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Cost Allocation and Convex Data Envelopment

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  • 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.

Suggested Citation

  • Jens Leth Hougaard & Jørgen Tind, 2008. "Cost Allocation and Convex Data Envelopment," Discussion Papers 08-02, University of Copenhagen. Department of Economics.
  • Handle: RePEc:kud:kuiedp:0802
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    File URL: http://www.econ.ku.dk/english/research/publications/wp/2008/0801.pdf/
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. Friedman, Eric & Moulin, Herve, 1999. "Three Methods to Share Joint Costs or Surplus," Journal of Economic Theory, Elsevier, vol. 87(2), pages 275-312, August.
    5. Banker, Rajiv D & Maindiratta, Ajay, 1988. "Nonparametric Analysis of Technical and Allocative Efficiencies in Production," Econometrica, Econometric Society, vol. 56(6), pages 1315-1332, November.
    6. 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.
    7. 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.
    8. Peter Bogetoft, 1996. "DEA on Relaxed Convexity Assumptions," Management Science, INFORMS, vol. 42(3), pages 457-465, March.
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    Cited by:

    1. Albizuri, M.J. & Díez, H. & Sarachu, A., 2014. "Monotonicity and the Aumann–Shapley cost-sharing method in the discrete case," European Journal of Operational Research, Elsevier, vol. 238(2), pages 560-565.
    2. Jens Leth Hougaard & Jørgen Tind, 2013. "Cost Allocation with Limited Information," MSAP Working Paper Series 01_2013, University of Copenhagen, Department of Food and Resource Economics.
    3. Bogetoft, Peter & Hougaard, Jens Leth & Smilgins, Aleksandrs, 2016. "Applied cost allocation: The DEA–Aumann–Shapley approach," European Journal of Operational Research, Elsevier, vol. 254(2), pages 667-678.
    4. Aldanondo, Ana M. & Casasnovas, Valero L., 2016. "A note on the impact of multiple input aggregators in technical efficiency estimation," MPRA Paper 75290, University Library of Munich, Germany.

    More about this item

    Keywords

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

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