•This paper proposes a model to calculate the cross efficiencies for two basic network systems.•The system efficiency is the product of the division efficiencies for the series system.•The system ...efficiency is a weighted average of the division efficiencies for the parallel system.
The data envelopment analysis (DEA) technique uses the most favorable weights for each decision making unit (DMU) to calculate efficiency. The resulting efficiency scores are thus incomparable and difficult to discriminate. This phenomenon is more prominent for network systems, which involves the ranking of the component divisions, in addition to the system. This paper applies the idea of cross evaluation, which has been demonstrated to be an effective approach in ranking DMUs for systems considered as a whole-unit, to measure the efficiency of the two basic structures of network systems, series and parallel. The proposed model is able to decompose the cross efficiency measure of the system into the product of those of the divisions for the series structure and a weighted average for the parallel structure. The results from two real-world cases, one for the basic series structure and another for the parallel one, show that the cross efficiency measures proposed in this paper not only increase the discriminating power in ranking systems and divisions, but also identify the relationship between the system and division efficiencies. Which division has stronger effects on the performance of the system is reflected from this relationship.
Cross-efficiency evaluation is a useful approach to ranking decision making units (DMUs) in data envelopment analysis (DEA). The possible existence of multiple optimal weights for the DEA may reduce ...the usefulness of the cross-efficiency evaluation since the ranking is according to the choice of weights that different DMUs make. Most of existing approaches for cross-efficiency evaluation employ the average cross-efficiency to further discriminate among the DEA efficient units or focus on how to determine input and output weights uniquely, but lay little emphasis on the consideration of the ranges and variances of cross-efficiencies as alternative ranking factors. In this paper we consider cross-efficiency intervals and their variances for ranking DMUs. The aggressive and benevolent formulations are taken into account at the same time. Consequently, a number of cross-efficiency intervals is obtained for each DMU. The signal-to-noise (SN) ratio, originally designed for optimizing the robustness of a process, is constructed as a numerical index for ranking DMUs. A nonlinear fractional program with bound constraints is formulated to find the optimal value of the SN ratio. By model reduction and variable substitution, this nonlinear fractional program is transformed into a quadratic one for deriving the global optimum solution. With the derived SN ratios, we are able to fully rank all DMUs accordingly. Two examples are given to illustrate the effectiveness of the methodology proposed in this paper.
In measuring the overall efficiency of a set of decision making units (DMUs) in a time span covering multiple periods, the conventional approach is to use the aggregate data of the multiple periods ...via a data envelopment analysis (DEA) technique, ignoring the specific situation of each period. This paper proposes using a relational network model to take the operations of individual periods into account in measuring efficiencies. The overall and period efficiencies of a DMU can be calculated at the same time. Notably, the overall efficiency is a weighted average of the period efficiencies, and the weights are the most favorable ones for the DMU being evaluated. This model, together with two existing ones, is applied to measure the efficiency of 22 Taiwanese commercial banks for the period of 2009–2011. The three-year multi-period analysis shows that the proposed model is more discriminative than the existing ones in ranking the performance of the banks. The period efficiencies for the three years increased steadily, indicating that the performances of the Taiwanese banks examined in this work were improving over this period.
•We construct a model for measuring the multi-period efficiency of banks.•The overall efficiency is a weighted average of period-specific efficiencies.•The performance of Taiwanese commercial banks improves steadily from 2009 to 2011.•The multi-period analysis results in more discriminative rankings.
•We propose an idea of aggregating expert opinions in data envelopment analysis.•Aggregating opinions at the data and efficiency levels leads to the same results.•For ranking, non-radial models ...produce more reliable efficiencies than radial models.•The proposed model helped a company select the best robot for the intended purpose.
Data envelopment analysis is a technique widely used to measure the relative efficiency of a set of decision making units and for ranking alternatives based on the measured efficiency. When there are data that need to be estimated, a group of experts is consulted. The opinions of the experts can be aggregated at either the data level, based on which the efficiency is calculated, or the efficiency level, where the efficiencies calculated from the data provided by individual experts are aggregated. However, the results may not be consistent, which leads to a puzzling situation as which result to follow. In this paper, a method of determining appropriate weights by which the opinions of the experts can be used to calculate the efficiency of alternatives is proposed. One radial model and one slacks-based measure (SBM) model are constructed based on this idea. It is shown that, for both models the results obtained from aggregating the opinions at the data level and at the efficiency level are the same. The final efficiencies are thus reliable. A case of a robot selection problem for a manufacturing company in Taiwan is used for the purpose of illustration. The results show that the radial efficiency is dependent on the non-Archimedean number and will overstate the performance of the robot. The SBM efficiency, which does not have this drawback, is more reliable than the radial efficiency to be used for ranking. A robot is suitably selected based on the SBM efficiency.
•We develop a slacks-based measure model to calculate cross efficiency.•The slacks-based measure model does not produce negative efficiencies.•The slacks-based measure model provides appropriate ...efficiencies for weakly efficient units.•The slacks-based measure model produces single-value efficiency scores.
Cross efficiency is a concept for solving the problem of incomparability among the efficiencies of a set of decision making units (DMUs) calculated from different weights in data envelopment analysis, and is helpful for ranking. Conventional cross efficiency is a radial measure, and the radial measure has some weaknesses. First, it is not able to provide appropriate efficiency scores for weakly efficient DMUs. Second, the efficiencies measured from the input and output sides under variable returns to scale are different which may cause difficulties in subsequent analyses. Third, negative values may appear when the efficiency is measured from the input side. To solve these problems, this paper proposes a slacks-based measure to calculate efficiency. The basic idea is the same as that of the radial measure using the frontier corresponding to a DMU to measure the efficiency of all DMUs, except that the efficiency measure is slacks-based instead of radial. Due to the nature of the slacks-based efficiency measure, the problems caused by weak efficiency and difference in input and output radial measures do not exist. More importantly, negative efficiencies are not produced. The proposed method is applied to a real case involving the selection of the most efficient robot to use for production. The results help identify the top-ranked robot.
There is industrial incentive to extract aromatics from ethylene cracker feeds, but the conventional sulfolane solvent was found not economical by Meindersma and coworkers. Ionic liquids (ILs) have ...long been considered alternative aromatic extraction solvents. This work develops energy‐optimum aromatic extraction processes for an ethylene cracker feed using IL solvents. We avoid pitfalls of using simplified feeds and a priori thermodynamic property estimates, with the largest set of experimentally regressed UNIQUAC binary parameters for the IL, 1‐ethyl‐3‐methylimidazolium bis(trifluoromethylsulfonyl)imide (EMIMNTf2). We screen process energy and operating conditions for EMIMNTf2 and sulfolane at varying aromatic feed contents and find EMIMNTf2 favorable at low aromatic feed contents. Adding light and heavy components of the ethylene cracker feed necessitates process modifications. Our novel steam‐assisted extractive distillation developed for EMIMNTf2 is also suitable for sulfolane. We show that the EMIMNTf2 solvent can reduce 10.7% of energy consumption compared to sulfolane using the same novel process.
Ionic liquids (ILs) are promising solvents for the aromatic extraction process. An attractive characteristic is the existence of hundreds of ILs that exhibit different properties. To identify key ...properties of IL solvents for an energy‐optimum aromatic extraction, we use process simulation to generate the process datasets for multivariate data analytics with partial least squares, and use science‐guided fundamentals to develop an IL heat load variable (HLV). We consider 16 well‐studied ILs and correlate process steam duty and process variables affecting equipment size to the HLV for ethylene cracker feeds of low aromatic content. For such feeds in an IL aromatic extraction process, 11 of 16 ILs show energy advantage compared with sulfolane solvent with the lowest energy IL process requiring 57% of total energy required for an equivalent sulfolane process. Our results facilitate the IL solvent selection for pilot tests and subsequent commercialization of an IL aromatic extraction process.
Ionic liquids (ILs) are promising alternatives to conventional solvents for selective separation of aromatics from hydrocarbon mixtures, and their implementations depend on economic feasibility ...demonstrated by process simulation. Prior process modeling studies typically assume simplified hydrocarbon feeds or use the COSMO‐SAC predictive model. Our goal is to evaluate how feed simplifications and COSMO‐SAC predictions impact process modeling. We collect experimental data for 1‐Ethyl‐3‐methylimidazolium bis(trifluoromethylsulfonyl)imide (EMIMNTf2) from the ILThermo database to regress UNIQUAC model binary interaction parameters for 17 hydrocarbons. We find that feed simplifications tend to significantly underpredict process energy requirements and fail to reveal important details in the extractive distillation section of the process. COSMO‐SAC predictions underpredict activity coefficient of aliphatics in EMIMNTf2 by a large margin, which leads to lower aromatic‐aliphatic selectivities and overprediction of process energy requirements. It is significant enough to lead to the conclusion of process infeasibility in the case of EMIMNTf2.
•We develop a stochastic data envelopment analysis model to handle correlated data.•We use a simulation technique to obtain the distribution of the stochastic efficiency.•The stochastic efficiency is ...able to differentiate the conventional efficient units.•The stochastic efficiency shows the probability that a unit outperforms another.
While the real world is stochastic in nature, in many cases deterministic data envelopment analysis (DEA) models are used to measure the relative efficiency of a set of production units for simplicity. However, deterministic DEA models are not able to differentiate efficient units. More seriously, the decision maker will be over-confident with the presumably uncertain and probably misleading results. By applying a standard normal transformation, this paper develops a stochastic DEA model which is able to take the correlation between the input/output factors of each production unit to be evaluated into account to obtain the distribution of the stochastic efficiency. The efficiency distribution is more discriminative and informative than the single-valued efficiency, in that the probability that the stochastic efficiency of a unit is greater than that of another unit can be calculated. The case of twenty-five Taiwanese commercial banks discussed in a previous study that assumed the input/output factors to be independent is used to illustrate the characteristics of different models. The data is shown to be correlated, and the results confirm that ignoring the correlations between the input/output factors in measuring efficiency obtains misleading rankings.
•The assurance region approach is applied to reduce weight flexibility.•A pair of two-level mathematical programs is used to derive the fuzzy efficiencies.•Fuzzy system efficiency is the product of ...the two fuzzy process efficiencies.•An example of the IT impact on firm performance is illustrated to explain the idea.
Data envelopment analysis (DEA) is a method for measuring the efficiency of peer decision making units (DMUs). Recently DEA has been extended to examine the efficiency of two-stage processes, where all the outputs from the first stage are intermediate measures that make up the inputs to the second stage. Two-stage DEA models do not require a priori specification of input and output weights (or multipliers) and by letting these weights run freely, estimates of system and process efficiencies are obtained. This paper proposes a methodology for a fuzzy two-stage DEA model, where the weights are restricted in ranges and input–output data are treated as fuzzy numbers. The assurance region approach is utilized to restrict weight flexibility in the model. Based on Zadeh’s extension principle, a pair of two-level mathematical programs is formulated to calculate the upper bound and lower bound of the fuzzy efficiency score. We then transform this pair of two-level mathematical programs into a pair of conventional one-level mathematical programs to calculate the bounds of the fuzzy efficiency scores. The examples of non-life insurance companies in Taiwan and IT impact on firm performance are illustrated to calculate the system and process efficiencies and how to derive their relationship when the data is fuzzy.
