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Appendix 5: Structure of DEA-based bid ranking models
We define value for money as the ratio of all expected outputs (environmental quality attributes) valued by the conservation agency over the bid amount: w'yi/bi, where yi are the output estimates offered by bidder i, w is a vector of output weights and bi is the bid amount. The agency is interested in acquiring as much of these quality characteristics as possible per unit of 'input', i.e. per pound of public money expended. The purpose of DEA is to construct a non-parametric envelopment frontier over these data points as a linear, piece-wise combination of observed maximum 'outputs' given observed bids ('inputs') such that all observed points lie on or below the value-for-money frontier. The frontier thus serves as a benchmark for assessing the relative merit of landholders' claims. Because of the need to aggregate multiple, incommensurable outputs, weights w must be determined for each output. To select optimal weights for each bid we specify the DEA model:
subject to 
DEA thus creates for each of the bids offered an optimal set of output weights - such that the value-for-money score of the i-th bidder is maximised subject to the constraint that all value-for-money scores must be less than or equal to one. That is, bids on the value-for-money frontier are assigned a value of one. Thus, given the information available on quality attributes and the corresponding bids, those ranked highest will provide the greatest value for money to the conservation agency.
Rather than solving the above problem directly, one can make use of duality in linear programming and solve the equivalent dual form. The dual solution provides additional information about slacks and targets and is generally the preferred form to solve. One would choose the input-oriented, variable-returns-to-scale model proposed by Banker, Charnes and Cooper (1984), the so-called BCC model. One would choose the input orientation (rather than the output orientation) because bidders have only control over the 'input' (the bid) while the 'outputs' (the quality attributes) are given and cannot be controlled by the bidders. The input-oriented specification addresses the question: by how much would the bid have to be lowered, given the quality characteristics, until the observation is on the value-for-money frontier? 11 This is not the place to review the DEA methodology in any detail. The reader may consult Charnes et al. (1994), Coelli, Rao and Battese (1998), and Cooper, Seiford and Tone (2000) for basic introductions to DEA.
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