scholarly journals Alternative Trade-Offs in Data Envelopment Analysis: An Application to Hydropower Plants

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Mohsen Mirzaei ◽  
Sohrab Kordrostami ◽  
Alireza Amirteimoori ◽  
Mehrdad G. Chegini
Keyword(s):  
Data Envelopment Analysis ◽  
Piecewise Linear ◽  
Extreme Points ◽  
Efficient Frontier ◽  
Data Envelopment ◽  
Frontier Point ◽  
Trade Offs ◽  
Hydropower Plants ◽  
Alternative Trade ◽  
Output Space

In multidimensional input/output space, the behavior of the firms can be analyzed by using efficient frontier or supporting surfaces of production technology. To this end, mathematicians are interested to use marginal rates of substitutions. The piecewise linear frontier of data envelopment analysis (DEA) technology is not differentiable at the extreme points and marginal rates calculation is valid only for small changes in one or more variables. The existing trade-off analysis methods calculate the maximum changes in a specific throughput when another throughput is changed. We will show that binding efficient supporting surfaces of an efficient point may be used to define different marginal rates of substitutions and in this sense, we get different marginal rates to each frontier point.

Interval Data Envelopment Analysis for Inter-Group Data Usage

2020 ◽  
Vol 24 (1) ◽  
pp. 113-122
Author(s):  
Tomoe Entani ◽  
Keyword(s):  
Data Envelopment Analysis ◽  
Efficient Frontier ◽  
Original Data ◽  
Weight Vector ◽  
The Other ◽  
Data Envelopment ◽  
Broad Perspective ◽  
Data Usage ◽  
Group Data ◽  
Multiple Groups

Organizations are interested in exploiting the data from the other organizations for better analyses. Therefore, the data related policies of organizations should be sensitive to the data privacy issue, which has been widely discussed recently. The present study is focused on inter-group data usage for a relative evaluation. This research is based on the data envelopment analysis (DEA), which is used to measure the efficiency of a decision making unit (DMU) relatively employed within a group. In DEA, establishing an efficient frontier consisting of efficient DMUs is essential. We can obtain the efficiency values of a DMU by projecting it to the efficient frontier, and including in the efficiency interval via the interval DEA. When the original data of multiple groups are not open to each other, the alternative is to exchange the information corresponding to the efficient frontiers to estimate the efficiency intervals of a DMU in such a manner that the alternative is in the other groups. Therefore, in this paper, we propose a method to replace the efficient frontier with a weight vector set, from which it is not possible to reconstruct the original data. Considering the weight vector sets of multiple groups, a DMU has three types of efficiency intervals: in its own group, in each of the other groups, and in the integrated group. They provide rich insights on the DMU from a broad perspective, and this encourages inter-group data usage. In this process, we focus on two types of information reduction: one is from the efficient frontier to the weight vector set, and the other is from a union of the groups to the integrated group.

scholarly journals Choosing weights in optimal solutions for DEA-BCC models by means of a N-dimensional smooth frontier

2009 ◽  
Vol 29 (3) ◽  
pp. 623-642 ◽  
Author(s):  
Flávia Badini Nacif ◽  
João Carlos Correia Baptista Soares de Mello ◽  
Lidia Angulo Meza
Keyword(s):  
Decision Making ◽  
Data Envelopment Analysis ◽  
Present Article ◽  
General Model ◽  
Piecewise Linear ◽  
Data Envelopment ◽  
Optimal Solutions ◽  
Single Output ◽  
Single Input ◽  
Decision Making Units

The DEA (Data Envelopment Analysis) smoothed frontier was introduced to solve the problem of multiple optimal solutions in the extreme efficient DMUs (Decision Making Units), which hinders the knowledge of the substitution rates (tradeoffs). It consists of changing the original frontier (piecewise linear) for a smoothed one, being as close as possible to the original one, and having continuous partial derivates at every point. First, a solution was developed only for the BCC (Banker, Charnes and Cooper) model with either a single input or a single output. Then, it was generalized for the N-dimensional BCC model with simultaneous multiplicity of inputs and outputs, but limited by the fact that the polynomial of the output needs to be a linear one. The present article presents a general model, which not only expunges the limitations of the previous models but also includes them.

scholarly journals Trade-offs analysis of sustainability dimensions using integer-valued data envelopment analysis

2020 ◽  
Vol 11 (2) ◽  
pp. 275-289
Author(s):  
Monireh Jahani Sayyad Noveiri ◽  
Sohrab Kordrostami
Keyword(s):  
Data Envelopment Analysis ◽  
Real World ◽  
Data Envelopment ◽  
Industrial Parks ◽  
Trade Offs ◽  
Dea Models ◽  
Marginal Rates Of Substitution

Conducting an in-depth exploration of trade-offs between sustainability aspects is a notable matter of taking decisions. Furthermore, there are many real world investigations that trade-offs and sustainability should be dealt with in the presence of desirable and undesirable materials while some of them accept integer amounts. Therefore, this study addresses trade-offs of sustainability dimensions when undesirable and integer-valued measures are presented. For this purpose, approaches based upon data envelopment analysis (DEA) are proposed. To explain, DEA models are introduced to calculate individual and group marginal rates of substitution and also directional marginal rates of substitution when integer and undesirable variables are observed. These procedures are applied to calculate trade-offs between different sustainability dimensions, including economic, environmental and social ones. The applications of ports and industrial parks are provided to clarify the approaches appeared in this study. The results derived from the proposed strategies show the usefulness and validity of them.

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