Data envelopment analysis cross-efficiency evaluation has been widely accepted as a useful tool for performance evaluation and ranking of decision making units. However, the non-uniqueness of optimal ...weights is a problem that has reduced the usefulness of this powerful method. In addition, current studies generally have not considered the situation in which undesirable outputs appear in the data envelopment analysis cross-efficiency evaluation. To solve these problems, firstly, we present an equitable model for efficiency evaluation of decision-making units with undesirable outputs and introduce a technique for cross-efficiency evaluation considering undesirable outputs. Then, a ranking priority model is proposed considering the decision making units' intentions of pursuing the best ranking positions. In addition, an aggressive model is given to guarantee the uniqueness of the optimal solution. The proposed approach can not only solve the problem of non-uniqueness of optimal weights in data envelopment analysis cross-efficiency evaluation but also considers undesirable outputs and ranking preferences of the decision-making units. Finally, the proposed approach is applied for eco-efficiency analysis of coal-fired power plants in a big data environment, and the results show that most coal-fired power plants in China have not performed well.
•The undesirable output is considered in DEA cross-efficiency evaluation.•An equitable model is given for measuring efficiency.•The ranking preference of each DMU is regarded as the secondary goal.•An aggressive model is given to guarantee the uniqueness of the optimal solution.•A case study of eco-efficiency analysis of coal-fired power plants is presented.
As the second largest economic entity in the world, China plays an important role in controlling global carbon dioxide (CO2) emissions. The land transportation sector (including railway ...transportation and road transportation) has been the most important source of emissions in China and the average CO2 emissions of land transportation were 529.31 million tons during the period 2009–2012. In this study, a parallel Slack-Based Measure Data Envelopment Analysis model is proposed, which is used for evaluating the overall efficiency of the land transportation sector and individual efficiencies of the railway transportation and highway transportation subsectors at the same time, considering CO2 emissions. The empirical results lead to three conclusions: (a) only Anhui province is efficient each year during 2009–2012. (b) The environmental efficiency of the Eastern area in China is the best, followed by the Central area, with the Western area being the worst. (c) The performance of railway transportation is better than that of highway transportation. These three conclusions lead to policy suggestions to promote highway transportation technological innovation and narrow the regional imbalances in land transportation. This paper makes two main contributions: the model advances improvements to methods used in the Data Envelopment Analysis technique, and also provides governments with a practical and yet easy-to-adopt perspective to implement land transportation performance measurement that aids in decision making.
In management decisions, situations frequently occur when the decision makers need to allocate some amount of fixed cost among a group of decision-making units (DMUs). In this paper, we propose an ...approach for allocating fixed cost among a group of DMUs based on the utility and data envelopment analysis (DEA) common-weight evaluation framework. First, we give the definition of utility of a DMU to a set of fixed cost allocation and common weights' selection result. Then, an approach, which contains a max-min model and an algorithm, is given for fixed cost allocation and common weights reselection of the DMUs. Specifically, the max-min model aims to generate for the DMUs the fixed cost allocation and common weights selection result that maximizes the minimum utility among all the DMUs. In addition, the algorithm is given to solve the max-min model linearly. Compared with the other fixed cost allocation approaches, our proposed approach not only has the ability to maximize the utilities of all the DMUs and guarantee the Pareto optimality of the utilities but also ensures the uniqueness of the fixed cost allocation and common-weight selection result. Finally, the proposed approach is applied for a real case study of allocating advertising expenditure among dealers of a car manufacturer.
•A new two-stage network data envelopment analysis approach is proposed.•It matches substages’ production scale with intermediate measure levels.•It uses a total value flow equivalence between a ...unit's two stages.•Primal-dual correspondence holds.•It avoids uncertainties in determining divisional efficiencies.
We develop a new network data envelopment analysis (DEA) approach for two-stage network systems considering a match between the production scale of the substages and the intermediate measure levels. Several explicit production axioms are introduced to build a production possibility set. New models are developed based on the production possibility set and a frontier projection procedure with the production scale matching process. Unlike the existing approach which assumes the intermediate measures are free-setting decision variables, the new envelopment network DEA models project the intermediate measures of a unit using the radial projection technique. Correspondingly, the resulting multiplier network DEA models allow for weight flexibility on the intermediate measures while holding a total value flow equivalence between a unit's two stages. We show that our approach does not suffer the known network DEA pitfalls. It identifies the overall efficiency, divisional efficiencies, and frontier projection using either an envelopment or a multiplier network DEA model, i.e., the primal-dual correspondence holds in our approach. Our approach also avoids uncertainties in determining divisional efficiencies by generating a unique pair of divisional efficiencies for each unit. Additionally, the adoption of the production scale matching process explains clearly the frontier projection procedure from the practical point of view. The proposed approach is illustrated with a numerical example and compared with the existing approaches with a case study of commercial bank branches.
•An improved equilibrium efficient frontier data envelopment analysis approach is proposed.•The constructed equilibrium efficient frontier consists of multiple hyperplanes.•Minor adjustments are ...required for decision-making units to achieve the EEF.•An expectation Maximization-based algorithm is developed to solve the model.•A case study of the global motor vehicle industry is provided.
In recent years, significant development has been made in efficiency evaluation for Decision-Making Units (DMUs) with fixed-sum outputs. The Generalized Equilibrium Efficient Frontier Data Envelopment Analysis (GEEFDEA) approach introduced by Yang et al. (2015) is one of the most representative methods. In the GEEFDEA approach, all DMUs are adjusted to become efficient under the same set of weights, indicating that the Equilibrium Efficient Frontier (EEF) constructed consists of only one hyperplane. However, in practical scenarios under the Variable Return to Scale (VRS) assumption, the production frontier always consists of multiple hyperplanes, presenting a more complex shape. To fill this research gap, we propose an improved Equilibrium Efficient Frontier Data Envelopment Analysis approach. Our approach allows DMUs to have different weights for inputs, variable-sum outputs, and fixed-sum outputs, resulting in an EEF with multiple hyperplanes. It is noted that our new approach uses a non-linear model to obtain the EEF. We show that the model can be linearized in the case of a single fixed-sum output. In situations involving multiple fixed-sum outputs, we propose an algorithm based on the Expectation Maximization (EM) mechanism to solve the model to obtain an EEF. Finally, we illustrate the advantages of our new approach through a numerical example and a case study in the global motor vehicle industry.
•This paper considers fixed-cost allocation in two-stage systems with data envelopment analysis.•We prove all decision making units can be made efficient with a common weight evaluation.•We propose ...game models by considering unions of the first stages and the second stages as players, respectively.•We propose leader-follower approaches for situations with dominance between the two stages.•When there is no dominance between stages, we propose a Nash bargaining approach with satisfaction degree as payoffs.•A method is proposed to obtain the Nash equilibrium.
This paper proposes new fixed cost allocation approaches for allocating a fixed cost among decision-making units (DMUs) with two-stage structures under the framework of data envelopment analysis (DEA). Firstly, we give the set of possible fixed cost allocations, prove that all DMUs can be overall efficient when evaluated by a common set of weights after fixed cost allocation. Secondly, from a centralized point of view, we consider the competition between the DMUs’ two stages in fixed cost allocation and regard these two kinds of stages as two unions. Then, we incorporate leader-follower models to propose a fixed cost allocation approach to handle the situation in which the two unions make decisions sequentially. Based on the result of these models, a concept of satisfaction degree of each union on a fixed cost allocation is presented. A satisfaction degree bargaining game model is then proposed to obtain a fixed cost allocation which is a bargaining equilibrium of the two unions. We show that the proposed approaches always obtain a fixed cost allocation that is proportionally invariant. Additionally, the satisfaction degree bargaining game approach automatically guarantees the uniqueness of the fixed cost allocation. These properties make the fixed cost allocation generated by our approaches more stable and more acceptable. Finally, a numerical example and an application of fixed cost allocation among bank branches are given to illustrate the proposed approach and to compare it with a benchmark approach among the current studies, respectively.
•We measure the efficiency of two-stage system with shared and reused resource.•We introduce additive and non-cooperative efficiency measures to this system.•A heuristic algorithm is suggested to ...transform nonlinear model into a linear one.•We prove the heuristic algorithm to be a good and effective approach.•The new approaches are applied to industrial production processes of China.
Data envelopment analysis (DEA) is an approach for measuring the performance of a set of homogeneous decision making units (DMUs). Recently, DEA has been extended to processes with two stages. Two-stage processes usually have undesirable intermediate outputs, which are normally considered be unrecoverable final outputs. In many real situations like industrial production however, many first-stage waste products can be immediately used or processed in the second stage to produce new resources which can be fed back immediately to the first stage. The objective of this paper is to provide an approach for analyzing the reuse of undesirable intermediate outputs in a two-stage production process with a shared resource. Shared resources are input resources that not only are used by both the first and second stages but also have the property that the proportion used by each stage cannot be conveniently split up and allocated to the operations of the two stages. Additive efficiency measures and non-cooperative efficiency measures are proposed to illustrate the overall efficiency of each DMU and respective efficiency of each sub-DMU. In the non-cooperative framework, a heuristic algorithm is suggested to transform the nonlinear model into a parametric linear one. A real case of industrial production processes of 30 provincial level regions in mainland China in 2010 was analyzed to verify the applicability of the proposed approaches.
•Energy and environmental efficiency of China’s transportation sector is investigated.•Uncertainty in estimation of CO2 emission is considered.•Stochastic multicriteria acceptability analysis and ...data envelopment analysis are used.•Results show that great efficiency disparities exist among regions.•Uneven development has occurred in areas of China’s transportation sectors.
China’s transportation sector suffers from energy over-consumption and CO2 over-emission, resulting in increasing pressure to improve energy and environmental efficiency. Current measurement techniques cannot produce precise CO2 emission data, and this uncertainty makes previous approaches problematic for analyzing energy and environmental efficiency. This study combines stochastic multicriteria acceptability analysis (SMAA-2) with data envelopment analysis (DEA) to evaluate the energy and environmental efficiency of Chinese transportation sectors in the presence of uncertain CO2 emission data. The improved SMAA-DEA approach effectively handles CO2 data uncertainty and also considers all possible input and output weights, thus providing meaningful information (such as maximum efficiency, average efficiency, and rank acceptability index) to guide the development of effective policies to improve efficiency. This study’s empirical findings show that the energy and environmental efficiency of transportation sectors in 30 provincial regions is poor, great efficiency disparities exist between regions, and uneven development has occurred in China.
In order to measure technological change and environmental efficiency precisely, and further to improve the technology and environmental efficiency of road transportation industry in “big data” ...context, a Hicks-Moorsteen Index model based on DEA is proposed in this study, and then is employed to assess the performance of road transportation industry. The empirical study concludes that: (a) all of the total factors productivity growth, technological progress and environmental efficiency of the road transportation sectors in the eastern, western and central regions all averagely increased. (b) The growth rates of mix efficiency of the road transportation sectors in the three regions were the highest among the various efficiency changes. (c) While the performances of technological progress in western and central region outperform that in eastern region, the performance of environmental efficiency change outperform those in western and central regions. This paper suggests the diffused utilization of optimal production technology should be superior to the pace of technological innovation in western and central regions, and road transportation industry in China should be sensitive to the influence of government policy such as “supply side reform”.
•The CO2 emission is considered in TFP growth evaluation.•Hicks-Moorsteen Index approach is employed to measure TFP growth and technological progress.•Technological progress and mix efficiency change are analyzed when decomposing the TFP growth.•Policy suggestions for road transportation are presented.
•We investigate the fixed cost allocation problem under DEA framework.•A bi-objective fixed cost allocation model is developed.•Tradeoffs between efficiency improvement and balance in fixed cost ...allocation are considered.•The trade-off approach generates a unique equilibrium Pareto-optimal solution.•A case study of China National Heavy Duty Truck Group is provided.
Fixed cost allocation (FCA) is a problem that decision-makers usually encounter in practice. The existing FCA studies based on data envelopment analysis (DEA) have not recognized the trade-off between improving efficiency and balancing FCA result and failed to provide an approach to generate an equilibrium solution between the two goals. In this study, under DEA common-weight evaluation mechanism, we propose an approach for centralized FCA using several principles featuring fairness in the situation where the fixed cost is regarded as a complement of one of the current inputs. It first considers the principle of making equal-proportional efficiency improvements for all the decision-making units (DMUs) in FCA. Then, we define a measure, called “balanced indicator”, to measure the balance of a FCA result. Finally, a bi-objective model is built that considers both the objectives of maximizing the proportional efficiency improvement of the DMUs and improving the balance of the FCA result. A bargaining-game-like model and a trade-off algorithm are provided to generate the final FCA result. Our research contributes by elucidating the trade-off between enhancing efficiency and achieving balance in FCA result. It also makes a distinct contribution by proposing a bargaining-game-like model and a trade-off algorithm to generate a FCA result that is an equilibrium solution between the two goals and ensures no DMU is allocated zero cost. Finally, we demonstrate the superiority of our approach by comparing it with a previous representative approach and applying it to a case study of China National Heavy Duty Truck Group.
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