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Efficiency analysis of non-homogeneous parallel sub-unit systems for the performance measurement of higher education

  • RAOTA-2016
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Abstract

Conventional Data Envelopment Analysis (DEA) models focus only on initial inputs and final outputs for efficiency evaluation. Thus, these models treat the production process as a ‘black box’, i.e., they do not take into account how exactly inputs are related to outputs. Various models that came later take care of internal processes of DMU. The existing models of internal processes for parallel sub-units consist of three stages: the first stage calculates the relative weights of sub-units, the second stage calculates the efficiencies of sub-units, and in the third stage efficiencies of sub-units are aggregated as the efficiency of DMU. It is observed that when existing models of internal processes are applied to non-homogeneous parallel sub-units, in the first stage, the weight assigned to the maximum efficient sub-unit is one and to other sub-units is zero. This implies that the efficiency of a DMU is equal to the maximum of efficiencies of its sub-units indicating that the efficiency of a DMU is not sensitive to the efficiencies of sub-units other than the sub-unit with maximum efficiency. This paper proposes a single stage DEA approach where the efficiency of a DMU and its sub-units can be measured simultaneously. The advantage of the proposed approach is that the efficiency of a DMU is sensitive to the changes in the efficiency of its sub-units, and weights of sub-units can be assigned a priori by the decision maker. The development of the proposed approach is inspired from the growing interest in evaluating efficiency of higher education system in India. In the proposed application, states are considered as DMUs and universities, colleges and stand-alone institutions are taken as three non-homogeneous parallel sub-units of DMUs.

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Notes

  1. Referred as input importance variable weight hereafter.

  2. Hereafter state refers to state, union territory and national capital territory.

  3. HEI includes universities, colleges, and stand-alone institutions.

  4. Sub-unit, a part of DMU, has its own production set-up and process. A DMU can consist of several sub-units. Non-homogeneous parallel sub-units: A DMU has similar sub-unit in other DMUs. Inputs and outputs of sub-units of a DMU are independent, i.e. no shared inputs and outputs exist, there is no flow from one sub-unit to another sub-unit, and no separate input or output for DMU exists.

  5. Although Yang et al. (2000) did not use input importance variable weight concept, their model was similar to model (1) and \(\mathop \sum \nolimits _{p=1}^q \mathop \sum \nolimits _{r=1}^{s_p } u_{rp} y_{rp}^k /\mathop \sum \nolimits _{p=1}^q \mathop \sum \nolimits _{i=1}^{m_p } v_{ip} x_{ip}^k \) was used in objective function directly.

  6. This limitation was not observed in research works (Chen et al. 2009; Imanirad et al. 2013) because production systems across sub-units are connected. For example, (i) output of a sub-unit is the input of another sub-unit (Chen et al. 2009), (ii) inputs are shared across sub-units (Imanirad et al. 2013).

  7. Since this analysis is based on 2012–2013 data, therefore Telangana as a separate state is not considered as it was formed on \(2{\mathrm{nd}}\) June 2014 after the division of Andhra Pradesh.

  8. In this situation, efficiency of non-existing \(h{\mathrm{th}}\) sub-unit is considered zero.

  9. These states were part of Uttar Pradesh, Bihar, and Madhya Pradesh respectively before 1999.

  10. Kerala and Puducherry are states of South Zone.

  11. AICTE regulates institutes offering courses of Engineering and Technology, Computer Application, Management, Pharmacy, Hotel Management and Catering, Architecture and Town Planning, and Applied Arts and Crafts.

  12. E.g., transportation by Agarwal et al. (2010), bank by Ray (2007), agriculture by Ray and Ghose (2014), insurance by Tone and Sahoo (2005).

  13. Reserve Bank of India is central bank of Indian banking system. See www.rbi.co.in for details.

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Acknowledgements

The authors wish to express their sincere gratitude to two anonymous reviewers and GE for their valuable comments and suggestions which have significantly improved the quality of the paper.

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    Sanjeet Singh & Prabhat Ranjan

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Singh, S., Ranjan, P. Efficiency analysis of non-homogeneous parallel sub-unit systems for the performance measurement of higher education. Ann Oper Res 269, 641–666 (2018). https://doi.org/10.1007/s10479-017-2586-0

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