Relative performance assessment of academic departments of higher educational institute using DEA with sensitivity analysis

Abstract

This study focuses on evaluating the performance of 15 academic departments of a Government Post Graduate College (GPGC), Gopeshwar, Chamoli, Uttarakhand (India) for the year 2011–2012 using data envelopment analysis (DEA) technique. Further, sensitivity analysis has also done in order to interpret the results more accurately. The study has been done to measure the overall performance and teaching performance using sensitivity analysis.

Keywords

DEA higher educational institute teaching and overall efficiency linear programming performance measurement sensitivity analysis

1. Introduction

Evaluation of performance is an important activity in the field of education as it may help in identifying the areas which need improvements. In the Uttarakhand State of India, there are more than 113 degree colleges, among these more than 99 are government funded degree colleges, while the remaining are government aided and self-financed degree colleges. Presently, in Uttarakhand there are only 23 colleges certified by NAAC (National Assessment and Accreditation Council). Out of these 23 colleges 6 are government aided colleges, one autonomous and 16 are government colleges. Government post graduate college (GPGC), Gopeshwar, Chamoli, Uttarakhand India is the only NAAC-A Grade awarded College in the State of Uttarakhand. This college, the focus of the present study, was established in the year 1966. In this PG college seventeen academic department run UG and PG programmed out of which six departments belong to Science group, one to Commerce and the remaining are of Arts group. Although, teaching is prime activity of this college research activities are also encouraged and promoted. In this study, we consider teaching and overall activities for the efficiency measurement of academic departments. We have considered 15 academic departments to assess the overall performance, teaching performance for the year 2011–2012, using DEA technique with sensitivity analysis. Among 15 departments, 5 are of Science side, one is the Commerce department and 9 are department of Art side.

Table 1
Country wise some relevant studies are conducted on education sector

Country	Literature
United State	Bessent et al. [4], Ahn et al. [55], Breu and
of America	Raab [56] and Bougnol and Dula [30]
United	Beasley [22], Izadi et al. [14] and Jonhes [20]
Kingdom
Australia	Avkiran [35] and Abbott and Doucouliagos [33]
China	Johnes and Li [19]
India	Tyagi et al. [39], Jauhar et al. [44], Ali et
	al. [17, 18], Mogha et al. [47]
Germany	Fandel [13]

There are several methods for measuring the efficiency of the departments of post graduate colleges like parametric methods such as stochastic frontier method, Izadi et al. [14] and non-parametric method such as Data Envelopment Analysis (DEA) Charne et al. [1], Kuah et al. [10], Banket et al. [9], Johnes and Yu [19], Bougnol and Dula [30]. Each method has its merits and demerits. When there is only one input and output handling data then parametric methods is used but in case of several input and output handling data non-parametric methods are applicable Ramanathan [41].

Table 2

Some recent studies (I/P and O/P variables) related to efficiency estimation of academic departments of HEI

Sr. No.	Author’s	Year	Inputs	Outputs
1	Rayeni and Saljooghi [32]	2010	Number of registered students, number of teaching staffs	Number of graduates, number of passed students, the performed research work
2	Chen and Chen [26]	2011	No. Of domestic students, No. of international members, Number of domestic fulltime faculty	Journal articles accepted and published (ESI), Quantity of financial support from the NSC, Research patents, No. of graduates and No. of operating foreign countries
3	Aziz et al. [36]	2012	Academic and non-academic staff, operating expenses	No. of graduates, research grant, total no. of publication
4	Aristovnik [2]	2013	Expenditure per student, Public expenditure per pupil as a % of GDP per capita, Expenditure per student, Total expenditure on education	School enrolment, teacher ratio, labor force education, PISA 2006 average
5	Selim and Bursalioglu [54]	2013	Central government budget appropriations, Own revenue, Project allocations (TUBITAK), Project allocations (Scientific Research Projects) and the total academic	Number of graduate students per academic, Number of post graduate students per academic, Number of doctorate students per academic, Number of publications, Number of employment
6	Alshayea and Battal [7]	2013	Number of students enrolled the number of teachers and staff	The total number of students with Bachelor’s degree and a number of research, use as Output
7	Aziz et al. [37]	2013	Total academic staff, non-academic staff and operating cost	Enrollment of under graduates, enrollment under post graduates, publications and research grants
8	Battal et al. [8]	2013	Two inputs related to education	Two outputs are taken related to education
9	Tomas [42]	2014	Expenses, no. of academic and non-academic staffs	No. of graduates, No. of publications, applied research
10	Yousfat et al. [3]	2015	Registered students, Academic Staffs	Net annual wages, Successful students
11	Jauhar et al. [44]	2016	Academic and non-academic staffs, no. of taught course students, average students qualifications, DOC, no. of research staffs, average research staff qualifications, no. of research students, research grants	No. of graduates from taught courses, average graduates results, graduate rates, graduate employment rate, GHG emission, no. of Ph. D. awards, no. of publications, no. of awards, no. of intellectual activities
12	Barra and Zotti [12]	2016	No. of academic staff, non-academic staff, operating cost on research activities, total amount of financial resources for teaching activities, total enrolled students	No. of Publications, Research funding, Research productivity index, Capacity resources index, no. of graduates, no. of undergraduates
13	Ali et al. [17]	2017	No. of academic staff, DOC, average students qualifications, no. of taught course students, no. of research staffs, average research staff qualifications, no. of research students, total enrolled research students index	No. of graduates from taught courses, average graduates results in percent, Graduates rate in percent; research award index, no. of publications, number of intellectual activity
14	Ali et al. [18]	2017	No. of academic staff, DOC, average students qualifications, no. of taught course students	No. of graduates from taught courses, average graduates results in percent, Graduates rate in percent
15	Mogha et al. [47]	2017	Nnumber of academic staff, umber of non-academic staff	Total enrolled students, total pass students, students placed for jobs, and research index

2. Literature survey

Country wise, selected studies conducted on education sector to measure the efficiency of various colleges, departments, higher education institutes (HEI) and university etc., is given in Table 1. We have also given in tabular form the input output variables that have been used recently in the last 9 years in earlier studies. Studies related to efficiency estimation of the academic departments of higher educational institutes have been discussed in Tables 1 and 2 (see Tables 1 and 2).

Some DEA based studies relevant to this study are given as follows: Puri and Yadav [23], Johan’s [24], Smith et al. [25], Mancebon and Mar Molinero [31], Paul and Paul [38], Korhonen et al. [40], Mogha et al. [43, 45, 46], Cook and Seiford [59], Ahn et al. [57]. Some other studies which are helpful in this study are given as follows: Gupta et al. [16], Mandal [27], Mandal et al. [28], Transtenjik and Donko [58] and Jauhar et al. [50, 51, 52, 53].

This research article is organized as follows: In Section 3, Mathematical form of DEA is given in brief. Institutions selected, DMUs, and description of selected inputs and outputs for performance assessment of the departments for this study is given in Section 4. In Sections 5 and 6, data and computation, choice of models and overall performance assessment of the departments is given. Assessment of teaching performance separately for the departments using sensitivity analysis is given in Section 7 and finally in Section 8, conclusions are given.

3. Mathematical form of DEA

Let us consider $\alpha$ and $\beta$ to be the input (I/P) and output (O/P) and let $\alpha_{i}$ and $\beta_{r}$ be the $i^{\rm th}$ I/P and $r^{\rm th}$ O/P of the DMU. Let the total number of I/Ps and O/Ps be denoted by $m$ and $s$ where $m$ and $s$ both are non-zero and positive. Let there be N DMUs whose efficiencies will be compared. Let us take one of the DMUs, say the $o^{\rm th}$ DMU and maximize its efficiency according to the formula given below. Here the $o^{\rm th}$ DMU is the reference DMU.

The mathematical program now in fractional form is given by

$\displaystyle\textit{Max }e_{o}=\frac{\sum\limits_{r=1}^{s}{v_{ro}\beta_{ro}}}% {\sum\limits_{i=1}^{m}{u_{io}\alpha_{io}}}$

Subject to

$\displaystyle o\leqslant\frac{\sum\limits_{r=1}^{s}{v_{ro}\beta_{rn}}}{\sum% \limits_{i=1}^{m}{u_{io}\alpha_{in}}}\leqslant 1;n=1,2,3,\ldots,o,\ldots,N;$ $\displaystyle\ \ \ r=12,3,\ldots,s;i=1,2,3,\ldots m;$ $\displaystyle\quad u_{io},v_{ro}\geqslant 0;\forall i,r$

where, $e_{0}$ is the efficiency of the $o^{\rm th}$ DMU, $\beta_{ro}$ is the $r^{\rm th}$ output of the $o^{\rm th}$ DMU, and $v_{ro}$ is the weight for the output $\beta_{ro}$ , $\alpha_{io}$ is the $i^{\rm th}$ input of the $o^{\rm th}$ DMU, and $u_{io}$ is the weight for the input $\alpha_{io}$ ; $\beta_{rn}$ and $\alpha_{in}$ are the $r^{\rm th}$ output and $i^{\rm th}$ input, respectively, of the $n^{\rm th}$ DMU, Where, $n=1,2,3,\ldots,o,\ldots,N$ ; note that here $n$ includes $o$ (Ramanathan [41, p. 40]).

General form of CCR (Charnes et al. [6]) DEA models can be written as

$\displaystyle\textit{Max }e_{0}=\sum\limits_{r=1}^{s}{v_{ro}\beta_{ro}}$ $\displaystyle\sum\limits_{i=1}^{m}{u_{io}}\alpha_{io}=1,$ $\displaystyle\text{subject to }\sum\limits_{r=1}^{s}{v_{ro}}\beta_{rn}-\sum% \limits_{i=1}^{m}{u_{io}}\alpha_{in}\leqslant 0,\forall n$ $\displaystyle\quad∼{}u_{io},v_{ro}\geqslant\varepsilon;\forall i,r$

Similarly, we can define a general input minimization CCR DEA model.

The general form of BCC (Banker et al. [9]) DEA model is given by

$\displaystyle\textit{Max }e_{0}=\sum\limits_{r=1}^{s}v_{ro}\beta_{ro}+u_{0o}$ $\displaystyle\text{subject to }\sum\limits_{i=1}^{m}{u_{io}}\alpha_{io}=1,$ $\displaystyle\sum\limits_{r=1}^{s}{v_{ro}}\beta_{rn}-\sum\limits_{i=1}^{m}{u_{% io}}\alpha_{in}+u_{0o}\leqslant 0,\forall n$ $\displaystyle\quad∼{}u_{io},v_{ro}\geqslant\varepsilon;\forall i,r\text{ and }% u_{0o}\text{ is unrestricted}$ $\displaystyle\quad∼{}\text{in }\,{\rm sign}\,.$

The efficiency of all DMUs varies between 0 and 1. If efficiency of a DMU is one then it is efficient, otherwise inefficient.

4. Research design

4.1 Institution selected

Government PG College Gopeshwar, Chamoli, Uttarakhand (India) with description given in Section 1.

4.2 Decision making units (DMUs)

Fifteen Academics departments of GPGC, gopeshwar, chamoli are taken as DMUs. Academic departments have been taken as DMUs in several previous studies (Ali et al. [17, 18]; Jauhar et al. [44]; Tyagi et al. [39]; Beasley [22]; Johnes and Johnes [21]).

4.3 Selection of inputs and outputs for performance assessment of departments

4.3.1 Inputs

4.3.1.1 Number of academic staff

Number of academic staff is requiredto measure the overall performance of the DMUs of an academic institution. Academic staff has been considered as an input parameter by the following researchers: Ali et al. [17, 18]; Jauhar et al. [44]; Tayagi et al. [39]; Kuah and Wong [11]; Johnes and Johnes [21].

4.3.1.2 Number of non-academic staff

This Input is also in the form of human resource and consists of staff that provides services to academic staff and to students. Such staff includes librarian, accountant, clerks, sweepers etc. This input has been used by the following researchers: Jauhar et al. [44]; Tyagi et al. [39]; Avkiran [35].

4.3.1.3 Departmental operating cost (DOC)

The Third input parameter is DOC which is needed to run the department and to manage all types of students and staff activities such as teaching, research and extracurricular activityetc. DOC has been considered as an input parameter by the following researchers Basely [18]; Abbott and Doucouliagos [33]; Tyagi et al. [39]; Jauhar et al. [44]; Ali et al. [17, 18].

4.3.2 Outputs

4.3.2.1 Total enrolled students

In The context of india, higher educational institutes generally have three categories of students: undergraduate (UG), postgraduate (PG) and research scholars. But in Degree colleges, affiliated to a university, like GPGC, which is the subject of this study, some departments have only UG students, some have both UG and PG students and some departments have all the three type of students. Here we take only 15 academic departments which have both UG and PG programs. The study is done for the academic year 2011–2012.

Here we selected the students for UG, PG and Ph.D. programs after normalization on the basis of educational background, number of years/time required for the completion of degree and credits/number of subjects/number of papers, completed for the degree. Using this criteria each UG level student has been counted as 1, Each PG level student has been counted as 1.125 and for the Ph.D. level student, we take Ph.D. scholar index (i.e. total enrolled research students index) due to the scarcity of number of doctoral students enrolled in the above 15 departments. Our aim is to measure the whole contribution of the department in teaching and research that comes out as the output variable “Total enrolled students”, defined as:

Total enrolled students $=$ Number of UG students $+$ 1.125 (Number of PG students) $+$ Ph.D. scholar index.

Total enrolled students as an output has been taken by the following researchers Tyagi et al. [39]; Abbott and doucouliagos [33]; Avkiran [35] and Beasely [22]. Output parameter, “Ph.D. scholar index (i.e. total enrolled research student’s index)”, is included in the output variable total enrolled students in this study and has been used by Ali et al. [17, 18].

4.3.2.2 Progress

In This study there are three academic disciplines: Science, arts and Commerce. All these 15 departments under these disciplines have UG, PG and doctoral students. Combining the two activities teaching and research, we obtained two parameters for each department (i) number of UG and PG students obtaining at least first division (i.e. obtaining marks $\geqslant$ 60%)(ii) Ph.D. (i.e. research) award index. Combining these two parameters we form an output variable known as “Progress”. This was used by Tyagi et al. [39]; as an output variable, Abbott and Doucouliagos [33], used a similar type of output variable EFTS which contains number of postgraduate and graduate degrees received. The “Ph.D. (i.e. research) award index” is used as a research output variable by Ali et al. [17].

Table 3
Descriptive statistics input output data

Characteristic	Inputs			Outputs
	No. of	No. of non-	Dept. operating	Total enrolled	Progress	Research
	academics staff	academics staff	cost (DOC)	students		index
Max	5	20	15000	395.75	107.75	31.8
Min	1	17	150	24.05	2.30	3.2
Average	2.867	17.6	2270	182.963	31.177	15.46
S.D.	2.121	0.707	3323.402	139.247	9.122	1.626

Table 4

Correlation coefficients between inputs and outputs

	Academic	Non-academic	Departmental	Total enrolled	Progress	Research
	staff	staff	operating cost	student		index
Academic staff	1
Non-academic staff	0.649 ${}^{**}$	1
Departmental operating cost	0.450	0.891	1
Total enrolled student	0.039	0.071	0.013	1
Progress	0.431	0.471	0.362	0.339	1
Research index	0.229	0.148	0.067	0.223	0.686 ${}^{**}$	1

${}^{**}$ Correlation is significant at 0.01 (1%) levels (2-tailed).

Table 5

Efficiency score based on overall performance model

Sr. No	Dept. code	Name of dept.	OTE (CRS score)	Peer dept.	Peer count	PTE (VRS score)	Peer dept.	Peer count	S.E.
			CCR model			BCC model
1	D1	Hindi	1	D1	12	1	D1	11	1
2	D3	English	0.721	D1	0	0.721	D1	0	1
3	D4	Geography	1	D4	6	1	D4	4	1
4	D5	History	0.539	D10, D1	0	1	D5	0	0.539
5	D6	Political Science	0.754	D1	0	0.754	D1	0	1
6	D7	Economics	0.499	D4, D1, D10	0	0.504	D1, D10	0	0.991
7	D8	Sociology	0.458	D1, D10	0	0.458	D1, D10	0	1
8	D9	Military Science	0.172	D10, D4, D1	0	0.218	D1, D10	0	0.789
9	D10	Education	1	D10	9	1	D10	8	1
10	D12	Commerce	0.230	D10, D1	0	0.244	D10, D1	0	0.944
11	D16	Physics	0.654	D1, D10	0	0.692	D1, D10	0	0.944
12	D17	Chemistry	0.567	D1, D4	0	0.638	D1, D4	0	0.889
13	D18	Geology	0.497	D1, D10, D4	0	0.506	D10, D4, D1	0	0.982
14	D19	Botany	0.622	D1, D10, D4	0	0.638	D1, D4, D10	0	0.975
15	D20	Zoology	0.907	D10, D1, D4	0	0.953	D10, D1, D4	0	0.951
Average			0.641			0.688			0.934
Standard deviation (S.D.)			0.066			0.033			0.035

4.3.2.3 Research index

Research index includes number of papers in journals and conference/seminar proceedings; number of dissertations taken by the departments; number of conference/seminar attended by the faculty members of the department our aim is to sum up each activity related to research that contributes to the performance of the departments. Here we have not included conferences/seminars organized by the department and number of research projects taken because of unavailability of sufficient data. There are several contradictory opinions among people about the quality of the research work. Based on the general opinion of the academic staff of the college and available research parameters at degree college level we form the “Research Index” as:

Research index $=$ Number of papers of the departments in journals $+$ 0.5 (Number of papers in Conference/seminar for the departments) $+$ 0.6 (Number of dissertations taken by the faculty members of the department) $+$ 0.3 (Number of conference/Seminar attended by the faculty members of the department).

Similar type of output variable research index is taken by the following researcher Tyagi et al. [39].

5. Data and computations

Input and output data has been collected from the GPGC, Gopeshwar, Chamoli Uttarakhand India, NAAC-2014 [15], staff statement register (SSR), and from the examination section of the college for the academic year 2011–2012. DEAP version 2.1 (Coelli 1996) [60], is used for all calculation related to DEA technique.

Input, output data and correlation coefficient between input and output variables are given in Tables 3 and 4.

5.1 Choice of model

CCR and BCC output oriented DEA model has been used for this study (i.e. constant return to scale (CRS) and variable return to scale (VRS) DEA approaches have been used).

6. Overall performance assessments of the departments

In this study for overall performance assessment of the departments, 3 inputs and 3 outputs are taken described in the above Section 6. The analysis has been carried out using both CRS and VRS assumptions with output orientation. The results have been given in the Table 5 (see Table 5). To study the results of Table 5, we see that out of 15 academic departments, only 3 departments (20%), namely, Hindi (D1), Geography (D4) and Education (D10) are technically efficient since there CRS efficiency score is one. All the remaining 12 departments (80%) are less technically efficient as the CRS efficiency score of these department is less than 1. The average of the efficiency score with respect to CRS assumption is 0.641. Eight departments, namely, History (0.539), Economics (0.499), Sociology (0.458), Military science (0.172), Commerce (0.230), Chemistry (0.567), Geology (0.497) and Botany (0.622) have scored lower than the average efficiency score (0.641). Among all the above efficiency scores the lowest efficiency score is calculated 0.172 (17.2%), for the Military science department. Therefore, the overall performance of Military science department is very poor. The Hindi department (D1) is the most technically efficient department since it has maximum number of peer count for other department.

On the basis of peer count, we classify the robustness of the department here Hindi department is highly robust department (peer count $=$ 12) and can be considered as a global leader in terms of OTE, Education department is middle robust department (peer count $=$ 9) and Geography department (peer count $=$ 6) is low robust department on the basis of OTE. Thus all the three departments are count as robust group a high, middle and low respectively in terms of OTE.

Further, from the Table 5 it is also clear that 4 departments out of 15 departments namely, Hindi, Geography, History and Education are VRS efficient as they have VRS efficiency equal to one. All other eleven departments namely English (VRS efficiency score $=$ 0.721), Political Science (0.754), Economics (0.504), Sociology (0.458), Military Science (0.218), Commerce (0.244), Physics (0.692), Chemistry (0.638), Geology (0.506), Botany (0.638), Zoology (0.953) are not efficient or less efficient, as their VRS efficiency score is less than one. Although 4 departments form the VRS efficient frontier, but one of them viz. History (D5) does not seem in the peer department for the inefficient departments. Therefore, it cannot be the role model for the inefficient departments to monitor their performances. From Table 5, it is also clear that some departments which have low CRS score namely, History (0.539) have VRS score equal to1. From this; we can say that this department has potential to convert its input into output efficiently, but its technical efficiency is low due to its injurious size. Hindi department have the highest peer count ( $=$ 12), so it is the most pure technically efficient.

Six (40%) departments, whose department codes are namely, D1, D3, D4, D6, D8 and D10, are scale efficient since there scale efficiency score is equal to one. So, these departments are operating at the most beneficial scale and there is no bad impact of scale size on their performance. Now remaining nine (60%) departments are scale inefficient, since there scale efficiency score is less than unit. These departments are either too large or too small compared to their best possible size. Here History department is the least scale efficient, since its scale efficiency is very low (0.539).

Finally from the Table 5 results, we can say that only three department out of 15 namely, Hindi, Geography and Education are overall technically efficient, pure technically efficient and scale efficient, since there CRS, VRS and scale efficiency (SE) score is one.

In the above section, we assessed the overall performance of the departments. Since all the departments are involved in both teaching and research activities, so we examine these activities separately of each department respectively.

With the help of DEA study we find the information about the efficiencies of DMUs, slacks, and peers, among others. Using sensitivity analysis we test the robustness of these results and to assess the performance of the departments from different criteria (like which department is better for first division students or for “Ph.D. award index” or Dissertation etc.).

Table 6
Comparison of VRS efficiency scores of the teaching performance models

Sr. No.	Dept. code	Dept. name	Model-1		Model-2		Model-3
			VRS score	Peer counts	VRS score	Peer counts	VRS score	Peer counts
1	D1	Hindi	1	11	1	12	0.892	0
2	D3	English	0.725	0	0.725	0	0.138	0
3	D4	Geography	1	5	0.728	0	1.0	6
4	D5	History	1	0	1.0	1	0.095	0
5	D6	Political Science	0.762	0	0.762	0	0.217	0
6	D7	Economics	0.497	0	0.497	0	0.428	0
7	D8	Sociology	0.457	0	0.457	0	0.236	0
8	D9	Military Science	0.227	0	0.103	0	0.220	0
9	D10	Education	1.0	2	0.879	0	1.0	8
10	D12	Commerce	0.061	0	0.061	0	0.021	0
11	D16	Physics	0.377	0	0.348	0	0.211	0
12	D17	Chemistry	0.626	0	0.499	0	0.530	0
13	D18	Geology	0.491	0	0.312	0	0.416	0
14	D19	Botany	0.590	0	0.481	0	0.475	0
15	D20	Zoology	0.595	0	0.490	0	0.469	0
Average			0.627		0.556		0.423
S.D.			0.286		0.361		0.299

7. Performance assessments of departments with sensitivity analysis

DEA is an extreme point technique, because the efficiency frontier is formed by the actual performance of best-performing departments. A direct effect of this characteristic is that errors in measurement can affect DEA results significantly. DEA efficiency is very sensitive to even small errors. DEA is a non-parametric technique; so the hypothetical tests of statistics are impossible to estimate the confidence with which DEA efficiencies are computed. Hence, as with any modeling technique the output generated by DEA should be used only after conducting appropriate sensitivity analysis.

According to DEA technique, it is possible for a department to become efficient if it achieves exceptionally better results in terms of one output but performs below average in terms of other outputs. However, such an unusual department will not be the peer for many inefficient departments. Thus, if a department is initially identified as efficient by DEA, a supplementary sensitivity analysis can be conducted by checking the number of inefficient departments for which it is a peer. If number is high, then the department is genuinely efficient. If number is low, then the efficiency of the departments should always be viewed with caution. Then other evidence for establishing the superiority of its performance is necessary. Another way of testing the stability/robustness of DEA results is conducting the analysis by omitting an input of output and then studying the results (Ramanathan [41, p. 176, 154]). We use these testing methods for our study. Finally, the weakness of DEA is that it is non-parametric technique and therefore hypothesis testing of statistics is very difficult to test the robustness of the DEA results. Therefore, to test the robustness of DEA results (like efficiencies of DMUs, slacks, and peers, among others) and to assess the performance of the departments from different criteria (like which departments is better for first division students or for “Ph.D. award index” or Dissertation etc.), we use sensitivity analysis.

7.1 Assessment of teaching performance for the departments using sensitivity analysis

For the assessment of teaching performance models, we develop three Models: Model-1, Model-2, and Model-3. At this moment, we give attention only to the teaching output. The result is presented in Table 6.

7.1.1 Model-1

Here in this Model-1 “academic and non-academic staff” has been taken as input variables and“ESTUGPG” and “FSTUGPG” are taken as outputs. “ESTUGPG” represents all the enrolled students of UG and PG in the departments. “FSTUGPG” represents all the first division students of UG and PG in the departments. Taking this combination it is clear that staff contributes to produce the first division students at the both level of UG and PG, which are possibly placed for different jobs and attract the students to their departments for study.

For Model-1, the average efficiency score is 0.627. Four departments, namely, Hindi, Geography, History and Education turned out to be efficient, since their efficiency score is one. Remaining eleven departments are inefficient. Two departments, namely, English (0.725) and Political science (0.762) from the above 11 departments have the more efficiency score under average efficiency score (0.627). Therefore we may consider the performance of these departments satisfactory, but cannot include in the group of efficient departments. The lowest efficiency score is 0.061; So Commerce department is less efficient in the entire 15 departments.

7.1.2 Model-2

Here in this Model-2 “academic and non-academic staff” have taken as input variables same as in Model-1, but we omit the one output variable “FSTUGPG” of Model-1 and take only “ESTUGPG” as output variable. By doing this, we want to examine which department is sensitive to this output and here we measure the performance of each department only for students’ enrollment in the department. Here 7 departments out of 15, namely, Hindi, English, History, Political Science, Economics, Sociology and Commerce have the same efficiency score as in Model-1. Eight departments have score lower for Model-2 than Model-1. This shows that omission of the output “FSTUGPG” affects these departments. We conclude that these 8 departments are better for the output “FSTUGPG” than for another output “ESTUGPG”.

Every department has its own specific quality. For example, in our study, the Arts department namely, Hindi and Geography have more teaching load at UG level than others because students are take Hindi as a subject due to combination requirement of B.Ed. and being a language subject also, while and Geography subject is taken by the students since it is a practical subject and students get the good marks and practical knowledge of the subject. All the science departments, at UG level, namely, Chemistry, Physics, Geology, Zoology and Botany have equal teaching load since in these departments seats are equally distributed at UG level and mostly at PG level. At the same time, Commerce department has no students from other departments and no contribution for the first division students individually. The reason is that this Commerce department has not included in science and art departments. It is separate department in itself. Since in this study of the year 2011–2012, there were no fixed criteria of the seats in Arts departments’. So it is not possible to allocate equal distribution of students to each department. This may be the reason why only few departments have scored 1 in Model-1 and Model-2.

7.1.3 Model-3

The main purpose of each department of Degree College is to produce the highest percentage degree awarded students in every year. So in this Model-3, we take only the output variable “FSTUGPG”. But input are same as in Model-1 and Model-2. Here “ESTUGPG” output is omitted used in Model-1 to make sensitivity analysis. From the Model-3 results, it is clear that only two departments, namely, Geography and Education are surviving the well for highest percentage (i.e. at least first division) and possibly placed for different jobs. All the remaining departments are not well for the highest percentage activity.

Table 7
Karl Pearson’s ( $r$ ) and Spearmen’s rank ( $\rho$ ) correlation coefficients among teaching performance models

	Model-1 ( $r$ , $\rho$ )	Model-2 ( $r$ , $\rho$ )	Model-3 ( $r$ , $\rho$ )
Model-1	1, 1
Model-2	0.958 ${}^{**}$ , 0.961	1, 1
Model-3	0.629 ${}^{*}$ , 0.473	0.464, 0.356	1, 1

${}^{**}$ Correlation is significant at 0.05 (5%) levels (2-tailed). ${}^{*}$ Correlation is significant at 0.01 (1%) levels (2-tailed).

Five departments, namely, Hindi (0.892), Economics (0.428), Chemistry (0.530), Botany (0.475) and Zoology (0.469) have scored above the average efficiency scored (0.423). Therefore the performance of these departments may be assumed satisfactory but not good and cannot be considered in the group of well performing departments. The lowest efficiency score is 0.021. So the performance of commerce department is very poor.

Some environmental and departmental factors may be responsible for such results. For example, in the department of Geography, from last 17 years the number of faculty has remained almost filled as required in the department. The other reason is that Geography and Education both are practical subjects. To gain practical knowledge and obtain good marks, these subjects are taken by the Arts discipline students. So the demand of the students for these subjects increased faster than the other disciplines (i.e. Science and Commerce) at UG and PG level. Thus leaving out such other external factors, results seem to be accurate according to data.

To test the robustness and stability among these three models Karle Pearson’s and Spearmen’s rank correlation coefficients are calculated. This is in the range of 0.356–0.961. The higher values of the coefficient represents that results are robust for these models (See Table 7).

8. Conclusions

In this study performance of the academic departments has been evaluated of the higher educational institute namely Government PG college Gopeshwar, Chamoli, Uttarakhand, India, using DEA models by taking different combinations of the used inputs and outputs. The main objective of this study is to analyze activity-wise performance assessment of the departments. It means that in this study we want to know that which departments are good performers for specific activity (like teaching). So for this, here we did two assessments, namely, overall performance assessment and teaching performance assessment by using three models. Sensitivity analysis (or post optimal analysis) is done in these models by changing the inputs and outputs.

Finally, we are giving below some concluding remarks of this study for the departments.

•

For overall performance assessment, only three departments out of 15 namely, Hindi, Geography and Education are overall technically efficient, pure technically efficient and scale efficient, since there CRS, VRS and scale efficiency (SE) score are reported one. These departments are good examples to be followed by the inefficient departments to monitor and improve their performance.

•

From the results of Model-1to Model-3, it is clear that Model-1 has the highest mean (0.627) and lowest standard deviation (0.286) than other teaching performance Models. Therefore, this indicates that the teaching performance is satisfactory when all activities related to teaching are used in to the Output variables “ESTUGPG” and “FSTUGPG”. The least mean (0.423) and the high standard deviation (0.299) are calculated for Model-3 for teaching performance assessment. This indicates that some improvements are needed in the field of obtaining the good academic marks (at least First divisions) by the students.

•

Some of the departments are not utilizing effectively their staff (both academic and non-academic) for some specific activities related to teaching and research.

Thus our study provides information about each activity of the departments and policy makers can use suggested improvements and deductions to improve the performance in different areas.

Footnotes

Acknowledgments

The first author is highly thankful to Dr. Awasthi (Assistant Professor) Government PG College Gopeshwar, Chamoli, Uttarakhand, India, who helped me in this study for collection of data and some theoretical discussion related to this research article.

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Relative performance assessment of academic departments of higher educational institute using DEA with sensitivity analysis

Abstract

Keywords

1. Introduction

Table 1 Country wise some relevant studies are conducted on education sector

3. Mathematical form of DEA

4. Research design

4.1 Institution selected

4.2 Decision making units (DMUs)

4.3 Selection of inputs and outputs for performance assessment of departments

4.3.1 Inputs

4.3.1.1 Number of academic staff

4.3.1.2 Number of non-academic staff

4.3.1.3 Departmental operating cost (DOC)

4.3.2 Outputs

4.3.2.1 Total enrolled students

4.3.2.2 Progress

Table 3 Descriptive statistics input output data

4.3.2.3 Research index

5.1 Choice of model

6. Overall performance assessments of the departments

Table 6 Comparison of VRS efficiency scores of the teaching performance models

7.1 Assessment of teaching performance for the departments using sensitivity analysis

7.1.1 Model-1

7.1.2 Model-2

7.1.3 Model-3

Table 7 Karl Pearson’s ( r ) and Spearmen’s rank ( ρ ) correlation coefficients among teaching performance models

Footnotes

Acknowledgments

References

Table 1
Country wise some relevant studies are conducted on education sector

Table 3
Descriptive statistics input output data

Table 6
Comparison of VRS efficiency scores of the teaching performance models

Table 7
Karl Pearson’s ( $r$ ) and Spearmen’s rank ( $\rho$ ) correlation coefficients among teaching performance models