A data envelopment approach to decision analysis
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#2002 Operational Research Society Ltd. All rights reserved. 0160-5682/02 $15.00 www.palgrave-journals.com/jors
A data envelopment approach to decision analysis PP Sutton1 and RH Green1,2* 1
University of Bath, Bath, UK; and 2University of South Australia, Adelaide, Australia
A decision aid to assist the development of a linear valuation function for multiple attribute problems is proposed, based on a linear programming formulation using a constraint set structured in a similar manner to data envelopment analysis (DEA). Value functions which favour each decision option are calculated, and efficient, potentially optimal, options identified. These are used to help a decision maker progressively to articulate preferences, indicators of his/her values, in an interactive, structurally flexible manner. As preference indications are provided, candidate value functions and hitherto efficient options inconsistent with his/her declarations are eliminated, thus proceeding towards an explicit value function and, if needed a corresponding complete option order. Journal of the Operational Research Society (2002) 53, 1215–1224. doi:10.1057/palgrave.jors.2601399 Keywords: decision analysis; value function; preferences; linear programming; data envelopment analysis
Introduction In this paper we suggest formulations for the prospective evaluation of decision choices, bearing a structural similarity to that used in data envelopment analysis (DEA), first introduced in mathematical programming form by Charnes et al1 for the retrospective evaluation of efficiency. We share the view of Stewart2 that DEA potentially allows the maximum extraction of (implicitly factual) information from decision data. Others including Belton,3 Doyle and Green4 have also pointed out the promise of DEA for insightful decision support. Doyle and Green4 and Cook and Green5 have sought selection indicators looking mainly endogenously within the data describing options. However, Bouyssou6 suggests dangers in using DEA for more than convex efficiency analysis without the introduction of preference information. Sarrico et al7 introduce value judgements into a decision situation though their interest remains primarily in generating general measures of performance efficiency rather than eliciting value or utility functions for the decisions of individuals. In the formulation here we use some of the ideas of DEA, including the notion of finding weights which show the performance of options in their most favourable light, not only to highlight good options on the basis of options’ factual content, but also to provide a framework to elicit and use information that is exogenous to the options. Specifically, we seek to elicit the information reflective of a decision maker’s ambitions or what Simon8 distinguishes as the value or ethical content of a decision. We seek a progressive quantitative articulation of a *Correspondence: RH Green, School of Management, University of Bath, Bath BA2 7AY, UK. E-mail: [email protected]
decision maker’s objectives, which may be quali
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