Skip to main content

Advertisement

Springer Nature Link
Log in

Plant capacity notions in a non-parametric framework: a brief review and new graph or non-oriented plant capacities

  • S.I.: Data Envelopment Analysis: Four Decades On
  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

Output-oriented plant capacity in a non-parametric framework is a concept that has been rather widely applied since about twenty-five years. Conversely, input-oriented plant capacity in this framework is a notion of more recent date. In this contribution, we unify the building blocks needed for determining both plant capacity measures and define new graph or non-oriented plant capacity concepts. We empirically illustrate the differences between these various plant capacity notions using a secondary data set. This shows the viability of these new definitions for the applied researcher.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

Notes

  1. For example, note that the convex variable returns to scale technology need not satisfy inaction.

  2. Note that L(0) can be equivalently defined by \(L(y_{min}) = \{ x \mid (x, y_{min}) \in T\}\), whereby \(y_{min} = \displaystyle \min _{k=1, \dots , K}y_k\). Thus, the minimum is taken in a component-wise manner for every output y over all observations K.

  3. This sub-vector input efficiency measure \(DF_i^{SR}(x^f,x^v,0)\) can be equivalently formulated as \(DF_i^{SR}(x^f,x^v,y_{min})\), where \(y_{min} = \displaystyle \min _{k=1, \dots , K}y_k\) whereby the minimum is taken in a component-wise manner for every output over all observations.

  4. A survey of similar input-oriented efficiency measures can be found in the earlier article of Russell and Schworm (2009).

  5. See Halická and Trnovská (2019) for more historical details and for new duality results.

  6. Note that Pastor et al. (1999) proceed in a similar way to transform the non-linear part of the non-radial Russell graph measure proposed by Färe et al. (1985, p. 154). Thereafter, Tone (2001) extends this proposal into the so-called slack-based measure (SBM). Sueyoshi and Sekitani (2007, Theorem 1) prove that a nonradial version of \(E_G(x,y)\) is less than or equal to the nonradial version of \(E_{FGL}(x,y)\).

  7. Banker (1984, p. 37) states: “the mpss for a given input and output mix is the scale size at which the outputs produced ‘per unit’ of the inputs is maximized. Thus, a production possibility \((x,y)\in T\) represents a mpss if and only if for all production possibilities \((\beta X,\alpha Y)\in T\) we have \(\frac{\alpha }{\beta } \le 1\).” The model introduced by Banker (1984) for determining mpss is as follows:

    $$\begin{aligned} \max \left\{ \frac{\alpha }{\beta } | \beta \ge 0, \alpha \ge 0, (\beta X,\alpha Y)\in T\right\} . \end{aligned}$$
    (19)

    Note that by decomposing inputs into their fixed and variable components, the above mpss model (19) can be written as model (17): i.e., \(E_G^{SR}(x^f,x^v,y)\).

  8. See Russell and Schworm (2011) for an almost complete overview of graph or non-oriented efficiency measures, including the directional distance function.

  9. Note that Yang and Fukuyama (2018) offer an output-oriented plant capacity notion with a directional distance function, but do not consider reductions in fixed inputs.

  10. See the web site: http://qed.econ.queensu.ca/jae/.

References

  • Banker, R., & Morey, R. (1986). Efficiency analysis for exogenously fixed inputs and outputs. Operations Research, 34(4), 513–521.

    Article  Google Scholar 

  • Banker, R. D. (1984). Estimating most productive scale size using Data Envelopment Analysis. European Journal of Operational Research, 17(1), 35–44.

    Article  Google Scholar 

  • Cesaroni, G., Kerstens, K., & Van de Woestyne, I. (2017). A new input-oriented plant capacity notion: Definition and empirical comparison. Pacific Economic Review, 22(4), 720–739.

    Article  Google Scholar 

  • Cesaroni, G., Kerstens, K., & Van de Woestyne, I. (2019). Short-and long-run plant capacity notions: Definitions and comparison. European Journal of Operational Research, 275(1), 387–397.

    Article  Google Scholar 

  • Chambers, R., Chung, Y., & Färe, R. (1998). Profit, directional distance functions, and Nerlovian efficiency. Journal of Optimization Theory and Applications, 98(2), 351–364.

    Article  Google Scholar 

  • Charnes, A., & Cooper, W. (1962). Programming with linear fractional functionals. Naval Research Logistics, 9(3–4), 181–186.

    Article  Google Scholar 

  • De Borger, B., & Kerstens, K. (2000). The Malmquist productivity index and plant capacity utilization. Scandinavian Journal of Economics, 102(2), 303–310.

    Article  Google Scholar 

  • Dupont, D., Grafton, R., Kirkley, J., & Squires, D. (2002). Capacity utilization measures and excess capacity in multi-product privatized fisheries. Resource and Energy Economics, 24(3), 193–210.

    Article  Google Scholar 

  • Fan, Y., & Ullah, A. (1999). On goodness-of-fit tests for weakly dependent processes using kernel method. Journal of Nonparametric Statistics, 11(1), 337–360.

    Article  Google Scholar 

  • Färe, R., & Grosskopf, S. (2000). Theory and application of directional distance functions. Journal of Productivity Analysis, 13(2), 93–103.

    Article  Google Scholar 

  • Färe, R., Grosskopf, S., & Kokkelenberg, E. (1989a). Measuring plant capacity, utilization and technical change: A nonparametric approach. International Economic Review, 30(3), 655–666.

    Article  Google Scholar 

  • Färe, R., Grosskopf, S., & Lovell, C. (1985). The measurement of efficiency of production. Boston: Kluwer.

    Book  Google Scholar 

  • Färe, R., Grosskopf, S., & Lovell, C. (1994). Production frontiers. Cambridge: Cambridge University Press.

    Google Scholar 

  • Färe, R., Grosskopf, S., Lovell, C., & Pasurka, C. (1989b). Multilateral productivity comparisons when some outputs are undesirable: A nonparametric approach. Review of Economics and Statistics, 71(1), 90–98.

    Article  Google Scholar 

  • Färe, R., Grosskopf, S., & Valdmanis, V. (1989c). Capacity, competition and efficiency in hospitals: A nonparametric approach. Journal of Productivity Analysis, 1(2), 123–138.

    Article  Google Scholar 

  • Färe, R., Grosskopf, S., & Zaim, O. (2002). Hyperbolic efficiency and return to the dollar. European Journal of Operational Research, 136(3), 671–679.

    Article  Google Scholar 

  • Färe, R., Margaritis, D., Rouse, P., & Roshdi, I. (2016). Estimating the hyperbolic distance function: A directional distance function approach. European Journal of Operational Research, 254(1), 312–319.

    Article  Google Scholar 

  • Felthoven, R. (2002). Effects of the American fisheries act on capacity, utilization and technical efficiency. Marine Resource Economics, 17(3), 181–205.

    Article  Google Scholar 

  • Hackman, S. (2008). Production economics: Integrating the microeconomic and engineering perspectives. Berlin: Springer.

    Google Scholar 

  • Halická, M., & Trnovská, M. (2018). The Russell measure model: Computational aspects, duality, and profit efficiency. European Journal of Operational Research, 268(1), 386–397.

    Article  Google Scholar 

  • Halická, M., & Trnovská, M. (2019). Duality and profit efficiency for the hyperbolic measure model. European Journal of Operational Research, 278(2), 410–421.

    Article  Google Scholar 

  • Hasannasab, M., Margaritis, D., Roshdi, I., & Rouse, P. (2019). Hyperbolic efficiency measurement: A conic programming approach. European Journal of Operational Research, 278(2), 401–409.

    Article  Google Scholar 

  • Ivaldi, M., Ladoux, N., Ossard, H., & Simioni, M. (1996). Comparing Fourier and translog specifications of multiproduct technology: Evidence from an incomplete panel of French farmers. Journal of Applied Econometrics, 11(6), 649–668.

    Article  Google Scholar 

  • Johansen, L. (1968). Production functions and the concept of capacity. Discussion Paper [reprinted in F. R. Førsund (ed.) (1987) Collected Works of Leif Johansen, Volume 1, Amsterdam, North Holland, 359–382], CERUNA, Namur.

  • Karagiannis, R. (2015). A system-of-equations two-stage DEA approach for explaining capacity utilization and technical efficiency. Annals of Operations Research, 227(1), 25–43.

    Article  Google Scholar 

  • Kerstens, K., Sadeghi, J., & Van de Woestyne, I. (2019a). Convex and nonconvex input-oriented technical and economic capacity measures: An empirical comparison. European Journal of Operational Research, 276(2), 699–709.

    Article  Google Scholar 

  • Kerstens, K., Sadeghi, J., & Van de Woestyne, I. (2019b). Plant capacity and attainability: Exploration and remedies. Operations Research, 67(4), 1135–1149.

    Google Scholar 

  • Li, Q. (1996). Nonparametric testing of closeness between two unknown distribution functions. Econometric Reviews, 15(1), 261–274.

    Article  Google Scholar 

  • Li, Q., Maasoumi, E., & Racine, J. (2009). A nonparametric test for equality of distributions with mixed categorical and continuous data. Journal of Econometrics, 148(2), 186–200.

    Article  Google Scholar 

  • Pastor, J. T., Ruiz, J. L., & Sirvent, I. (1999). An enhanced DEA Russell graph efficiency measure. European Journal of Operational Research, 115(3), 596–607.

    Article  Google Scholar 

  • Rasmussen, S. (2011). Production economics: The basic theory of production optimisation. Berlin: Springer.

    Book  Google Scholar 

  • Russell, R., & Schworm, W. (2009). Axiomatic foundations of efficiency measurement on data-generated technologies. Journal of Productivity Analysis, 31(2), 77–86.

    Article  Google Scholar 

  • Russell, R., & Schworm, W. (2011). Properties of inefficiency indexes on \(\langle \)Input, Output\(\rangle \) space. Journal of Productivity Analysis, 36(2), 143–156.

    Article  Google Scholar 

  • Sueyoshi, T., & Sekitani, K. (2007). Computational strategy for Russell measure in DEA: Second-order cone programming. European Journal of Operational Research, 180(1), 459–471.

    Article  Google Scholar 

  • Tone, K. (2001). A slacks-based measure of efficiency in Data Envelopment Analysis. European Journal of Operational Research, 130(3), 498–509.

    Article  Google Scholar 

  • Vestergaard, N., Squires, D., & Kirkley, J. (2003). Measuring capacity and capacity utilization in fisheries: The case of the Danish Gill-net fleet. Fisheries Research, 60(2–3), 357–368.

    Article  Google Scholar 

  • Yang, G.-L., & Fukuyama, H. (2018). Measuring the Chinese regional production potential using a generalized capacity utilization indicator. Omega, 76, 112–127.

    Article  Google Scholar 

  • Yang, G.-L., Fukuyama, H., & Song, Y.-Y. (2019). Estimating capacity utilization of Chinese manufacturing industries. Socio-Economic Planning Sciences, 67, 94–110.

    Article  Google Scholar 

  • Zofío, J., & Prieto, A. M. (2001). Environmental efficiency and regulatory standards: The case of \(\text{ CO }_2\) emissions from OECD industries. Resource and Energy Economics, 23(1), 63–83.

    Article  Google Scholar 

  • Zofío, J. L., & Lovell, C. (2001). Graph efficiency and productivity measures: An application to US agriculture. Applied Economics, 33(11), 1433–1442.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IESEG School of Management, CNRS-LEM (UMR 9221), Université de Lille, 3 rue de la Digue, 59000, Lille, France

    Kristiaan Kerstens

  2. IESEG School of Management, 3 rue de la Digue, 59000, Lille, France

    Jafar Sadeghi

  3. KU Leuven, Research Unit MEES, Warmoesberg 26, 1000, Brussels, Belgium

    Ignace Van de Woestyne

Authors
  1. Kristiaan Kerstens
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Jafar Sadeghi
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Ignace Van de Woestyne
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Kristiaan Kerstens.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

We are grateful to two referees of this journal for most useful comments. The usual disclaimer applies.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (pdf 411 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kerstens, K., Sadeghi, J. & Van de Woestyne, I. Plant capacity notions in a non-parametric framework: a brief review and new graph or non-oriented plant capacities. Ann Oper Res 288, 837–860 (2020). https://doi.org/10.1007/s10479-019-03485-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-019-03485-8

Keywords

JEL Classification