Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 3s (2025) 732 https://internationalpubls.com Measurement of Super Efficiency for Management Colleges in India: A Case Study Ashok R1*, V. Rajagopalan2, Dr. R. Ramakrishna3, Raju Nellutla4 1Research Scholar, Department of Statistics, Annamalai University, Tamilnadu, India. Email: ashokpts@gmail.com 2Professor, Department of Statistics, Annamalai University, Tamilnadu, India. 3Professor, Department of Mathematics, Vidya Jyothi Institute of Technology, CB Post, Aziznagar, Hyderabad, Telangana, India. Email: ramakrishna@vjit.ac.in 4Associate Professor, Department of Mathematics & Statistics, Guru Nanak Institutions Technical Campus (A), Telangana *Correspondence Author: Ashok R, Email: ashokpts@gmail.com Article History: Received: 20-09-2024 Revised: 24-10-2024 Accepted: 30-11-2024 Abstract: Objectives: The objective of this study is to measure the technical efficiency of 20 management colleges listed in the National Institutional Ranking Framework (NIRF) for the academic years 2019, 2020, 2021, and 2022. The analysis evaluates how efficiently these institutions transform multiple inputs (e.g., student strength, faculty- student ratio) into outputs (e.g., research output, graduation outcomes) using Data Envelopment Analysis (DEA) models. Methods: Data Envelopment Analysis (DEA) was employed using the CCR (Charnes, Cooper, and Rhodes) and BCC (Banker, Charnes, and Cooper) models. Inputs considered were 'Student Strength Including Ph.D. Students (SS)', 'Faculty-Student Ratio (FSR)', 'Faculty with PhD and Experience (FQE)', and 'Financial Resources and their Utilization (FRU)', while outputs were Research and Professional Practice (RP), Graduation Outcomes (GO), and Peer Perception (PR). The analysis calculated technical efficiency (under the assumption of Output orientation of Constant Returns to Scale), pure technical efficiency (under the assumption Output orientation of Variable Returns to Scale) and Super efficiency (under the assumption of CRS). Findings: The findings show that out of the 20 management colleges analyzed, 8 colleges consistently demonstrated technical efficiency scores across all years under the CCR model. In contrast, 12 institutions exhibited inefficiencies in resource utilization, with efficiency scores below unity in at least two years. The top-performing institution achieved a super-efficiency score of 1.454 in overall four years average, indicating its superior ability to utilize inputs compared to peers. The study also found a slight year- on-year improvement in efficiency for several institutions, Novelty: This study is unique in applying DEA models to four years of NIRF data, allowing for a robust comparative assessment of efficiency across multiple time frames. By identifying specific areas where colleges underperform in resource utilization, the study offers actionable insights for improving operational efficiency in higher education. Keywords:BCC Model, CCR Model, CRS, NIRF, Technical efficiency, VRS mailto:ashokpts@gmail.com mailto:ramakrishna@vjit.ac.in mailto:ashokpts@gmail.com Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 3s (2025) 733 https://internationalpubls.com 1. Introduction In recent years, the Indian higher education sector has undergone substantial changes, with a growing focus on enhancing institutional effectiveness, openness, and responsibility. Assessing higher education institutions, especially management schools, are vital for identifying areas of efficiency and potential improvement. Data Envelopment Analysis (DEA), a non-parametric method that evaluates the comparative efficiency of decision-making units (DMUs) by analysing inputs and outputs, has emerged as a valuable tool for such assessment. Within the competitive and resource- constrained environment of Indian management schools, the notion of super-efficiency in DEA has gained traction. This approach expands on traditional DEA models by allowing for the ranking of already efficient units, thus providing a more nuanced understanding of institutional performance beyond simple efficient or inefficient classifications. Super-efficiency DEA models offer deeper insights into how management schools can enhance resource allocation, teaching methods, and research productivity. Management schools in India play a crucial role in producing qualified professionals for the business and entrepreneurial sectors. However, the rapid growth of educational institutions has resulted in performance disparities, with a few institutions achieving global recognition while others struggle to meet basic standards. To promote sustainable development, it is essential to implement robust evaluation tools like DEA that can thoroughly assess both quantitative and qualitative aspects of educational performance. In response to this need, the Indian government introduced the National Institutional Ranking Framework (NIRF), which aims to provide an objective ranking of educational institutions based on multiple criteria. While NIRF is a valuable tool, it does not fully address operational inefficiencies or the specific contextual challenges faced by management schools. Integrating DEA with super-efficiency models helps address this gap by identifying not only how effectively resources are utilized but also how top-performing institutions can serve as benchmarks for others, assessed the efficiency of Indian universities but did not consider super-efficiency, limiting the ability to differentiate among top performers. By incorporating super- efficiency, this study offers a more detailed ranking of the top 20 NIRF-ranked management schools. While studies like[1], [2] applied DEA to engineering and undergraduate departments, respectively, focusing on technical and resource efficiency, they lacked a longitudinal approach. This study bridges that gap by analyzing four years of NIRF data, offering a more comprehensive evaluation of performance over time. Furthermore, peer perception a critical factor in higher education rankings has been incorporated as an output variable, addressing limitations in studies suchas[3]is focused on evaluating the technical efficiency of the Indian higher education sector using the Data Envelopment Analysis (DEA) method.which focused primarily on technical efficiency without accounting for this important metric. An innovative framework for evaluating the performance of Indian Premier League (IPL) cricket teams using Data Envelopment Analysis (DEA)[4]. The study aims to provide insights into how effectively each team converts their resources into performance outcomes, thereby identifying areas for improvement and strategic development. The technical efficiency of agricultural decision-making entities in Telangana State using a Data Envelopment Analysis framework,[5]aims to evaluate the efficiency of various farming units in utilizing resources to achieve optimal agricultural output.The evaluation of technical efficiency in higher education institutions (HEIs) is increasingly important for optimizing resource use and improving educational outcomes, contribute Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 3s (2025) 734 https://internationalpubls.com to this discourse in their study, "Technical Efficiency of Universities in Telangana State through Data Envelopment Analysis (DEA) Approach," which assesses the efficiency of universities in Telangana, India. 2. Methodology The Data Envelopment Analysis is mostly "Data oriented," with a mathematical approach used to evaluate the performance of a group of patrician bodies known as decision making entities, which translate many inputs into multiple outputs. The CCR DEA model, introduced in 1978 by Charnes,Cooper, and Rhodes, has played a significant role in the field of DEA by providing a standardized method to assess the technical efficiency of Decision Making Units (DMU). Suppose there are n number of DMU’s D1, D2,…Dn , i=1,2,…n is to be evaluated by m inputs ( j=1,2…m) and s outputs ( r=1,2,…s). m Inputs s Outputs DMU 1 2 .. j .. m 1 2 .. r .. s 1 X11 X12 .. X1j .. X1m y11 y12 .. y1r .. y1s 2 X21 X22 .. X2j .. X2m y21 y22 .. y2r .. y2s : : : : : i Xi1 Xi2 .. Xij .. Xim yi1 yi2 .. yir .. yis : : : : n Xn1 Xn1 .. Xnj .. Xnm yn1 yn2 .. ynr .. yns Where Matrix X is an dimension of (n x m) and Matrix Y is an dimension of (n x s) matrix. By the CCR model, we calculate the efficiency score of the th DMUeo is eO ................................................................................................................................................................... ( 2.1) …………………………………..(2.2) Where xij is the amount of jthinput belongs to ithDMU, yir is the amount of rth output corresponding ith DMU. In the education sector, we used to calculate the performance of the colleges can see by the best performance in terms of no of students passed, no of students placed and no of students went for higher education. First, some formal relationship between inputs and outputs exists and a ‘‘best performance’’ can be identified by comparing different units transforming in to inputs to output; are the weights corresponding to be CCR efficient if eo = 1, otherwise DMU is inefficient. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 3s (2025) 735 https://internationalpubls.com 2.1. CCR Model: The CCR (Charnes, Cooper, and Rhodes) model is a foundational approach in Data Envelopment Analysis (DEA), a performance measurement technique used to evaluate the efficiency of decision-making units (DMUs) like businesses, schools, or hospitals. We have two approaches input and output orientation, the former minimizes inputs for a given output level, while the latter maximizes outputs for a given input level. 2.1.1. Input Orientated CCR Model: and S.T: = 1 …………………………………(2.3) 2.1.2. Output Orientated CCR Model: eO o = 1,2,….n and S.T: = 1 ………………………………..(2.4) The technical efficiency of the DMU for o = 1,2,….n. A DMU was considered efficient if its technical efficiency score, , was equal to 1; otherwise, it was considered technically inefficient. 2.2. The BCC Model The pure technical efficiency of DMUs is calculated by the input-oriented BCC model. By solving the linear programming problem in its enveloped form: Min eBS.T: = ; ; ; e ……… ………….(2.5) …..………………………………………………………………………. (2.6) Dual multiplier form of the linear programming problem (BCC) is expressed as Maximize = :S.T: : , ……(2.7) The CCR model operates under Constant Returns to Scale, whereas the BCC model operates under Variable Returns to Scale. The efficiency score in the CCR model is known as Overall Technical Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 3s (2025) 736 https://internationalpubls.com Efficiency or Technical Efficiency Score. A DMU is deemed efficient if = 1 and the corresponding slacks are zero. In the VRS model, the efficiency score is referred to as Pure Technical Efficiency score. The Scale efficiency refers to the ability of a decision making unit to operate at an optimal scale or size. In other words, scale efficiency measures the extent to which a DMU is able to achieve maximum output with its given input level. Scale efficiency (SE ) = The BCC model optimal solution is presented by . Where and represents maximal Pure Technical Efficiency (PTE), peer weight, input excesses and output short fall respectively. 2.3. Radial Super-Efficiency Model To address this, Andersen and Petersen proposed a super-efficiency model that allows the score of an efficient unit to exceed 100% by removing that unit from the reference set The vector form of this model is Super Radial: , Sub.To: Where all components of the are constrained to be non negative, is the usual non- Archimedean element and e is a row vector with unity for all elements. We refer equation as a “Radial Supper-Efficiency” model and note that the vectors are omitted from the expression on the right in the constraints.This super-efficiency approach has been applied in several studies, including evaluations of university department performance and bank efficiency. 2.4 Data Consideration We applied CCR and BCC models of DEA to calculate the technical and pure efficiency of Indian management colleges using NIRF data from 2019 to 2022. The study used inputs and outputs based on secondary data collected from the NIRF website. This study assesses the technical efficiency of management institutions using inputs for teaching resources and outputs like graduation outcomes, placements, median salary, further education, research quality, and peer perception. Table 2. Definitions and Measurement of Input and Output Variables Variable and Definition Inputs: Outputs: Student Strength Including PhD Students (SS) Combined metric for Publications (PU) Faculty Student Ratio (FSR) Footprint of Projects, Professional Practice and Executive Development Programs (FPPP) Combined metric for Faculty with PhD and Experience (FQE) Quality Publications (QP) Combined metric for Placement and Higher Studies Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 3s (2025) 737 https://internationalpubls.com (GPH) Financial resources and their utilization(FRU) Metric for University Examinations (GUE) Median Salary (GMS)& Peer Perception ( PR ) 2.5. Calculation of Technical, Pure and Super Efficiency: The assessment of technical, pure, and super efficiency was performed using Data Envelopment Analysis (DEA) models, specifically the CCR (Constant Returns to Scale) and BCC (Variable Returns to Scale) models. Additionally, the Radial Super Efficiency model was employed to provide a comprehensive evaluation of the performance of management college 2.6 Selection of DMU’s Table 3 The 20 selected Indian management colleges with DMU’s DMU Name of the College DMU Name of the College D1 IIM Ahmedabad D11 IIM Tiruchirappalli D2 IIM Bangalore D12 IIM Udaipur D3 IIM Calcutta D13 IIT Bombay D4 IIM Indore D14 IIT Delhi D5 IIM Kozhikode D15 IIT Kanpur D6 IIM Lucknow D16 IIT Kharagpur D7 IIM Raipur D17 IITRoorkee D8 IIM Ranchi D18 Management Development Institute D9 IIMRohtak D19 S. P. Jain Institute of Management D10 IIM Tiruchirappalli D20 Symbiosis Institute of Business Management 3. Results and Discussion Table 4.T.E, P.T.E& Supper Efficiency of 20 selected Indian management colleges (2019&2020) Year 2019 Year 2020 DM U NIRF Super Efficienc y NIRF Super Efficienc y Sco Ra TE RT Ref PT TE Ra Sco Ra TE RT Ref PT TE Ra Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 3s (2025) 738 https://internationalpubls.com re nk S eren ces E nk re nk S ere nce s E nk D1 80. 2 1 CR 0 1 1. 13 82. 1 1 CR 0 1 1. 7 61 S 04 75 S 15 D2 81. 1 1 CR 0 1 1. 8 81. 2 1 CR 0 1 1. 10 34 S 19 32 S 11 D3 79. 3 1 CR 0 1 1. 15 80. 3 1 CR 0 1 1. 5 05 S 02 39 S 18 D4 67. 5 0. DR 4 1 0. 19 69. 7 0. DR 5 0.9 0. 19 01 88 S 88 04 9 S 3 9 D5 64. 8 1 CR 0 1 1. 14 69. 6 1 CR 0 1 1. 12 82 S 02 96 S 09 D6 67. 4 0. DR 4 1 0. 18 73. 4 0. DR 6 0.9 0. 16 29 88 S 89 85 93 S 4 94 D7 53. 19 0. DR 4 1 0. 16 56. 19 1 CR 0 1 1. 11 86 95 S 95 12 S 09 D8 51. 28 1 CR 0 1 1. 12 55. 20 0. DR 3 1 0. 13 02 S 05 97 99 S 99 D9 53. 23 1 CR 0 1 1. 10 55. 21 1 CR 0 1 1. 4 11 S 08 91 S 19 D1 59. 14 1 CR 0 1 1. 9 60. 15 1 CR 0 1 1. 9 0 15 S 09 79 S 12 D1 60. 13 1 CR 0 1 1. 11 59. 17 0. DR 5 0.8 0. 20 1 79 S 06 57 83 S 8 83 D1 62. 10 1 CR 0 1 2. 1 65. 11 0. DR 4 1 0. 15 2 74 S 01 76 93 S 94 D1 62. 9 1 CR 0 1 1. 3 67. 8 1 CR 0 1 1. 1 3 89 S 45 19 S 76 D1 53. 22 1 CR 0 1 1. 2 60. 16 1 CR 0 1 1. 8 4 37 S 66 53 S 14 D1 66. 6 1 CR 0 1 1. 4 70. 5 1 CR 0 1 1. 6 5 64 S 44 43 S 16 D1 62. 11 1 CR 0 1 1. 7 62. 12 1 CR 0 1 1. 3 6 11 S 24 87 S 33 Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 3s (2025) 739 https://internationalpubls.com D1 7 61. 89 12 0. 89 DR S 3 1 0. 89 17 65. 95 10 0. 92 DR S 4 1 0. 92 18 D1 8 55. 67 16 1 CR S 0 1 1. 42 5 56. 93 18 1 CR S 0 1 1. 51 2 D1 9 53. 56 20 1 CR S 0 1 1. 26 6 55. 82 22 0. 97 DR S 4 1 0. 97 14 D2 0 65. 33 7 0. 86 DR S 4 1 0. 86 20 67. 11 9 0. 93 DR S 4 1 0. 93 17 The results in Table 4 illustrate the Technical Efficiency (TE), Pure Technical Efficiency (PTE), and Super Efficiency (SE) scores for 20 management colleges across 2019 and 2020. Here's a summary of the findings: 2019 Analysis: Out of the 20 colleges, 15 were technically efficient, while the remaining 5 were inefficient, indicating that the efficient colleges had an optimal ratio of inputs to outputs. Super Efficiency (SE) analysis further differentiated the 15 efficient colleges. Among them, college D12 achieved the highest ranking with an SE-TE score of 2.01. This score suggests that D12 had an output level exceeding 100% of what is considered efficient, showing a substantial excess in performance compared to its peers. The remaining efficient colleges were ranked based on their Supper efficiency scores in descending order. 2020 Analysis: The number of technically inefficient colleges increased to 8, leaving 12 colleges as technically efficient. In the Super Efficiency ranking for 2020, college D13 took the top spot, indicating the highest level of output relative to its peers among the efficient colleges. These findings suggest a shift in efficiency dynamics between 2019 and 2020, with an increase in the number of inefficient colleges. Super Efficiency analysis helped to rank the efficient colleges more precisely by identifying those that exceeded the benchmark efficiency levels. Table 5T.E, P.T.E & Supper Efficiency of 20 selected Indian management colleges (2021 & 2022) Year 2021 Year 2022 Super D NIRF M Efficienc y NIRF Super Efficiency U Ref P Ref Sco Ra T RT eren T TE Ra Sc Ra T RT ere PT TE Ran re nk E S ces E nk ore nk E S nce E k s D1 83. 69 1 1 CR S 0 1 1.0 3 10 83. 35 1 1 C RS 3 1 1 10 Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 3s (2025) 740 https://internationalpubls.com D2 83. 48 2 1 CR S 0 1 1.1 48 7 82. 62 2 1 C RS 0 1 1.0 9 6 D3 80. 04 3 1 CR S 0 1 1.0 71 8 78. 64 3 1 C RS 0 1 1.1 3 5 D4 71. 1 6 0. 89 DR S 5 1 0.8 94 18 70. 66 7 0. 81 D RS 3 1 0.8 1 18 D5 73. 34 4 1 CR S 0 1 1.0 63 9 74. 74 5 0. 96 D RS 3 1 0.9 6 12 D6 71. 02 7 0. 98 DR S 4 1 0.9 8 11 74. 55 6 0. 9 D RS 3 1 0.9 15 D7 62. 12 15 0. 87 DR S 3 1 0.8 7 19 63. 57 14 0. 78 D RS 2 1 0.7 8 19 D8 58. 26 21 0. 96 DR S 3 1 0.9 62 12 62. 33 15 0. 98 D RS 3 1 0.9 8 11 D9 55. 4 28 1 CR S 0 1 1.4 72 2 62. 2 16 0. 91 D RS 3 1 0.9 1 14 D1 0 61. 1 17 0. 96 DR S 3 1 0.9 62 13 61. 88 18 1 C RS 0 1 1.0 3 8 D1 1 60. 94 18 0. 79 DR S 3 1 0.7 89 20 59. 28 22 0. 73 D RS 2 1 0.7 3 20 D1 2 68. 08 10 0. 91 DR S 2 1 0.9 12 16 61. 2 20 1 C RS 0 1 1.5 2 3 D1 3 72. 15 5 1 CR S 0 1 1.4 57 4 66. 24 11 1 C RS 0 1 1.0 3 9 D1 4 61. 31 16 1 CR S 0 1 1.4 97 1 75. 1 4 1 C RS 0 1 1.5 2 4 D1 5 69. 5 9 1 CR S 0 1 1.1 97 6 65. 15 12 1 C RS 0 1 1.7 7 1 D1 6 63. 79 14 1 CR S 0 1 1.4 69 3 61. 76 19 1 C RS 0 1 1.7 2 D1 7 67. 59 11 0. 96 DR S 3 1 0.9 61 14 64. 7 13 0. 88 D RS 2 1 0.8 8 16 D1 8 58. 73 19 1 CR S 0 1 1.2 92 5 59. 51 21 1 C RS 0 1 1.0 4 7 D1 58. 20 0. DR 4 1 0.9 15 61. 17 0. D 4 1 0.9 13 Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 3s (2025) 741 https://internationalpubls.com 9 64 94 S 45 97 93 RS 3 D2 0 69. 93 8 0. 9 DR S 4 1 0.9 17 69. 67 8 0. 84 D RS 3 1 0.8 4 17 Table 5 presents the Technical Efficiency (TE), Pure Technical Efficiency (PTE), and Super Efficiency (SE) scores for the years 2020 and 2021. Here is a summary of the results: For the year 2020:Ten DMUs were technically efficient, achieving a TE score of 1, indicating their position on the efficiency frontier. In contrast, DMUs D1, D4, D5, D6, D7, D8, D9, D11, D17, D19, and D20 were technically inefficient, with TE scores below 1, falling short of the efficiency frontier. According to the BCC Model, all DMUs were technically efficient, with PTE scores of 1. To rank these DMUs, Super Efficiency scores were used, with the highest score ranked first. The next highest ranked DMU was D1, which had an NIRF score of 1. Under the CCR model, D1's TE score was also 1, confirming its technical efficiency. Its Super Efficiency score of 1.03044 placed it 10th among the top 20 management colleges. The top-ranked DMU was D14, with a Super Efficiency score of 1.497, despite being ranked 16th in the NIRF rankings. For the year 2021: There was an equal split, with ten DMUs being technically efficient and ten inefficient. when ranked by Super Efficiency scores, D15 took the top spot with a score of 1.77, while it was ranked 9th in the NIRF rankings.These findings provide insights into the performance and ranking discrepancies between the Super Efficiency scores and NIRF rankings, indicating opportunities for enhancing efficiency among the management colleges. Table 6 Overall Technical and Scale Efficiency of top Management colleges in India D M U Overall Technical Efficiency Overall Scale Efficiency Overrall Supper Efficiency 20 19 20 20 20 21 20 22 Aver age TE 20 19 20 20 20 21 20 22 A ve ra ge T E 20 19 20 20 2021 202 2 Ave rage Ran king D1 1 1 1 1 1 1 1 1 1 1 1.0 4 1.1 5 1.03 1 1.06 10 D2 1 1 1 1 1 1 1 1 1 1 1.1 9 1.1 1 1.14 8 1.09 1.14 8 D3 1 1 1 1 1 1 1 1 1 1 1.0 2 1.1 8 1.07 1 1.13 1.10 9 D4 0. 88 0. 9 0.8 9 0.8 1 0.87 0. 88 0. 97 0. 89 0. 81 0. 89 0.8 8 0.9 0.89 4 0.81 0.87 19 Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 3s (2025) 742 https://internationalpubls.com D5 1 1 1 0.9 6 0.99 1 1 1 0. 96 0. 99 1.0 2 1.0 9 1.06 3 0.96 1.03 12 D6 0. 88 0. 93 0.9 8 0.9 0.92 0. 88 0. 99 0. 98 0. 9 0. 94 0.8 9 0.9 4 0.98 0.9 0.93 15 D7 0. 95 1 0.8 7 0.7 8 0.9 0. 95 1 0. 87 0. 78 0. 9 0.9 5 1.0 9 0.87 0.78 0.92 16 D8 1 0. 99 0.9 6 0.9 8 0.98 1 0. 99 0. 96 0. 98 0. 98 1.0 5 0.9 9 0.96 2 0.98 1.00 14 D9 1 1 1 0.9 1 0.98 1 1 1 0. 91 0. 98 1.0 8 1.1 9 1.47 2 0.91 1.16 7 D1 0 1 1 0.9 6 1 0.99 1 1 0. 96 1 0. 99 1.0 9 1.1 2 0.96 2 1.03 1.05 11 D1 1 1 0. 83 0.7 9 0.7 3 0.84 1 0. 94 0. 79 0. 73 0. 87 1.0 6 0.8 3 0.78 9 0.73 0.85 20 D1 2 1 0. 93 0.9 1 1 0.96 1 0. 93 0. 91 1 0. 96 2.0 1 0.9 4 0.91 2 1.52 1.35 5 D1 3 1 1 1 1 1 1 1 1 1 1 1.4 5 1.7 6 1.45 7 1.03 1.42 3 D1 4 1 1 1 1 1 1 1 1 1 1 1.6 6 1.1 4 1.49 7 1.52 1.45 1 D1 5 1 1 1 1 1 1 1 1 1 1 1.4 4 1.1 6 1.19 7 1.77 1.39 4 D1 6 1 1 1 1 1 1 1 1 1 1 1.2 4 1.3 3 1.46 9 1.7 1.44 2 D1 7 0. 89 0. 92 0.9 6 0.8 8 0.91 0. 89 0. 92 0. 96 0. 88 0. 91 0.8 9 0.9 2 0.96 1 0.88 0.91 17 D1 8 1 1 1 1 1 1 1 1 1 1 1.4 2 1.5 1 1.29 2 1.04 1.32 6 D1 9 1 0. 97 0.9 4 0.9 3 0.96 1 0. 97 0. 94 0. 93 0. 96 1.2 6 0.9 7 0.94 5 0.93 1.03 13 D2 0 0. 86 0. 93 0.9 0.8 4 0.88 0. 86 0. 93 0. 9 0. 84 0. 88 0.8 6 0.9 3 0.9 0.84 0.88 18 Me an 0. 97 0. 97 0.9 6 0.9 4 0.96 0. 97 0. 98 0. 96 0. 94 0. 96 1.1 8 1.1 1 1.09 1.08 1.11 Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 3s (2025) 743 https://internationalpubls.com Table 6 shows the Average TE, which indicates the colleges' ability to optimally utilize their resources over the four years. An average TE of 1 reflects that the college has maintained perfect technical efficiency, and the Average SE indicates how well the colleges have managed their operational scale over the four-year period. An Average SE of 1 suggests optimal scale efficiency. Here, D1, D2, D3, D13, D14, D15, D16, and D18 have maintained an average technical and scale efficiency score of 1 over the four years, reflecting consistently optimal performance. Also it shows the overall ranking of the top Indian management colleges ranking by the supper efficiency models. Few colleges were top ranking with the low ranking in NIRF ranking system. For the years 2019, 2020, 2021, and 2022, we computed the Technical Efficiency (TE), Pure Technical Efficiency (PTE), and Super Efficiency for 20 management colleges. The results are summarized as follows: 2019: Out of 20 Decision Making Units (DMUs), five were found to be technically inefficient, while fifteen were technically efficient under the CCR Model. However, under the BCC Model, all DMUs were technically efficient, with PTE scores equal to unity. Super efficiency scores were used to rank the DMUs, which differed from NIRF rankings. For instance, D1 ranked second in NIRF but was 13th in super efficiency ranking, while DMU D2 ranked first in NIRF but only 8th in terms of super efficiency. [14] Found that out of DMU D61, D3- IITB, D4-IIT Delhi and D5- IIT Kharagpur were super-efficient and consistent during 2016-18. 2020: In 2020, twelve of the 20 DMUs were technically efficient under the CCR Model, indicating that these 12 institutions maximized their output with the given inputs. For rankings, DMU D1, which ranked first in NIRF, was ranked 7th by super efficiency, while DMU D2 ranked second in NIRF but 10th in super efficiency. 2021: In 2021, ten of the 20 DMUs were technically efficient, and ten were inefficient under the CCR Model. By contrast, 17 DMUs were deemed technically efficient under the BCC Model, indicating unity PTE scores. Super efficiency scores were used to rank the efficient DMUs. 2022: In 2022, only nine of the 20 DMUs were technically efficient under the CCR Model, while the remaining DMUs were inefficient. However, under the BCC Model, all DMUs were technically efficient. The ranking of these DMUs was determined using super efficiency scores. 4. Conclusion In this paper, the conclusions were made with the help of comparing the references on the application of DEA with the evaluation of the efficiency of the Indian management colleges. The following are the synthesized comparison of the relevant studies: Comparison of Efficiency Models: Efficiency is what has received much attention in the higher education sector although the authors have suggested that DEA should be used[6]. The current paper extends this by using both the CCR and BCC models on data for four years through National Institutional Ranking Framework (NIRF). However, this paper contributes by accurately implementing the super-efficiency model to rank efficient units, addressing the gap identified by [7] that did not use super-efficiency, it employs the Data Envelopment Analysis (DEA) approach to achieve a full ranking of Decision-Making Units (DMUs). Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 3s (2025) 744 https://internationalpubls.com Technical Efficiency over Time: Where as considers short term analysis of engineering and undergraduate departments this paper concerns with mapping management colleges from 2019 to 2022. The results reveal firms’ technical efficiency trends over time: Most firms experienced a technical efficiency increase similar to those of [8]on higher education efficiency escalations. However, more worrisome is the fact that only nine institutions were strictly and continually efficient which supports [9]observation that, sustaining efficiency over time is a major issue. Peer Perception and Outputs: Another improvement is the identification of peer perception as an output variable.The research presented in this paper demonstrates how incorporating peer perception into efficiency analysis can enhance the multi-dimensional evaluation of college performance. Super Efficiency Ranking: One advantage of the super-efficiency approach used in this study is that it offers a better demarcation of the efficient institutions in contrast to previous, which introduced a new DEA model for slacks-based measures and super-efficiency, providing more precise identification of highly efficient institutions.By applying this method in the current study, it is evident that the rankings reflecting technical efficiency are not always reflective of super-efficiency rankings like [10]that also employed similar models in other contexts. In conclusion, this paper builds upon prior research by using super-efficiency DEA models for a span of four years with peer perception and identifies how management colleges could enhance utilisation of resources. They complement existing studies, fill the identified gaps, and provide practical suggestions for institutional change. References: 1. Mishra, N. K., Chakraborty, A., Singh, S., &Ranjan, P. (2023). Efficiency analysis of engineering colleges in India: Decomposition into parallel sub-processes systems. Socio- Economic Planning Sciences, 89, 101708. https://doi.org/10.1016/j.seps.2023.101708. 2. Bhaskara, V., Ramesh, K. T., &Chakraborty, S. (2023). Data Envelopment Analysis: A Tool for Performance Evaluation of Undergraduate Engineering Programs. In Proceedings of the International Conference on Advanced Computing Applications (pp. 363-377). Springer. https://doi.org/10.1007/978-981-19-6634-7_24. 3. Kaur, H. (2021). Assessing Technical Efficiency of the Indian Higher Education: An Application of Data Envelopment Analysis Approach. SAGE Open, 8(2), 197-218. https://doi.org/10.1177/23476311211011932 4. Ashok R., RajuNellutla, Rajagopalan V. (2023). Measuring the Performance of the Indian Premier League Teams through an Integrated Optimality Analytics by Data Envelopment Analysis Approach. Mathematical Statistician and Engineering Applications, 71(4), 8918– 8940. https://doi.org/10.17762/msea.v71i4.1607 5. DonthulaPavan&Nellutla, Raju&Vajjha, Haragopal. (2023). Technical Performance of Agriculture Farming Decision Making Entities in Telangana State: A New Integrated Evaluation Using Data Envelopment Analysis (DEA) Approach. Communications in Mathematics and Applications. https://doi.org/10.26713/cma.v14i1.1929 https://doi.org/10.1016/j.seps.2023.101708 https://doi.org/10.1007/978-981-19-6634-7_24 https://doi.org/10.1177/23476311211011932 https://doi.org/10.17762/msea.v71i4.1607 https://doi.org/10.26713/cma.v14i1.1929 Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 3s (2025) 745 https://internationalpubls.com 6. Singh, A. P., Yadav, S. P., &Tyagi, P. (2022). Performance assessment of higher educational institutions in India using data envelopment analysis and re-evaluation of NIRF Rankings. International Journal of System Assurance Engineering and Management, 1- 12.https://doi.org/10.1007/s13198-021-01380-9 7. Ekiz, M.K. and TuncerŞakar, C. (2020), A new DEA approach to fully rank DMUs with an application to MBA programs. Intl. Trans. in Op. Res., 27: 1886- 1910. https://doi.org/10.1111/itor.12635 8. Pratap Singh, A., Yadav, S., &Tyagi, P. (2021). Performance assessment of higher educational institutions in India using data envelopment analysis and re-evaluation of NIRF Rankings. International Journal of System Assurance Engineering and Management, 13, 1-12. https://doi.org/10.1007/s13198-021-01380-9. 9. Oanh, N. H. (2016). An Application of the Data Envelopment Analysis Method to Evaluate the Performance of Academic Departments within a Higher Education InstitutionJournal of Economics and Development, 18(2), 71-87. https://doi.org/10.33301/2016.18.02.05 10. FazılGökgöz, E., &Erkul, E. (2019). Investigating the energy efficiencies of European countries with super efficiency model and super SBM approaches. Energy Efficiency, 12(3), 601-618. Available from: https://doi.org/10.1007/s12053-018-9652-6 https://doi.org/10.1007/s13198-021-01380-9 https://doi.org/10.1111/itor.12635 https://doi.org/10.1007/s13198-021-01380-9 https://doi.org/10.33301/2016.18.02.05 https://doi.org/10.1007/s12053-018-9652-6