Cost Allocation and Convex Data Envelopment

Jens Hougaard () and Jørgen Tind
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Jørgen Tind: Department of Mathematical Sciences, University of Copenhagen

No 08-02, Discussion Papers from University of Copenhagen. Department of Economics

Abstract: This paper considers allocation rules. First, we demonstrate that costs allocated by the Aumann-Shapley and the Friedman-Moulin cost allocation rules are easy to determine in practice using convex envelopment of registered cost data and parametric programming. Second, from the linear programming problems involved it becomes clear that the allocation rules, technically speaking, allocate the non-zero value of the dual variable for a convexity constraint on to the output vector. Hence, the allocation rules can also be used to allocate inefficiencies in non-parametric efficiency measurement models such as Data Envelopment Analysis (DEA). The convexity constraint of the BCC model introduces a non-zero slack in the objective function of the multiplier problem and we show that the cost allocation rules discussed in this paper can be used as candidates to allocate this slack value on to the input (or output) variables and hence enable a full allocation of the inefficiency on to the input (or output) variables as in the CCR model.

Keywords: cost allocation; convex envelopment; data envelopment analysis; slack allocation (search for similar items in EconPapers)
Pages: 17 pages
Date: 2008-01
New Economics Papers: this item is included in nep-eff
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Journal Article: Cost allocation and convex data envelopment (2009)
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