Fixed-sum Outputs Research Articles

Measuring environmental efficiency of thermoelectric power plants: a common equilibrium efficient frontier DEA approach with fixed-sum undesirable output

China’s rapid development in economy has intensified many problems. One of the most important issues is the problem of environmental pollution. In this paper, a new DEA approach is proposed to measure the environmental efficiency of thermoelectric power plants, considering undesirable outputs. First, we assume that the total amount of undesirable outputs of any particular type is limited and fixed to current levels. In contrast to previous studies, this study requires fixed-sum undesirable outputs. In addition, the common equilibrium efficient frontier is constructed by using different input/output multipliers (or weights) for each different decision making unit (DMU), while previous approaches which considered fixed-sum outputs assumed a common input/output multiplier for all DMUs. The proposed method is applied to measure the environmental efficiencies of 30 thermoelectric power plants in mainland China. Our empirical study shows that half of the plants perform well in terms of environmental efficiency.

Context-based competition strategy and performance analysis with fixed-sum outputs: an application to banking sector

In the prior literature on performance measurement of firms with fixed-sum outputs, an equilibrium-efficient frontier is constructed. This paper shows that a single equilibrium-efficient frontier needs a significant trade-off between efficient and inefficient firms, and this may be impossible in practical applications. We develop a data envelopment analysis (DEA) model to construct multiple equilibrium-efficient frontiers in the presence of fixed-sum outputs. The approach uses context-dependent DEA that refers to a DEA approach where a set of firms are assessed against a particular assessment context. Numerical examples are used to illustrate the applicability of the approach.

A new approach for achievement of the equilibrium efficient frontier with fixed-sum outputs

In a recent paper, Yang et al developed an algorithm based on the extended minimal adjustment strategy and the equilibrium competition strategy to achieve a common equilibrium efficient frontier. However, the computational burden of their algorithm is challenging when a sample contains many inefficient decision-making units (DMUs). In this paper, we propose a linear programming model that can achieve a common equilibrium efficient frontier in a single step, regardless of the number of inefficient DMUs. Furthermore, we demonstrate the existence and the non-uniqueness of the equilibrium efficient frontier and identify its shortcomings through an example. Next, we extend our approach to incorporate weight restrictions to indicate the relative importance of the different inputs and outputs and introduce the secondary goal of minimizing the maximal relative deviation for each fixed-sum output, which can result in a unique equilibrium efficient frontier.

A generalized equilibrium efficient frontier data envelopment analysis approach for evaluating DMUs with fixed-sum outputs

The recently published equilibrium efficient frontier data envelopment analysis (EEFDEA) approach (Yang et al., 2014) represents a step forward in evaluating decision-making units (DMUs) with fixed-sum outputs when compared to prior approaches such as FSODEA (fixed-sum outputs DEA) approach (Yang et al., 2011) and ZSG-DEA (zero sum gains DEA) approach (Lins et al., 2003) and so on. Based on the EEFDEA approach, in this paper, we proposed a generalized equilibrium efficient frontier data envelopment analysis approach (GEEFDEA) which improves and strengthens the EEFDEA approach. Compared to EEFDEA approach, this approach makes several improvements in evaluation, namely that (1) it is not necessary to determine the evaluation order in advance, which overcomes the limitation that different evaluation orders will lead to different results; (2) the equilibrium efficient frontier can be achieved in only one step no matter how many DMUs they are, which greatly simplifies the procedure to reach the equilibrium efficient frontier especially when the number of DMUs is large; and (3) the constraint that signs of outputs’ adjustment of each DMU must be same (all non-positive or all non-negative) in prior approaches has been relaxed. In this sense, the result obtained by the proposed approach is more consistent with the demand of practical applications. Finally, the proposed approach combined with assurance regions (AR) is applied to the data set of 2012 London Olympic Games.

An equilibrium efficiency frontier data envelopment analysis approach for evaluating decision-making units with fixed-sum outputs

Based on the minimal reduction strategy, Yang et al. (2011) developed a fixed-sum output data envelopment analysis (FSODEA) approach to evaluate the performance of decision-making units (DMUs) with fixed-sum outputs. However, in terms of such a strategy, all DMUs compete over fixed-sum outputs with “no memory” that will result in differing efficient frontiers’ evaluations. To address the problem, in this study, we propose an equilibrium efficiency frontier data envelopment analysis (EEFDEA) approach, by which all DMUs with fixed-sum outputs can be evaluated based on a common platform (or equilibrium efficient frontier). The proposed approach can be divided into two stages. Stage 1 constructs a common evaluation platform via two strategies: an extended minimal adjustment strategy and an equilibrium competition strategy. The former ensures that original efficient DMUs are still efficient, guaranteeing the existence of a common evaluation platform. The latter makes all DMUs achieve a common equilibrium efficient frontier. Then, based on the common equilibrium efficient frontier, Stage 2 evaluates all DMUs with their original inputs and outputs. Finally, we illustrate the proposed approach by using two numerical examples.

Competition strategy and efficiency evaluation for decision making units with fixed-sum outputs

This paper develops a DEA (data envelopment analysis) model to accommodate competition over outputs. In the proposed model, the total output of all decision making units (DMUs) is fixed, and DMUs compete with each other to maximize their self-rated DEA efficiency score. In the presence of competition over outputs, the best-practice frontier deviates from the classical DEA frontier. We also compute the efficiency scores using the proposed fixed sum output DEA (FSODEA) models, and discuss the competition strategy selection rule. The model is illustrated using a hypothetical data set under the constant returns to scale assumption and medal data from the 2000 Sydney Olympics under the variable returns to scale assumption.