Two-Stage Network DEA with Bad Outputs

Part of the International Series in Operations Research & Management Science book series (ISOR, volume 208)


Conventional black-box DEA models allow producer performance to be measured for technologies where undesirable outputs are jointly produced by-products of desirable output production. These models allow for non-radial scaling of desirable outputs, undesirable outputs, and inputs and can account for slacks in the constraints that define the technology. We review some of these black-box performance measures and show how to measure performance in two-stage network models. In these kinds of network models inputs are used to produce intermediate outputs in a first stage and then, those intermediate outputs become inputs to a second stage where final desirable outputs and undesirable outputs are produced. The bias from using a black-box model when a network technology exists is examined as well as the bias from ignoring slacks in the constraints defining the network technology.


DEA Two-stage network DEA Network directional inefficiency Network slacks-based inefficiency Bad outputs Black-box directional Russell inefficiency Network directional Russell inefficiency Budget-constrained inefficiency Output loss indicator Slack bias Weakly efficient Strongly efficient 



This research is partially supported by the Grants-in-aid for scientific research, fundamental research (B) 19310098 and (C) 23510165, the Japan Society for the Promotion of Science.


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© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Faculty of CommerceFukuoka UniversityFukuokaJapan
  2. 2.Department of Economics and FinanceSoutheast Missouri State UniversityCape GirardeauUSA

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