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Probabilistic Bounds on the Virtual Multipliers in Data Envelopment Analysis: Polyhedral Cone Constraints

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  • Ole Olesen
  • Niels Petersen

Abstract

The paper is concerned with the incorporation of polyhedral cone constraints on the virtual multipliers in DEA. The incorporation of probabilistic bounds on the virtual multipliers based upon a stochastic benchmark vector is demonstrated. The suggested approach involves a stochastic (chance constrained) programming model with multipliers constrained to the cone spanned by confidence intervals for the components of the stochastic benchmark vector at varying probability levels. Consider a polyhedral assurance region based upon bounded pairwise ratios between multipliers. It is shown that in general it is never possible to identify a “center-vector” defined as a vector in the interior of the cone with identical angles to all extreme rays spanning the cone. Smooth cones are suggested if an asymmetric variation in the set of feasible relative prices is to be avoided. Copyright Kluwer Academic Publishers 1999

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  • Ole Olesen & Niels Petersen, 1999. "Probabilistic Bounds on the Virtual Multipliers in Data Envelopment Analysis: Polyhedral Cone Constraints," Journal of Productivity Analysis, Springer, vol. 12(2), pages 103-133, September.
    • Handle: RePEc:kap:jproda:v:12:y:1999:i:2:p:103-133
    DOI: 10.1023/A:1007820512934
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    References listed on IDEAS

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    Cited by:

    1. Ole Olesen & Niels Petersen, 2002. "The Use of Data Envelopment Analysis with Probabilistic Assurance Regions for Measuring Hospital Efficiency," Journal of Productivity Analysis, Springer, vol. 17(1), pages 83-109, January.
    2. Lovell, Knox, 2001. "Future Research Opportunities in Efficiency and Productivity Analysis," Efficiency Series Papers 2001/01, University of Oviedo, Department of Economics, Oviedo Efficiency Group (OEG).
    3. Park, K. Sam, 2010. "Duality, efficiency computations and interpretations in imprecise DEA," European Journal of Operational Research, Elsevier, vol. 200(1), pages 289-296, January.

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