Search

Performance evaluation for universities or research institutions has become a hot topic in recent years. However, the previous works rarely investigate the multiple departments’ performance of a university, and especially, none of them consider the non-homogeneity among the universities’ departments. In this paper, we develop data envelopment analysis (DEA) models to evaluate the performance of general non-homogeneous decision making units (DMUs) with two-stage network structures and then apply them to a university in China. Specifically, the first stage is faculty research process, and the second stage is student research process. We first spit each DMU (i.e. department) into a combination of several mutually exclusive maximal input subgroups and output subgroups in terms of their homogeneity in both stages. Then an additive DEA model is proposed to evaluate the performance of the overall efficiency of the non-homogeneous DMUs with two-stage network structure. By analyzing the empirical results, some implications are provided to support the university to promote the research performance of each department as well as the whole university.

How to evaluate the performance of decision-making units (DMUs) with fixed-sum outputs is a timely and challenging question in data envelopment analysis (DEA). Two major challenges are (1) how to determine a common equilibrium efficient frontier and (2) how to deal with multiple feasible equilibrium efficient frontiers. This paper first uses a simple dataset to illustrate the possibility of multiple equilibrium efficient frontiers and the corresponding major differences in the DMUs’ efficiencies and rankings resulting from these frontiers. We address these challenges by considering all feasible equilibrium efficient frontiers and develop several models to obtain the corresponding efficiency intervals, ranking intervals and dominance relations for the DMUs with fixed-sum outputs. We illustrate the proposed approach with two numerical examples and show that it gives more informative results than previous DEA approaches. For example, there are interesting dominance relations between DMUs under the fixed-sum outputs; yet these relations do not exist when there are no fixed-sum outputs. In addition, the efficiency ranges and ranking intervals can be narrowed by accounting for policy suggestions such as adjustment constraints of fixed-sum outputs for DMUs.

The majority of data envelopment analysis (DEA) models can be linearized via the classical Charnes–Cooper transformation. Nevertheless, this transformation does not apply to sum-of-fractional DEA efficiencies models, such as the secondary goal I (SG-I) cross efficiency model and the arithmetic mean two-stage network DEA model. To solve a sum-of-fractional DEA efficiencies model, we convert it into bilinear programming. Then, the obtained bilinear programming is relaxed to mixed-integer linear programming (MILP) by using a multiparametric disaggregation technique. We reveal the hidden mathematical structures of sum-of-fractional DEA efficiencies models, and propose corresponding discretization strategies to make the models more easily to be solved. Discretization of the multipliers of inputs or the DEA efficiencies in the objective function depends on the number of multipliers and decision-making units. The obtained MILP provides an upper bound for the solution and can be tightened as desired by adding binary variables. Finally, an algorithm based on MILP is developed to search for the global optimal solution. The effectiveness of the proposed method is verified by using it to solve the SG-I cross efficiency model and the arithmetic mean two-stage network DEA model. Results of the numerical applications show that the proposed approach can solve the SG-I cross efficiency model with 100 decision-making units, 3 inputs, and 3 outputs in 329.6 s. Moreover, the proposed approach obtains more accurate solutions in less time than the heuristic search procedure when solving the arithmetic mean two-stage network DEA model.

Data envelopment analysis (DEA) has proven to be a powerful technique for performance evaluation since its inception. Since the traditional DEA approaches lack discrimination power among efficient decision-making units (DMUs), the cross efficiency method has been proposed for peer appraisal in the literature. However, the previous cross efficiency approaches imposed a single and identical evaluation strategy across all DMUs simultaneously. In addition, all the related studies have considered a static issue without the dynamic alternation of evaluation strategies. In this paper, the reciprocal behaviors among DMUs are considered to address the cross efficiency evaluation, and a novel threshold value is used to determine positive or negative reciprocal behaviors by comparing the peer-evaluated efficiency with the threshold value based efficiency. This study assumes that a DMU would show positive behavior and apply a benevolent strategy toward other DMUs that evaluate it friendly, while it also shows negative behavior and apply an aggressive strategy toward DMUs that evaluate it hostilely. Furthermore, a game-like iteration process is developed for each DMU to determine and further adjust its evaluation strategy toward other DMUs in the evaluation process. Afterward, we calculate the optimal ultimate cross efficiency score with reciprocal behaviors. Finally, the proposed approach is applied to both a numerical example and an empirical study of 31 Chinese manufacturing industries to demonstrate its usefulness and efficacy.

With the rapid development of economy, China faces a considerable challenge from environmental problems especially with the waste of gas pollution emitted by China’s industry. To assess the environ...

The field of engineering management usually involves evaluation issues, such as program selection, team performance evaluation, technology selection, and supplier evaluation. The traditional self-evaluation data envelopment analysis (DEA) method usually exaggerates the effects of several inputs or outputs of the evaluated decision-making unit (DMU), resulting in unrealistic results. To address this problem, scholars have proposed the cross-efficiency evaluation (CREE) method. Compared with the DEA method, CREE can rank DMUs more completely by using reasonable weights. With the extensive application of this technique, several problems, such as non-unique weights and non-Pareto optimal results, have arisen in CREE methods. Therefore, the improvement of CREE has attracted the attention of many scholars. This paper reviews the theory and applications of CREE, including the non-uniqueness problem, the aggregation of cross-efficiency data, and applications in engineering management. It also discusses the directions for future research on CREE.

In this study, a data envelopment analysis-based approach is proposed for estimating and decomposing the potential gains from the horizontal integrations of two-stage production systems. In the first tier, the gains of the potential merger are measured by a composite efficiency index. The potential efficiency gains are then decomposed as the product of coordination efficiency and two divisional potential efficiency gains. In the second tier, the divisional potential efficiency gains are decomposed into scope, size, and learning efficiencies. We develop a multiplicative framework for decomposing potential efficiency gain in mergers of the two-stage production systems, and the coordination efficiency is considered. In the case study of commercial banks in mainland China, we develop an algorithm for estimating and decomposing potential efficiency gain for a two-stage bank production system.

This paper studies the impact of two decision makers’ interaction with conflicts on the efficiencies of the system. We start with a general principal-agent framework where the principal and the agent make decisions independently and the principal has a contradictive objective to that of the agent. We develop data envelopment analysis (DEA) models in the principal’s and the agent’s perspectives respectively. Non-cooperation between the principal and the agent is discussed to illustrate how one decision maker affects the other and the corresponding efficiency and incentive contract of the system. In addition, cooperation of the two parties is also analyzed to better derive how the performance of the system is influenced by the parties and their interactions as well. Then, this study illustrates the proposed models and effective incentive contracts by applying them to the efficiency evaluations of 22 China listed electric power companies.

Corporate diversification has been an important research topic in the field of business administration. Although it is regarded as an essential strategy for firms, its relationship with firm performance seems inconclusive in the literature. To fill this gap, our study uses data envelopment analysis (DEA) to develop models that help diversified firms more accurately calculate productivity at both the firm and its business segment levels, and then reallocate resources among business segments in order to achieve better firm overall performance. We empirically test the models using a sample of U.S. public firms for a period of 2012–2016. The results show that in comparison with two conventional DEA models, our model provides more useful productivity expression for diversified firms, and that the model-suggested resource reallocation is linked to better firm performance.

One of the hot topics is how to achieve more accurate results of economic and environmental efficiency evaluation in China. Previous data envelopment analysis (DEA) literature on environmental performance measurement often follow the concept of non-radial efficiency measure for calculating the performance on resources and economic-environmental factors respectively. This paper proposes a non-radial and multi-objective generalized DEA model for economic-environmental efficiency evaluation. The results illustrate that this model can not only analyze the relationship between DEA efficiency and Pareto optimality of the multi-objective programming problem defined on the production possibility set, but also obtain the performance improvement direction by using the projection of decision making units. Finally, a case on measuring the economic-environmental performance of Chinese provincial regions is employed to indicate that the proposed model can be helpful to promote the accuracy of economic-environmental efficiency evaluation.

Environmental problems brought by industry are attracting extensive attention so a comprehensive analysis of industrial environmental performance is increasingly important. However, the comparison of industrial sector efficiencies is complicated by the fact that the natural resources consumed and/or the pollutants discharged by each sector may differ. In this paper, we extend the DEA model to consider two-sided non-homogeneous problems, handling DMU sets that have non-homogeneity in both inputs and outputs. This is different from the previous researches which generally focus on regional data to avoid non-homogeneity. Today environmental reform and energy conservation in various industrial sectors are both parts of the basic state policy of China. The empirical results show that: (1) Sectors' efficiencies are still low and unbalanced. The Recycling and Disposal of Waste department achieves the best energy saving and emission reduction efficiency. (2) 38 sectors can be clustered into four groups and set new benchmark in each group. (3) The overall efficiency of 38 industrial sectors in China maintained a rising trend in five years. With this more realistic analysis of environmental efficiency, the Chinese government can make more informed decisions to realize sustainable industrial development.

In a two-stage system with two divisions connected in series, fairly setting the target outputs for the first stage or equivalently the target inputs for the second stage is critical, in order to ensure that the two stages have incentives to collaborate with each other to achieve the best performance of the whole system. Data envelopment analysis (DEA) as a non-parametric approach for efficiency evaluation of multi-input, multi-output systems has drawn a lot of attention. Recently, many two-stage DEA models were developed for studying the internal structures of two-stage systems. However, there was no work studying the fair setting of the target intermediate products (or intermediate measures) although unreasonable setting will result in unfairness to the two stages because setting higher (fewer) intermediate measures means that the first (second) stage must make more efforts to achieve the overall production plan. In this chapter, a new DEA model taking account of fairness in the setting of the intermediate products is proposed, where the fairness is interpreted based on the Nash bargaining game model, in which the two stages negotiate their target efficiencies in the two-stage system based on their individual efficiencies. This approach is illustrated by an empirical application to insurance companies.

Many studies have concentrated on fixed cost allocation and resource allocation issues by using data envelopment analysis (DEA). Existing approaches allocate fixed cost and resource primary based on the efficiency maximization principle. However, due to the existing of technology heterogeneity among DMUs, it is impractical for all the DMUs to achieve a common technology level, especially when some DMUs are far from the efficient frontier. In this chapter, under the centralized decision environment, we present a new approach to deal with fixed cost and resource allocation issues for a two-stage production system by considering the factor of technology heterogeneity. Specifically, technology difference is analyzed in the performance evaluation framework firstly. Then, by taking the technology heterogeneity into account, the two-stage DEA-based fixed cost allocation and resource allocation models are proposed. In addition, two illustrated examples are calculated to show the feasibility of the two proposed models. Finally, this chapter is concluded.

Allocating the fixed cost among a set of users in a fair way is an important issue both in management and economic research. Recently, Du et al. (Eur J Oper Res 235(1): 206–214, 2014) proposed a novel approach for allocating the fixed cost based on the game cross-efficiency method by taking the game relations among users in efficiency evaluation. This paper proves that the novel approach of Du et al. (Eur J Oper Res 235(1): 206–214, 2014) is equivalent to the efficiency maximization approach of Li et al. (Omega 41(1): 55–60, 2013), and may exist multiple optimal cost allocation plans. Taking into account the game relations in the allocation process, this paper proposes a cooperative game approach, and uses the nucleolus as a solution to the proposed cooperative game. The proposed approach in this paper is illustrated with a dataset from the prior literature and a real dataset of a steel and iron enterprise in China.

In many real managerial applications, an issue of considerable importance is allocating a total fixed cost across a set of competing decision making units (DMUs). The fixed cost allocation problem has also become one of the most important applications of the data envelopment analysis (DEA) methodology. In this paper, we will approach the fixed cost allocation problem by explicitly considering both competition and cooperation relationships among DMUs. To this end, we integrate cooperative game theory and the cross efficiency method to develop a DEA-game cross efficiency approach to generate a unique and fair allocation plan. With the proposed approach, each DMU is considered as a player and a super-additive characteristic function is defined for coalitions of DMUs. Then, the Shapley value is calculated for each DMU and accordingly associated common weights are optimized to determine the final allocation plan. Since the cross efficiency method considers peer appraisal and the cooperative game theory allows for equitable negotiations, all DMUs are supposed to reach a consensus on the equitable allocation scheme through our novel approach. From this perspective, our proposed approach is promising and attractive for allocating a fixed cost in large organizations. Finally, the DEA-game cross efficiency approach is demonstrated with a numerical example derived from previous literature and the results are compared to some existing methods. Additionally, we apply the proposed approach to an empirical application concerning city commercial bank activities in China.

In many real applications, there exist situations where some independent and decentralized entities will construct a common platform for production processes. A natural and essential problem for the common platform is to allocate the fixed cost or common revenue across these entities in an equitable way. Since there is no powerful central decision maker, each decision-making unit (DMU) might propose an allocation scheme that will favor itself, giving itself a minimal cost and/or a maximal revenue. It is clear that such allocations are egoistic and unacceptable to all DMUs except for the distributing DMU. In this paper, we will address the fixed cost allocation problem in this decentralized environment. For this purpose, we suggest a non-egoistic principle which states that each DMU should propose its allocation proposal in such a way that the maximal cost would be allocated to itself. Further, a preferred allocation scheme should assign each DMU at most its non-egoistic allocation and lead to efficiency scores at least as high as the efficiency scores based on non-egoistic allocations. To this end, we integrate a goal programming method with data envelopment analysis methodology to propose a new model under a set of common weights. The final allocation scheme is determined in such a way that the efficiency scores are maximized for all DMUs through minimizing the total deviation to goal efficiencies. Finally, both a numerical example from prior literature and an empirical study of nine truck fleets are provided to demonstrate the proposed approach.

A balance between environmental regulation and economic prosperity has become a major issue of concern to attain a sustainable society in China. This study proposes the application of Data Envelopment Analysis (DEA) for measuring the efficiencies of the ecological systems in various regions of that country. The proposed approach differs from most of the previous ecological systems models in that we view it in a two stage setting; the first stage models the ecological system itself, and from an economic perspective, while the second stage (decontamination system) models water recycling as a feedback process, and the treatment of other undesirable outputs coming from the first stage. There, we separate polluting gases and water into two parts; one part is treated, while the other is discharged. The model considers two major desirable outputs from the first stage, namely Population and Gross Region Product by expenditure (GRP), as well as undesirable variables in the form of consumed water, and certain pollutants, namely nitrogen oxide, sulfur dioxide and soot. At the same time, these undesirable outputs from the first stage are inputs to the second decontamination stage. As well, recycled water is fed back into stage 1. Thus, intermediate variables such as consumed water and waste gas emission simultaneously play dual roles of both outputs and inputs in the ecological system.

In multi-division organizations, goal congruence between different divisions and top management is critical to the success of management. In this paper, drawing upon a nonparametric framework to model production technology, we derive a necessary and sufficient condition for a firm with multiple divisions to be goal-congruent, and then extend it to a goal congruence testing measure, which coincides with a data envelopment analysis (DEA) model. The goal congruence measure not only shows empirically whether the firm is goal-congruent or not, but also provides a measurement for the degree of goal incongruence. To be goal-congruent, resources shared among divisions are suggested to be allocated so that the conditions for an optimizable operation are satisfied. In addition, goal-congruent firms are verified to be cost efficient. All findings in this research are examined and illustrated with a dataset of 20 bank branches with shared resources for service and sales divisions.

Based on the equilibrium efficient frontier data envelopment analysis (EEFDEA) approach, Fang (J Oper Res Soc 67:412–420, 2015a) developed an equivalent linear programming model to improve and stre...

Many studies have dealt with the problem of fixed cost allocation by using data envelopment analysis. However, existing models allocate the fixed cost by treating the decision-making units (DMUs) as black-boxes and ignore the internal production structures of DMUs. To our knowledge, only a few work has considered the fixed cost allocation problem for an elementary two-stage production structure without external inputs and outputs. This paper deals with the fixed cost allocation problem for a general two-stage network production structure, in which both external inputs and outputs exist. Specifically, additive two-stage models are first presented to evaluate the performance for each DMU when allocating the fixed cost. Then, by introducing the concepts of satisfaction degree and fairness degree, we propose an approach to obtain an optimal allocation plan under the control of the centralized authority. Finally, an application to 27 banks is utilized to illustrate the proposed approach.

Data envelopment analysis (DEA) is a technique for measuring the performance of peer decision making units (DMUs) that have multiple performance metrics. If the performance is viewed as efficiency, then the DEA frontier can be viewed as a production function along with the performance metrics characterized as inputs and outputs. However, DEA can be used as a benchmarking tool where the DEA frontier represents best practice frontier. A significant body of work has been directed at problem settings where the DMU is characterized by multistage or network processes. The current paper first examines weighted additive performance of two-stage process and then extends the methodology to examine general network structures. Under the condition of isolating the impact of stage weights on the overall performance, we propose a new overall performance as convex linear combination of multi-stage performance and prove that the existence of maximum score for the resulting new overall performance. We illustrate our findings through numerical and empirical data sets.

Resource allocation is a popular and important issue in the enterprise management. Recently, data envelopment analysis (DEA) as a non-parametric method for measuring the performance of decision-mak...

In order to break the tie of efficient decision-making units, super-efficiency data envelopment analysis is proposed to fully discriminate them. Recently, a slacks-based version of the super slacks-based measure (S-SBM) is developed and a novel two-stage approach is proposed to calculate both super-efficiency score by the S-SBM model and efficiency score by the slacks-based measure model. In this paper, we extend the approach to consider continuity of efficiency scores. We illustrate the discontinuity of efficiency measure, and define a continuous slacks-based measure which is proved continuous and directly calculated. An interesting efficiency zone category is also provided. In addition, this paper investigates the relationship among the super-efficiency measures of the proposed approach and some existing approaches under variable returns to scale.

In the usual data envelopment analysis (DEA) setting, as pioneered by Charnes et al. (1978) [1], it is assumed that a set of decision making units (DMUs) is to be evaluated in terms of their relative efficiencies in converting a bundle of inputs into a bundle of outputs. The usual assumption in DEA is that each output is impacted by each and every member of the input set. One particular area of recent research is that relating to partial input to output impacts where the main issue addressed is that in many settings not all inputs impact all outputs. In that situation the authors view the DMU as consisting of a set of mutually exclusive subunits, with each subunit having its own unique bundle of inputs and outputs. Examined as well in this area, is the presence of multiple processes for generating sets of outputs. Missing from that earlier work is consideration of the presence of outputs in the form of by-products, giving rise to a parent-offspring phenomenon. One of the modeling complications there is that the parent assumes two different roles; as an input affecting the offspring, while at the same time being the dominant output. This gives rise to a model that we refer to as conditional two-stage. Another complication is that in the presence of multiple processes, by-products often arise out of only a subset of those processes. In the current paper we develop a DEA-type of methodology to handle partial input to output impacts in the presence of by-products.

In recent years, performance evaluation of sustainable operations has attracted a significant amount of research. The current paper seeks to evaluate sustainable manufacturing performance when wastes are recycled and re-used. For example, a typical sustainable process in iron and steel making involves in the first stage forging iron and steel products and in the second stage disposing the wastes. The sustainable manufacturing process then re-uses the recycled waste water in the first stage production. It is important that performance metrics include the operations related to recycling and re-use of the wastes. In a simplified view, such a sustainable operation is a two-stage process. Due to the ability of incorporating multiple performance metrics, data envelopment analysis (DEA) is used to develop our evaluation approach. While traditional DEA treats such two-stage manufacturing process as a black box by ignoring the internal conflicts and cooperation among multiple manufacturing stages, this paper proposes a modified two-stage network DEA model that deals with good and undesirable outputs from the sustainable manufacturing process. A Nash bargaining game between efficiencies of two-stages is proposed to produce unique and fair efficiency decomposition for the two-stage sustainable manufacturing process. The modified two-stage network DEA model is applied to wastewater recycling and reusing in a set of iron and steel makers in China. The results show that the proposed model is more effective than the black box DEA model in calculating efficiency of both two-stages and in identifying the sources of the inefficiency of overall sustainable manufacturing processes.

The traditional data envelopment analysis model allows the decision-making units (DMUs) to evaluate their maximum efficiency values using their most favourable weights. This kind of evaluation with...

The decision makers always suffer from predicament in choosing appropriate variable set to evaluate/improve production efficiencies in many applications of data envelopment analysis (DEA). The selected data set may exist information redundancy. On that account, this study proposes an alternative approach to screen out proper input and output variables set for evaluation via Akaike’s information criteria (AIC) rule. This method mainly focuses on assessing the importance of subset of original variables rather than testing the marginal role of variables one by one in many other methods. In terms of the proposed approach, the most optimized variable set contains the least redundant information, which provides decision support to the decision makers. Besides, we also define redundant/cross redundant variables with the form of theorems and give the proofs subsequently. In addition, the AIC approach is firstly extended to stochastic data set to select an appropriate set of stochastic variables as well. Finally, the proposed approach has been applied to some data sets from given data and prior DEA literatures.

The data envelopment analysis (DEA) methodology is a benchmarking tool where it is generally assumed that decision making units (DMUs) constitute a homogeneous set; specifically, it is assumed that all DMUs have a common (input, output) bundle. In earlier work by the authors the issue of non-homogeneity on the output side was investigated. There we examined a set of steel fabrication plants where not all plants produced the same set of products/outputs. In the current research we investigate non-homogeneity on the input side. Such can occur in manufacturing plants, for example, when the output bundle can be produced using different mixes of machines, robots and laborers. Thus, we can have an input configuration existing in a DMU that is different from the configuration in another DMU. As a practical application of this phenomenon, we examine the measurement of efficiencies of a set of provinces in China. There, all provinces have the same common set of outputs in the form of GDP, supported population, and an undesirable output, nitrogen dioxide. On the input side, however, this commonality is missing. While all provinces have water, capital investment and natural resources, the latter of these (natural resources) takes several different forms, namely coal, natural gas and petroleum. However, not all provinces have the same mix of these resources, nor are there clear exchange rates among these very different, albeit substitutable inputs. This means that that one cannot directly apply the conventional DEA methodology. This then raises the question as to how to fairly evaluate efficiency when the configuration or mix of inputs can differ from one DMU to another. To address this, we view the generation of outputs for a province as a set of processes created by the different configurations of natural resources available. We develop a DEA type of methodology to evaluate these processes. This evaluation provides important insights into not only the overall performance of each province, but as well provides measures of the efficiency of the various configurations of the three natural resources.

Because of China’s rapid economic development, its transportation system has become one of China’s high-energy-consumption and high-pollution-emission sectors. However, little research has been done which pays close attention to China’s transportation system, especially in terms of energy and environmental efficiency evaluation. In this paper, data envelopment analysis (DEA) is applied to measure the energy and environment performance of transportation systems in China with the goal of sustainable development. This paper treats transportation as a parallel system consisting of subsystems for passenger transportation and freight transportation, and extends a parallel DEA approach to evaluate the efficiency of each subsystem. An efficiency decomposition procedure is proposed to obtain the highest achievable subsystem efficiency. Our empirical study on 30 of mainland China’s provincial-level regions shows that most of them have a low efficiency in their transportation system and the two parallel subsystems. There are large efficiency differences between the passenger and freight transportation subsystems. In addition, unbalanced development has occurred in the three large areas of China, with the east having the highest efficiency, followed by central China and then west. Therefore, more measures should be taken to balance and coordinate the development between the three large areas and between the two subsystems within them. Our analysis approach gives data for determining effective measures.