increase the amount of CO2 emission. They include an economic activity, a technology change on a desirable output and a potential energy intensity change. Second, two sources are important in reducing the amount of CO2 emission. They are an operational efficiency change on a desirable output and a change in energy saving technology. Finally, conflicting results exist in some sources in the manner that they increase CO2 emission in some provinces but decrease it in the other provinces.

Introduction

China has experienced rapid economic growth and consequently it has drastically increased the Carbon Dioxide (CO2) emission. According to National Bureau of Statistics of China (2018), China’s Gross Domestic Product (GDP) reached 82,712.17 billion RMB (i.e. China’s currency unit) in 2017, which was 1.67 times higher than 2010 and 4.54 times of the amount in 2000. The average annual economic growth rates were 10.34% from 2000 to 2009 and 7.95% from 2010 to 2017. Along with the rapid economic growth, China has increased the amount of CO2 emission. For example, British Petroleum (BP, 2018) has reported that China’s CO2 emission has increased from 3352.7 million tons in 2000 to 9123.0 million tons in 2016. The share of China’s CO2 emission has also increased in the world total. For example, the share increased from 13.97% in 2000 to 27.29% in 2016. Under such a situation, it has attracted great policy attention on how to reduce the emission amount. Along with the increase, China faces a growing international pressure to reduce the amount of CO2 emission. The Chinese government has pledged to control the amount. According to State Council (2015), the target was to reduce the CO2 emission by 2030. Under the policy direction, a top priority for the Chinese government is to set the target on CO2 emission. In following the direction, this study is concerned with identifying potential sources which influence China’s CO2 emission changes at a provincial level.

1- Introduction

2- Data and tools

3- Data envelopment analysis (DEA)

4- Investment scenarios and benchmarking of individual asset

5- Cross-asset investment benchmarking

6- Conclusions and discussions

References

Abstract

Highway agencies have been using many of the elements of asset management with the support of various decision-making tools. To determine the most effective investment strategy with scarce resources, the integration, and hence better utilization, of existing tools and practices across asset classes is generally lacking. This paper applies data envelopment analysis (DEA) to benchmark different highway investment scenarios using existing data or data readily available through existing models. Three asset types, pavements, bridges, and traffic signage, are investigated. Asset investment analysis results from the Highway Economic Requirements System State Version (HERS-ST) application, the PONTIS bridge management system software, and purpose-built traffic signage spreadsheet are obtained to capture the changes of performance measures under various budget scenarios and are further used as the inputs for the DEA process to benchmark investment scenarios for each individual asset. Subsequently, the performance measures and budget levels are assembled in the Asset Manager-NT software, whose results are input into DEA to benchmark cross-assets resource allocation scenarios. Planning for the management of highway network is addressed via case studies in a systematic manner that recognizes the tradeoffs among different funding periods and objectives such as preserving existing investments, safety, roughness and user costs. This study has established a preliminary implementable framework of highway asset management by linking DEA approach and current widely used decision-making tools for more efficient investments within and cross assets, and better understand of the tradeoffs, costs and consequences of various asset management decisions.

Introduction

At its core, asset management is about using limited transportation dollars in the most cost-effective way possible (AASHTO, 2011; Adey, 2017; McNeil et al., 2008; Taggart et al., 2014). A fundamental challenge in managing transportation infrastructure assets is to determine how to allocate scarce resources among disparate asset categories (roads, bridges, safety, mobility, etc.) and types of needs (replacement, rehabilitation, routine maintenance, etc.) (Bai et al., 2011, 2015; Cambridge Systematics, Inc., 2006; Dehghanisanij et al., 2010; Fwa and Farhan, 2012; Li et al., 2012; Li and Sinha, 2004; Mrawira and Amador, 2009; Pagano et al., 2005; Wu et al., 2012). Allocating resources between these areas is a complex problem requiring consideration of multiple objectives and constraints. To achieve the best results at both the individual asset system and the overall system levels, given a budget, five types of approaches are traditionally used for fund appropriation among competing highway asset components (Fwa and Farhan, 2012): (1) appropriation of funds based on historical allocations to the individual asset with minor adjustments to allow for special requirements (OECD, 2001); (2) formulabased appropriation, whose funds are allocated according to a predetermined formula based on engineering judgment or past experience consisting of selected parameters from the various assets (such as empirical regression models); (3) asset value-based appropriation, which implicitly assumes that the maintenance needs of each asset is proportional to its asset value (Jani, 2007; Sirirangsi et al., 2003); (4) maintenance needs-based appropriation, which allocates the available funds in proportion to the maintenance needs of each individual asset, but does not address optimality for the overall asset system (Flintsch and Bryant Jr., 2006); and (5) performance-based appropriation, which ties fund appropriation with the desired performance level of each asset component (Cowe et al., 2006; Gharaibeh et al., 1999, 2006). All approaches suffer limitations as they do not achieve optimality at both individual and overall system levels simultaneously.

Slacks that arise when nonparametrically constructing technologies are relevant because they can be an important source of technical inefficiency. This paper extends the measurement of dynamic inefficiency in the full input-output space in the adjustment-cost theory framework to account for slacks. In particular, the paper develops the dynamic weighted additive model in Data Envelopment Analysis (DEA) and shows its main properties. Additionally, the approach is illustrated by a real application. The empirical application concerns data on large firms in the dairymanufacturing industry in the main dairy-producing countries in the European Union (France, Germany, Italy, Spain, Poland, and the Czech Republic) from 2005 to 2012. The results show the differences in average dynamic inefficiency between the analyzed countries. The findings also indicate that, not surprisingly, firms are, on average, closer to their own-country frontier than the common frontier comprising all firms, regardless of country. Greater inefficiency was also found, on average, in the new approach when related to the dynamic framework that does not account for slacks.

Introduction

The measurement of production (in)efficiency attracts considerable attention in the scientific literature, as it is a relevant topic for managers and policy-makers. 1 Since Farrell’s (1957) work showing how to empirically estimate production functions enveloping all observations in the sample, research on inefficiency measurement focuses on developing and applying static inefficiency models through the nonparametric method of data-envelopment analysis (DEA) (Charnes et al., 1978; Banker et al., 1984) or parametric approaches of deterministic and stochastic frontier models (Aigner and Chu, 1968; Aigner et al., 1977). Static models of inefficiency ignore the dynamic interdependence of firms’ production decisions over time and treat firms’ capital and other quasi-fixed inputs as fixed. If there is dynamic interdependence, assuming a static theory of production results in biased measurements of inefficiency. More recent inefficiency literature, both in DEA and parametric contexts, recognizes the importance of modelling the dynamics of firms’ production decisions (Serra et al., 2011; Silva et al., 2015; Kapelko et al., 2014; Fallah-Fini et al., 2014; Tone and Tsutsui, 2010, 2014). Despite different approaches developed to measure dynamic inefficiency of production, one can broadly classify them into two main groups. The first group of studies, initiated by Shephard and Färe (1975), Sengupta (1995), and Färe and Grosskopf (1996) rely on the idea of multi-stage production systems, in which some activities are carried over from one period to the next. For example, an output in one period is used as an input for the next, or a quasi-fixed input at the end of the period is treated as an additional output in that period. As such, this group of studies is closely related with network inefficiency models (see Avkiran, 2009; Tone and Tsutsui, 2009). Chronologically speaking, Nemoto and Goto (1999, 2003), Sueyoshi and Sekitani (2005), Chen (2009), Chen and Van Dalen (2010), Tone and Tsutsui (2010, 2014), and Skevas et al. (2012) are all examples of this research line of dynamic inefficiency studies. The second group of studies employs the adjustment-cost technology framework, in which the dynamic interdependence of firms’ production decisions is in the form of adjustment costs. These costs that represent transaction or reorganization costs, such as for learning, arise in this framework from the changes in quasi-fixed factors of production associated with investments in these factors.

In data envelopment analysis, the existing methods for measuring the relative efficiencies of decision making units (DMUs) are to compare DMUs relative to the best or the worst of all DMUs. In this paper, we consider both the best DMU and the worst DMU as the reference DMUs and propose the normalized efficiency. Further, from the optimistic and pessimistic viewpoints, we construct two DEA models to obtain the upper and lower bounds of the normalized efficiency and then achieve an interval efficiency evaluation to rank all DMUs completely. Finally, two examples are presented to illustrate the performance of the interval efficiency evaluation.

Introduction

Data envelopment analysis (DEA) has been proved to be an effective approach for measuring the performance of a group of decision making units (DMUs) with multiple inputs and multiple outputs. For a DMU, the CCR efficiency, developed by Charnels, Cooper and Rhodes (1978), is achieved by maximizing the ratio of the weighted sum of its outputs to that of its inputs under the constraint that the ratio should not exceed one for every DMU. Accordingly, the CCR efficiency is regarded as the best relative efficiency. The CCR efficiency evaluation can classify all DMUs into two groups, namely CCR efficient units and CCR inefficient units, but cannot rank all the DMUs completely. In recent years, a variety of DEA methods have been proposed to rank the performance of all DMUs. Adler, Friedman, and Sinuany-Stern (2002) divided these ranking methods into six areas. Cross-efficiency evaluation and super efficiency evaluation are the first and the second areas. Cross-efficiency evaluation, first proposed by Sexton, Silkman, and Hogan (1986), requests each DMU not only to be self-evaluated but also to be peer-evaluated. Specifically, based on the CCR model, a DMU determines a set of weights to evaluate the other DMUs. Yet, due to the non-uniqueness of the CCR optimal weights, the secondary goals have to be proposed to deal with the non-uniqueness issue. Doyle and Green (1994, 1995a) constructed several aggressive or benevolent cross-efficiency models. For more contributions to the cross-efficiency evaluation, readers are referred to the literature (Chen 2002; Contreras 2012; Liang, Wu, Cook, & Zhu, 2008a, 2008b; Oral, Amin, & Oukil, 2015; Wang & Chin 2010; Wu, Sun, & Liang, 2012; Yang, Ang, Xia, & Yang, 2012; Jeong and OK 2013; Hong and Jeong 2017). Andersen and Petersen (1993) considered a reference technology spanned by all the other DMUs except the evaluated DMU and then achieved the super efficiency evaluation. Indeed, when DMUs are evaluated, the reference technology is crucial. Doyle and Green (1995b) pointed out three reference points which occur naturally in everyday comparison, namely comparison relative to the best, to the average or to the worst of the rest. For each of these reference points of comparison, they presented two DEA models to obtain the best performance and the worst performance of each DMU, respectively, and then constructed the upper and lower bound evaluation. The traditional DEA models are usually built to achieve the best performance of DMUs from the optimistic viewpoint. Accordingly, the maximum ratio of the weighted sum of outputs to the weighted sum of inputs under some constraints is called the best relative efficiency or the optimistic efficiency. In fact, the worst relative efficiency or the pessimistic efficiency of a DMU, namely the minimum ratio of the weighted sum of outputs to that of inputs under some constraints, should still be paid enough attention to. The best relative efficiency and the worst relative efficiency measure the two kinds of extreme performances of a DMU. It is easily biased if considering only the best relative efficiency or the worst relative efficiency while neglecting the other one. Recently, many pessimistic DEA models have been presented to obtain the pessimistic efficiency of a DMU.

Data envelopment analysis (DEA) is a self-evaluation method which assesses the relative efficiency of a particular decision making unit (DMU) within a group of DMUs. It has been widely applied in real-world scenarios, and traditional DEA models with a limited number of variables and linear constraints can be computed easily. However, DEA using big data involves huge numbers of DMUs, which may increase the computational load to beyond what is practical with traditional DEA methods. In this paper, we propose novel algorithms to accelerate the computation process in the big data environment. Specifically, we firstly use an algorithm to divide the large scale DMUs into small scale and identify all strongly efficient DMUs. If the strongly efficient DMU set is not too large, we can use the efficient DMUs as a sample set to evaluate the efficiency of inefficient DMUs. Otherwise, we can identify two reference points as the sample in the situation of just one input and one output. Furthermore, a variant of the algorithm is presented to handle cases with multiple inputs or multiple outputs, in which some of the strongly efficient DMUs are reselected as a reduced-size sample set to precisely measure the efficiency of inefficient DMUs. Last, we test the proposed methods on simulated data in various scenarios.

Introduction

Data envelopment analysis (DEA), developed by Charnes et al. [10], is a nonparametric mathematical method used to measure relative efficiency within a group of homogenous decision making units (DMUs), particularly a group with multiple inputs and multiple outputs (see, e.g., [6, 14, 26, 31]). As a nonparametric technique, DEA is not limited by any functional form, and does not require the numerous assumptions that arise from the use of statistical methods for function estimation and efficiency measurement, yet it can evaluate efficiency well (see, e.g., [27, 32, 3, 24]). To date, DEA has been extensively applied in the performance evaluation of hospitals (see, [23, 15]), universities (see, [25, 21]), banks (see, [29, 30]), supply chains (see, [5]), and in many other situations (see, e.g., [19, 28, 33, 35]). DEA measures relative efficiency for a DMU against its peer n-1 DMUs, supposing there are n DMUs in the evaluation system. Traditional DEA models require the solution of a linear programming problem with n+1 variables and m+s constraints, where m and s are the numbers of inputs and outputs, respectively. The traditional DEA models can be solved by using standard linear programming techniques, thus, are theoretically considered computationally easy. However, in practice, the solution time increases significantly for large cases [12]. Emerging in 1980s, the concept of “big data” has become a hot issue in the computer industry and financial businesses. Wu et al. [34] indicated that big data has rapidly expanded in all science and engineering domains, including physical, biological and biomedical sciences. The emergence of the big data paradigm over the past few years, with its five major features (volume, velocity, variety, veracity, and valorization), has created a new set of problems and challenges [36, 8]. For example, Chen et al. [11] highlighted that we can obtain new science, discovery, and insights from the overwhelming amount of web-based, mobile, and sensor-generated data arriving at a terabyte and even exabyte scale. Michael and Miller [22] indicated that the development of big data could bring comprehensive analyses to support the development of improved policy regime-based systems. In the DEA field, big data has brought many problems for researchers. For example, the larger scale number of DMUs in the big data context is the biggest issue since it may take an impractical amount of time to finish the evaluation of all DMU efficiencies. Therefore, methods for reducing solution time for DEA problems are practically beneficial, especially in the big data environment.

Based on the CCR model, we propose an extended data envelopment analysis to evaluate the efficiency of decision making units with historical input and output data. The contributions of the work are threefold. First, the input and output data of the evaluated decision making unit are variable over time, and time series method is used to analyze and predict the data. Second, there are many sample decision making units, which are divided into several ordered sample standards in terms of production strategy, and the constraint condition consists of one of the sample standards. Furthermore, the efficiency is illustrated by considering the efficiency relationship between the evaluated decision making unit and sample decision making units from constraint condition. Third, to reduce the computation complexity, we introduce an algorithm based on the binary search tree in the model to choose the sample standard that has similar behavior with the evaluated decision making unit. Finally, we provide two numerical examples to illustrate the proposed model.

Introduction

In conventional data envelopment analysis (DEA) models, such as CCR model named after Charnes et al. [] and BCC model proposed by Banker et al. [], the inputs and outputs are assumed to be precise. In addition, the constraint condition consists of the evaluated decision making units (DMUs). In practical studies, the input and output data of the evaluated DMUs are frequently variable over multiple time periods (time series data), and it is important to analyze the change of efficiency over time. For example, in the evaluation of travel agencies, transportation, ticket price, accommodation, and labor are always regarded as the inputs, whereas profits and satisfaction of tourists are the outputs. The inputs and outputs are affected by various influential factors, such as the tourism policy, investment of infrastructure, level of starred hotel, annual per-capita income, and level of economic development. However, since the influential factors are variable over time, the inputs, outputs, and efficiencies of travel agencies are variable over time accordingly. Given the current upsurge in interest in DEA, it is surprising that the dynamic DEA attracts very little attention. The only methods we know of this area are Malmquist Productivity Index (MPI) and window analysis. MPI was originally proposed by Caves et al. [] to estimate changes in the overall productivity growth of each DMU over a two-year period by calculating the efficiency value. To deal with the productivity changes of DMUs over time, Färe et al. [] constructed a DEA-based MPI by combining the efficiency measurement of Farrell [] with the productivity measurement of Caves et al. Window analysis, proposed by Charnes et al. [], is adopted to overcome the constraint of limited DMUs and is a benefit to detect the tendency of DMUs over long period with large inputs and outputs. Since then, some improved approaches on the DEA-based MPI or window analysis have been proposed [–]. However, both the DEA-based MPI and window analysis models suffer from one shortcoming: they neglect predicting efficiency of the evaluated DMU. In many practical evaluation problems, efficiency of every evaluated DMU in a particular period may not be contrasted with the evaluated DMUs, but rather with sample standards determined by manufacturing parameters. The purpose of the contrast is not only to evaluate efficiency, but also to locate the standard with which the evaluated DMU has similar behavior. For instance, there are many grade standards for the evaluation of travel agencies. Travel agencies from the same region can be evaluated by the same standards separately, and those from different regions should not be evaluated by the same standards because of regional disparities. The standards should be formulated by the regional parameters. Taking outbound tourism as an example, it is an important part for travel agency business in developed regions, but it may not be contained in the travel agency business in some developing regions. Clearly, it is unreasonable that the outbound tourism is included in input measures to evaluate the travel agencies from different regions, and then grade standards in different regions should be formulated in terms of different manufacturing parameters.