System efficiency evaluation of homogeneous parallel production systems: An aggregation approach

Abstract

Existing models, for efficiency evaluation of DMUs with homogeneous parallel production-units, have limitations in the sense that production process of a DMU is compared with the production possibility set of all production-units. Moreover, same set of input-output weights is used to evaluate the efficiency, project inputs-outputs of a DMU and all its production-units. This means, all the production-units of a DMU operate in a similar way in the long run as if they are not separate production-units but one single entity. We propose an aggregation approach to evaluate the efficiency of DMUs with homogeneous parallel production-units. We also introduce Weighted Average Efficiency and System Efficiency. As opposed to the existing methodology, different set of weights are used to evaluate efficiency of different production-units of a DMU. Finally, the proposed methodology has been used to evaluate the efficiency of higher education sector of Bihar, one of the largest states in India.

Keywords:

• Data Envelopment Analysis
• efficiency
• production-unit
• homogeneous parallel system
• higher education

Acknowledgements

The authors wish to express their sincere thanks to the anonymous esteemed reviewers for their insightful comments which have significantly improved the quality of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 The term ‘production-unit’ and ‘sub-unit’ are used interchangeably by researchers; we use the term ‘production-unit’.

2 The first three conditions were mentioned in Castelli et al., (2010).

3 Although, the term ‘homogeneous parallel production systems’ is not used in all of these works, the production system described in these works are homogeneous parallel production systems. In other way ‘DMUs of homogeneous parallel production systems’ are referred as ‘groups of DMUs’ and ‘production-units of homogeneous parallel production systems’ are referred as ‘individual DMUs’ or simply DMUs.

4 Hereafter, referred to as ‘Kao’s parallel model’.

5 GER is the number of students enrolled in higher education for every 100 persons in the age group 18-23.

6 CD is the number of colleges for 1,00,000 persons in the age group 18-23.

7 For ease of notations, uniform number q has been assumed. Practically, j^th $\left(j=\mathrm{1,2},\dots ,n\right)$ DMU can have $q_j$ homogeneous production-units.

8 Model (7) is different from the model, based on input-importance variable weight (Chen et al., 2009; Cook et al., 2000; Du, Chen, et al., 2015; Imanirad et al., 2013), as the weights of respective inputs and outputs are similar across all production-units in the input-importance variable weight model, whereas weights of respective inputs and outputs of different production-units may be different in Model (7).

9 ‘Final system input slack’ is described in next sub-section.

10 ‘Final system output slack’ is described in next sub-section.

11 if the first part $\left({\sum }_{p=1}^q\left(x_{ik}^p-E_p{x}_{ik}^p\right)>0, \forall i\right)$ follows, then at least one $E_p<1$; if the second part $\left({\sum }_{p=1}^q\left(E_p{x}_{ik}^p-{\sum }_{g=1}^t{\lambda }_p^g{x}_i^g\right)>0, \forall i\right)$ follows, then either at least one $E_p<1$ or all $E_p=1$, $[{\sum }_{p=1}^q\left(E_p{x}_{ik}^p-{\sum }_{g=1}^t{\lambda }_p^g{x}_i^g\right)>0, \forall i$, and $E_p=1$ imply that any one efficient production-unit cannot have all its input slacks greater than zero, hence all input slacks must belong to at least two production-units]

12 ${\sum }_{p=1}^q\left({\sum }_{g=1}^t{\lambda }_p^g{y}_r^g-y_{rk}^p\right)>0, \forall r$, ${\sum }_{g=1}^t{\lambda }_p^g{y}_r^g-y_{rk}^p$ is output slack of p^th production-unit. As the primary goal is to measure input-oriented CCR efficiency at production-unit level, a production-unit cannot have all its output slacks greater than zero (radial increase in all outputs of a production-units is not possible), hence all output slacks must belong to at least two production-units.

13 On the other hand, if the uncertainty of the input-output dataset is at DMU level, Fuzzy DEA, Imprecise DEA, or Uncertain DEA models can be used. This type of uncertainty can exist when dataset for DMU is provided.

14 MHRD conducts survey of higher education in India annually and publishes state-wise summary in the form of annual publication ‘All India Survey of Higher Education’. It also provides institutional level data through the government of India online data portal data.gov.in.

15 42% of total public expenditure on higher education is contributed by the union government. 90% of students are enrolled in HEIs regulated by state government.

16 For administrative purpose, a district is divided into several sub-divisions, and a sub-division is divided into several blocks.