Open Access Peer-reviewed

Stochastic DEA with a Perfect Object and Its Application to Analysis of Environmental Efficiency

Alexander Y. Vaninsky
Mathematics Department, City University of New York/Hostos Community College, New York, USA
American Journal of Applied Mathematics and Statistics. 2013, 1(4), 57-63. DOI: 10.12691/ajams-1-4-2
Published online: August 25, 2017


The paper introduces stochastic DEA with a Perfect Object (SDEA PO). The Perfect Object (PO) is a virtual Decision Making Unit (DMU) that has the smallest inputs and greatest outputs. Including the PO in a collection of actual objects yields an explicit formula of the efficiency index. Given the distributions of DEA inputs and outputs, this formula allows us to derive the probability distribution of the efficiency score, to find its mathematical expectation, and to deliver common (group–related) and partial (object-related) efficiency components. We apply this approach to a prospective analysis of environmental efficiency of the major national and regional economies.


Data Envelopment Analysis, DEA analytical solutions, stochastic DEA with a perfect object, efficiency decomposition, environmental efficiency
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