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Cost Allocation and Convex Data Envelopment

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Author Info

  • Jens Leth Hougaard

    (Department of Economics, University of Copenhagen)

  • Jørgen Tind

    (Department of Mathematical Sciences, University of Copenhagen)

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.

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Bibliographic Info

Paper provided by University of Copenhagen. Department of Economics in its series Discussion Papers with number 08-02.

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Length: 17 pages
Date of creation: Jan 2008
Date of revision:
Handle: RePEc:kud:kuiedp:0802

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Related research

Keywords: cost allocation; convex envelopment; data envelopment analysis; slack allocation;

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  1. Peter Bogetoft & Joseph M. Tama & Jørgen Tind, 2000. "Convex Input and Output Projections of Nonconvex Production Possibility Sets," Management Science, INFORMS, vol. 46(6), pages 858-869, June.
  2. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
  3. Peter Bogetoft, 1996. "DEA on Relaxed Convexity Assumptions," Management Science, INFORMS, vol. 42(3), pages 457-465, March.
  4. Cook, Wade D. & Kress, Moshe, 1999. "Characterizing an equitable allocation of shared costs: A DEA approach," European Journal of Operational Research, Elsevier, vol. 119(3), pages 652-661, December.
  5. Beasley, J. E., 2003. "Allocating fixed costs and resources via data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 147(1), pages 198-216, May.
  6. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
  7. Eric Friedman & Moulin, Herve, 1995. "Three Methods to Share Joint Costs or Surplus," Working Papers 95-38, Duke University, Department of Economics.
  8. Banker, Rajiv D & Maindiratta, Ajay, 1988. "Nonparametric Analysis of Technical and Allocative Efficiencies in Production," Econometrica, Econometric Society, vol. 56(6), pages 1315-32, November.
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