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The hybrid returns-to-scale model and its extension by production trade-offs: an application to the efficiency assessment of public universities in Malaysia

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Abstract

Most applications of data envelopment analysis (DEA) employ standard constant or variable returns-to-scale models. In this paper we suggest that these models may sometimes underutilize our knowledge of the underlying production process. For example, in the context of higher education considered in the reported application, individual universities often maintain a certain student-to-staff ratio which points that there should be an approximately proportional relationship between students and staff, at least in the medium to long run. A different example is an observation that the teaching of postgraduate students generally requires more resources than the teaching of the same number of undergraduate students. In order to incorporate such information in a DEA model, we propose a novel approach that combines the recently developed hybrid returns-to-scale DEA model with the use of production trade-offs. The suggested approach leads to a better-informed model of production technology than the conventional DEA models. We illustrate this methodology by an application to Malaysian public universities. This approach results in a tangibly better efficiency discrimination than would be possible with the standard DEA models.

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Notes

  1. The use of weight restrictions as a means to incorporate value judgements in DEA models and related theoretical issues are discussed in Allen et al. (1997), Pedraja-Chaparro et al. (1997), Podinovski (1999, 2001) and Thanassoulis et al. (2004).

  2. The treatment of selective proportionality in the HRS model is somewhat similar to the treatment of good and bad outputs in the weakly disposable VRS technology of Kuosmanen (2005). The latter is further explored and extended in Kuosmanen and Podinovski (2009) and Podinovski and Kuosmanen (2011).

  3. Podinovski (2004b) shows that production trade-offs are mathematically equivalent to weight restrictions in the dual multiplier models. The assessment of trade-offs in DEA applications to different sectors, other than higher education, using conventional DEA models was illustrated, for example, by Amado and Dyson (2009), Amado and Santos (2009), Santos and Amado (2014).

  4. Throughout our paper we use the abbreviated names of universities as shown on the official webpage (MOE 2014).

  5. We consider these data as representative of the two academic years 2011–2012 and 2012–2013.

  6. Similar to the higher education systems in other countries, academic staff at Malaysian universities are expected to engage both in teaching and research.

  7. By Assumption 1, we do not mean that research publications do not increase with respect to academic staff. We only accept that the actual increase cannot be described by a proportion. Below we argue that a suitable relationship between academic staff and research publications can still be formalised by an appropriate production trade-off—see Assumption 7.

  8. A further extension to the HRS technology in developed in Podinovski (2009).

  9. We further make a usual assumption required for the unproblematic definition of technology and efficiency measures. Namely, we assume that each observed DMU has at least one positive input and at least one positive output. We also assume that no input and no output is equal to zero for all observed DMUs.

  10. If, as in Remark 1, research funding is treated as output, the set \(\mathrm{I}^{NP}\) is empty and the set \(\mathrm{O}^{NP}\) includes both research funding and publications.

  11. We use bold notation 0 for the vector of zeros of appropriate dimension.

  12. Podinovski et al. (2014) illustrate the importance of the minimum extrapolation principle by the following example. It is well known (Banker et al. 1984) that the VRS technology is defined by Axioms 1–3, stated above. Note that there are many other technologies (e.g., CRS) that also satisfy the same three axioms. However, the VRS technology is the smallest of all such technologies—it is the intersection of all of them.

  13. The exact numerical values of the trade-offs expressed by Assumptions 3–8 are specific to the described context. Similar trade-offs are likely to be valid in other applications to the higher education sector, e.g., in other countries, but the numerical values and the logic leading to them obviously need to be verified.

  14. We assume that the changes stated in Assumptions 3–8 do not result in negative inputs and outputs. Thus, Assumption 3 applies to any university that has at least one master student.

  15. In Assumptions 4–8 we identify only the changes to certain inputs and outputs that are assumed possible. To avoid repetitive statements, we assume without mentioning that the remaining inputs and outputs are kept constant.

  16. In the absence of a suitable reliable methodology, we estimate that, by supervising a doctoral student, academics may earn 10 % or more of their annual teaching credit. Consider a typical university with the ratio of undergraduate students to staff equal to 20. Then each undergraduate student equates to 5 % of the annual teaching credit. Based on this, we estimate that a doctoral student may require at least twice the amount of teaching resources compared to an undergraduate student, leading to Assumption 5. The upper bound on the ratio between the resources required for the doctoral and undergraduate students may be larger than 2 and is difficult to estimate. To be on the safe side, we assume that in no university it is greater than 10. Although this value may appear over-cautious, the resulting trade-off in Assumption 6 is certainly feasible in the technology sense and its use leads to a meaningful expansion of the technology (see Sect. 5).

  17. Note that Assumption 7 stating that an additional member of academic staff should be able to publish at least 0.25 papers a year (without extra research funding) does not contradict Assumption 1 that excludes publications from the proportion with respect to staff.

  18. Further theoretical results concerning the role of production trade-offs in expanding the model of technology were obtained by Podinovski and Bouzdine-Chameeva (2013, 2015). The dual relationship between trade-offs and weight restrictions of different types was demonstrated in Podinovski (2005, 2007a).

  19. A proper term here is “weakly efficient”. In order to investigate whether a weakly efficient university is fully efficient (in the Pareto sense), we need to perform the second-stage procedure maximizing the sum of input and output slacks, or an analogous one-stage approach—see Thanassoulis et al. (2008) for a discussion. For the CRS and VRS models with production trade-offs an appropriate procedure was developed in Podinovski (2007b).

  20. As discussed in Sect. 2.2, our model has a number of limitations arising from the available data. This model does not account for all measures and factors available to MOE in their own assessment.

  21. The corresponding efficiency of UiTM is only marginally reduced from 0.33 to 0.32, while there is no reduction for the remaining 18 universities.

  22. As shown in Podinovski (2004b), generally neither the HRS technology is a subset of the CRS technology, nor is the latter a subset of the former. The exception is the case \(\mathrm{I}^{NP}=\emptyset \). In this case the HRS technology is a subset of the CRS technology.

References

  • Allen, R., Athanassopoulos, A., Dyson, R. G., & Thanassoulis, E. (1997). Weights restrictions and value judgements in data envelopment analysis: Evolution, development and future directions. Annals of Operations Research, 73, 13–34.

    Article  Google Scholar 

  • Amado, C. A. F., & Dyson, R. G. (2009). Exploring the use of DEA for formative evaluation in primary diabetes care: An application to compare English practices. Journal of the Operational Research Society, 60(11), 1469–1482.

    Article  Google Scholar 

  • Amado, C. A. F., & Santos, S. P. (2009). Challenges for performance assessment and improvement in primary health care: The case of the Portuguese health centres. Health Policy, 91(1), 43–56.

    Article  Google Scholar 

  • Athanassopoulos, A. D., & Shale, E. (1997). Assessing the comparative efficiency of higher education institutions in the UK by means of data envelopment analysis. Education Economics, 5(2), 117–134.

    Article  Google Scholar 

  • Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science, 30(9), 1078–1092.

    Article  Google Scholar 

  • Beasley, J. E. (1990). Comparing university departments. Omega, 18(2), 171–183.

    Article  Google Scholar 

  • Beasley, J. E. (1995). Comparing teaching and research efficiencies. Journal of the Operational Research Society, 46(4), 441–452.

    Article  Google Scholar 

  • Blackburn, V., Brennan, S., & Ruggiero, J. (2014). Nonparametric estimation of education production and costs using data envelopment analysis. New York: Springer.

    Google Scholar 

  • Brennan, S., Haelermans, C., & Ruggiero, J. (2014). Nonparametric estimation of education productivity incorporating nondiscretionary inputs with an application to Dutch schools. European Journal of Operational Research, 234(3), 809–818.

    Article  Google Scholar 

  • Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2(6), 429–444.

    Article  Google Scholar 

  • Cooper, W. W., Seiford, L. M., & Tone, K. (2007). Data envelopment analysis. A comprehensive text with models, applications, references and DEA-Solver software (2nd ed.). New York: Springer.

    Google Scholar 

  • Flegg, A. T., Allen, D. O., Field, K., & Thurlow, T. W. (2004). Measuring the efficiency of British universities: A multi-period data envelopment analysis. Education Economics, 12(3), 231–249.

    Article  Google Scholar 

  • Johnes, J. (2006). Measuring teaching efficiency in higher education: An application of data envelopment analysis to economics graduates from UK Universities 1993. European Journal of Operational Research, 174(1), 443–456.

    Article  Google Scholar 

  • Johnes, J. (2008). Efficiency and productivity change in the English higher education sector from 1996/97 to 2004/5. The Manchester School, 76(6), 653–674.

    Article  Google Scholar 

  • Johnes, J., & Johnes, G. (1995). Research funding and performance in U.K. university departments of economics: A frontier analysis. Economics of Education Review, 14(3), 301–314.

    Article  Google Scholar 

  • Johnes, J., & Yu, L. (2008). Measuring the research performance of Chinese higher education institutions using data envelopment analysis. China Economic Review, 19(4), 679–696.

    Article  Google Scholar 

  • Johnson, A. L., & Ruggiero, J. (2014). Nonparametric measurement of productivity and efficiency in education. Annals of Operations Research, 221, 197–210.

    Article  Google Scholar 

  • Khalili, M., Camanho, A. S., Portela, M. C. A. S., & Alirezaee, M. R. (2010). The measurement of relative efficiency using data envelopment analysis with assurance regions that link inputs and outputs. European Journal of Operational Research, 203(3), 761–770.

    Article  Google Scholar 

  • Kuosmanen, T. (2005). Weak disposability in nonparametric productivity analysis with undesirable outputs. American Journal of Agricultural Economics, 87(4), 1077–1082.

    Article  Google Scholar 

  • Kuosmanen, T., & Podinovski, V. V. (2009). Weak disposability in nonparametric production analysis: Reply to Färe and Grosskopf. American Journal of Agricultural Economics, 91(2), 539–545.

    Article  Google Scholar 

  • Liu, J. S., Lu, L. Y. Y., Lu, W.-M., & Lin, B. J. Y. (2013). A survey of DEA applications. Omega, 41(5), 893–902.

    Article  Google Scholar 

  • MOE. (2014). Ministry of Education Malaysia. http://www.moe.gov.my. Accessed October 2014.

  • Ng, Y. C., & Li, S. K. (2000). Measuring the research performance of Chinese higher education institutions: An application of data envelopment analysis. Education Economics, 8(2), 139–156.

    Article  Google Scholar 

  • Pedraja-Chaparro, F., Salinas-Jimenez, J., & Smith, P. (1997). On the role of weight restrictions in data envelopment analysis. Journal of Productivity Analysis, 8(2), 215–230.

    Article  Google Scholar 

  • Podinovski, V. V. (1999). Side effects of absolute weight bounds in DEA models. European Journal of Operational Research, 115(3), 583–595.

    Article  Google Scholar 

  • Podinovski, V. V. (2001). DEA models for the explicit maximisation of relative efficiency. European Journal of Operational Research, 131(3), 572–586.

    Article  Google Scholar 

  • Podinovski, V. V. (2004a). Bridging the gap between the constant and variable returns-to-scale models: Selective proportionality in data envelopment analysis. Journal of the Operational Research Society, 55(3), 265–276.

    Article  Google Scholar 

  • Podinovski, V. V. (2004b). Production trade-offs and weight restrictions in data envelopment analysis. Journal of the Operational Research Society, 55(12), 1311–1322.

    Article  Google Scholar 

  • Podinovski, V. V. (2005). The explicit role of weight bounds in models of data envelopment analysis. Journal of the Operational Research Society, 56(12), 1408–1418.

    Article  Google Scholar 

  • Podinovski, V. V. (2007a). Improving data envelopment analysis by the use of production trade-offs. Journal of the Operational Research Society, 58(10), 1261–1270.

    Article  Google Scholar 

  • Podinovski, V. V. (2007b). Computation of efficient targets in DEA models with production trade-offs and weight restrictions. European Journal of Operational Research, 181(2), 586–591.

    Article  Google Scholar 

  • Podinovski, V. V. (2009). Production technologies based on combined proportionality assumptions. Journal of Productivity Analysis, 32(1), 21–26.

    Article  Google Scholar 

  • Podinovski, V. V., & Bouzdine-Chameeva, T. (2013). Weight restrictions and free production in data envelopment analysis. Operations Research, 61(2), 426–437.

    Article  Google Scholar 

  • Podinovski, V. V., & Bouzdine-Chameeva, T. (2015). Consistent weight restrictions in data envelopment analysis. European Journal of Operational Research, 244(1), 201–209.

  • Podinovski, V. V., Ismail, I., Bouzdine-Chameeva, T., & Zhang, W. (2014). Combining the assumptions of variable and constant returns to scale in the efficiency evaluation of secondary schools. European Journal of Operational Research, 239(2), 504–513.

    Article  Google Scholar 

  • Podinovski, V. V., & Kuosmanen, T. (2011). Modelling weak disposability in data envelopment analysis under relaxed convexity assumptions. European Journal of Operational Research, 211(3), 577–585.

    Article  Google Scholar 

  • Portela, M. C. S., Camanho, A. S., & Borges, D. (2012). Performance assessment of secondary schools: The snapshot of a country taken by DEA. Journal of the Operational Research Society, 63(8), 1098–1115.

    Article  Google Scholar 

  • Santos, S. P., & Amado, C. A. F. (2014). On the need for reform of the Portuguese judicial system—Does data envelopment analysis assessment support it? Omega, 47, 1–16.

    Article  Google Scholar 

  • Sarrico, C. S., & Dyson, R. G. (2004). Restricting virtual weights in data envelopment analysis. European Journal of Operational Research, 159(1), 17–34.

    Article  Google Scholar 

  • Sarrico, C. S., Hogan, S. M., Dyson, R. G., & Athanassopoulos, A. D. (1997). Data envelopment analysis and university selection. Journal of the Operational Research Society, 48(12), 1163–1177.

    Article  Google Scholar 

  • Thanassoulis, E., Kortelainen, M., Johnes, G., & Johnes, J. (2011). Costs and efficiency of higher education institutions in England: A DEA analysis. Journal of the Operational Research Society, 62(7), 1282–1297.

    Article  Google Scholar 

  • Thanassoulis, E., Portela, M. C., & Allen, R. (2004). Incorporating value judgements in DEA. In W. W. Cooper, L. M. Seiford, & J. Zhu (Eds.), Handbook on data envelopment analysis (pp. 99–138). Boston: Kluwer.

    Chapter  Google Scholar 

  • Thanassoulis, E., Portela, M. C. S., & Despić, O. (2008). Data envelopment analysis: The mathematical programming approach to efficiency analysis. In H. O. Fried, C. A. K. Lovell, & S. S. Schmidt (Eds.), The measurement of productive efficiency and productivity growth (pp. 251–420). New York: Oxford University Press.

    Chapter  Google Scholar 

  • Wilkinson, R., & Yussof, I. (2005). Public and private provision of higher education in Malaysia: A comparative analysis. Higher Education, 50(3), 361–386.

    Article  Google Scholar 

  • Worthington, A. C., & Lee, B. L. (2008). Efficiency, technology and productivity change in Australian universities, 1998–2003. Economics of Education Review, 27(3), 285–298.

    Article  Google Scholar 

  • Yu, M. L., Hamid, S., Ijab, M. T., & Soo, H. P. (2009). The e-balanced scorecard (e-BSC) for measuring academic staff performance excellence. Higher Education, 57(6), 813–828.

    Article  Google Scholar 

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Acknowledgments

The authors are grateful to Educational Planning and Research Division (EPRD) of the Ministry of Education Malaysia for permission to collect and use the data for this study.

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Authors and Affiliations

  1. Warwick Business School, University of Warwick, Coventry, CV4 7AL, UK

    Victor V. Podinovski

  2. Business Administration Department, KENMS, International Islamic University Malaysia, Jalan Gombak, 53100 , Kuala Lumpur, Malaysia

    Wan Rohaida Wan Husain

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  1. Victor V. Podinovski
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Correspondence to Victor V. Podinovski.

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Podinovski, V.V., Wan Husain, W.R. The hybrid returns-to-scale model and its extension by production trade-offs: an application to the efficiency assessment of public universities in Malaysia. Ann Oper Res 250, 65–84 (2017). https://doi.org/10.1007/s10479-015-1854-0

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