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Mathematical Problems in Engineering
Volume 2016, Article ID 1531282, 8 pages
Research Article

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

1Department of Applied Mathematics, Islamic Azad University, Lahijan, Iran
2Department of Applied Mathematics, Islamic Azad University, Rasht, Iran
3Department of Management, Islamic Azad University, Rasht, Iran

Received 27 September 2015; Accepted 6 December 2015

Academic Editor: Fazal M. Mahomed

Copyright © 2016 Mohsen Mirzaei et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.