Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 911 https://internationalpubls.com Evaluation of Comprehensive Performance Scorecard of State Transport Organizations Using Geometric Similarity-Based MCDM Methods VSSS Prasad Jakkuva1, V.V.S. Kesava Rao2 1Executive category Ph.D. Scholar in Department of Mechanical Engineering, College of Engineering(A), Andhra University, Visakhapatnam-3. Email: murtyamvi@gmail.com 2Professor, Department of Mechanical Engineering, College of Engineering(A), Andhra University, Visakhapatnam. Email: kesava9999@gmail.com Article History: Received: 12-11-2024 Revised: 15-12-2024 Accepted: 11-01-2025 Abstract: The performance evaluation of State Road Transport Organizations (SRTUs) is essential for ensuring the effective delivery of public transportation services. This study presents a novel multi-criteria decision-making (MCDM) framework employing three geometric similarity-based ranking methods—Ranking by Alternatives Median Similarity (RAMS), Ranking the Alternatives using the Trace to Median Index (RATMI), and Ranking by Alternatives Perimeter Similarity (RAPS). The evaluation is structured around three key dimensions: Physical, Operational, and financial performance. Each dimension comprises a set of relevant indicators to capture the comprehensive functionality of SRTUs. By integrating these advanced ranking techniques, the study facilitates comparison of transport units, enabling more informed managerial decisions. The proposed methodology not only highlights the relative efficiency of different organizations but also provides insights into specific areas of improvement. The results demonstrate the robustness and discriminatory power of the geometric similarity-based methods in prioritizing and benchmarking public transport performance. The results of the geometric similarity based MCDM methods are compared with Multi Attributive Ideal-Real Comparative Analysis (MAIRCA) method Keywords: MAIRCA method, RAPS, MCDM. 1. Introduction State Road Transport Undertakings (SRTUs) play a pivotal role in delivering accessible, affordable, and reliable public transportation across India. As the backbone of mobility for millions, especially in rural and semi-urban areas, their efficient functioning is critical to socio-economic development. Given their wide operational footprint and public responsibility, there is a growing need to continuously evaluate and enhance their performance. However, performance evaluation in the public transport sector is inherently complex due to its multi-dimensional nature, involving diverse criteria ranging from physical infrastructure and fleet maintenance to service efficiency and financial viability. Traditionally, the assessment of SRTUs has been fragmented, focusing on isolated indicators such as fuel efficiency, fleet utilization, or financial ratios. While these metrics provide valuable insights, they often fail to capture the holistic performance picture necessary for effective decision-making and policy formulation. A multidimensional and integrated evaluation framework is, therefore, essential to assess the true effectiveness of transport undertakings and guide future improvements. mailto:murtyamvi@gmail.com mailto:kesava9999@gmail.com Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 912 https://internationalpubls.com To address this need, the present study introduces a Comprehensive Performance Scorecard (CPS) framework encompassing three major dimensions—Physical, Operational, and Financial performance. These dimensions collectively represent the core functional pillars of any transport organization. The Physical dimension includes indicators related to infrastructure and fleet assets, such as fleet strength, vehicle availability, and maintenance. The Operational dimension captures the efficiency and effectiveness of service delivery through measures like fleet utilization, load factor, kilometers operated per day, and staff productivity. The Financial dimension focuses on cost control, revenue generation, and profitability, incorporating variables such as cost per kilometer, earnings per kilometer, and operating ratios. In order to synthesize these multiple criteria into a unified assessment and ranking of SRTUs, this study applies a set of emerging Multi-Criteria Decision-Making (MCDM) techniques based on geometric similarity measures—namely, RAMS (Ranking by Alternatives Median Similarity), RATMI (Ranking the Alternatives using the Trace to Median Index), and RAPS (Ranking by Alternatives Perimeter Similarity). These methods offer a structured, objective, and mathematically grounded approach to evaluate alternatives based on their proximity to an ideal solution. Unlike conventional methods, geometric similarity-based models consider the spatial orientation of alternatives in a multi-dimensional space, ensuring a balanced and nuanced comparison across all criteria. By applying RAMS, RATMI, and RAPS methods to the data collected from various State Road Transport Undertakings, this study aims to: 1. Develop a robust performance ranking model for SRTUs. 2. Identify the relative strengths and weaknesses of each undertaking. 3. Offer practical insights and policy recommendations for performance enhancement. 4. The integration of geometric MCDM techniques with a Comprehensive Performance Scorecard framework represents a novel contribution to the domain of public transport evaluation. This methodology not only provides a reliable basis for ranking and benchmarking transport organizations but also supports strategic planning and resource optimization in the public transportation sector. Ultimately, the findings of this study are intended to empower stakeholders, including policymakers, administrators, and transport managers, with actionable data to improve public transport services and ensure sustainable urban and regional mobility. 2. Literature Review Evaluating the performance of State Road Transport Corporations (SRTCs) is a complex but crucial task given their multifaceted roles in public mobility, economic development, and social inclusion. The literature offers a variety of frameworks and methodologies to assess the effectiveness and efficiency of such undertakings. This section reviews the existing body of work in three major areas: public sector performance frameworks, transport sector evaluations, and the use of MCDM techniques in operational assessment. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 913 https://internationalpubls.com 2.1 performance evaluation in public transport Public transport performance studies have historically focused on individual indicators such as fleet utilization, occupancy ratio, and fuel efficiency. Gwilliam (2003) emphasized the need for cost- efficiency in public transport operations, particularly in developing countries where resource constraints prevail. Pucher et al. (2005) extended this analysis by highlighting passenger-centric metrics such as service quality, affordability, and accessibility. In the Indian context, Tiwari and Jain (2012) assessed the effectiveness of urban transport services based on indicators like passenger-km per bus and average fleet age, noting significant inter-state variability. Research by Kale and Godbole (2014) evaluated the operational efficiency of Maharashtra State Road Transport Corporation using DEA (Data Envelopment Analysis), pointing to managerial inefficiencies in some regions. Several researchers have examined the operational efficiency of State Road Transport Undertakings (SRTUs) using benchmarking techniques. Studies such as those by Jaiswal and Sharma (2013) applied Data Envelopment Analysis (DEA) to evaluate technical efficiency across Indian SRTUs, emphasizing discrepancies in resource allocation and vehicle utilization. Similarly, Ghosh (2011) used Stochastic Frontier Analysis (SFA) to examine the productivity growth in the Indian public transport sector. 2.2 Scorecard-based frameworks for transport assessment The Balanced Scorecard (BSC) introduced by Kaplan and Norton (1992) has been widely used to align operational metrics with strategic goals. However, its direct application to the public sector, especially SRTCs, has limitations due to its reliance on intangible and subjective criteria. In contrast, the Core Performance Scorecard (CPS) model, focusing on Physical, Operational, and Financial dimensions, offers a more quantifiable, bottom-up framework suited for technically grounded evaluations. Bhattacharya and Sharma (2011) proposed a CPS approach tailored to Indian SRTCs, using fleet performance and cost components to derive operational benchmarks. Similarly, Ramasamy and Ramanathan (2015) advocated for integrating CPS with MCDM tools to create a hybrid framework capable of reflecting both technical efficiency and financial sustainability. 2.3 Multi-criteria decision-making in transport systems Given the multi-dimensionality of transport operations, MCDM techniques have gained popularity in performance assessment. Traditional methods such as TOPSIS (Hwang & Yoon, 1981), AHP (Saaty, 1980), and DEA have been applied to rank transport units based on efficiency, productivity, and sustainability indicators. However, geometric similarity-based methods like RAMS (Ranking by Alternatives Median Similarity), RAPS (Ranking by Alternatives Perimeter Similarity), and RATMI (Ranking by Alternatives Trace to Median Index) offer novel perspectives by evaluating alternatives based on spatial similarity in a multi-dimensional performance space. These methods overcome the limitations of linearity in traditional MCDM approaches by incorporating vector geometry and structural decomposition of performance attributes. Petrović et al. (2020) further validated these methods by comparing them with traditional MCDM tools and demonstrating their superior discriminatory capacity and resistance to rank reversal. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 914 https://internationalpubls.com The introduction of geometric similarity-based MCDM models is relatively recent. Stanujkic and Zavadskas (2019) proposed distance-based evaluation models that focus on closeness to an ideal solution using vector geometry. These models offer more intuitive and spatially coherent ranking strategies, especially suitable for performance measurement scenarios with normalized and weighted data. Recent works by Petrović and Stanujkic (2020) have introduced geometric similarity-based ranking models that demonstrate improved discriminatory power and ranking stability. These approaches have been applied in logistics, energy policy, and public services, but their application in SRTC performance benchmarking remains underexplored—providing a significant research gap that this study addresses. MCDM approaches have long been recognized as effective tools for decision-making in complex transport environments. Ramírez-Nafarrate et al. (2014) applied TOPSIS for evaluating bus rapid transit performance in Latin America, while Duleba and Mishina (2017) combined AHP and PROMETHEE to model stakeholder preferences in urban transport planning. Additionally, Zolfani and Saparauskas (2013) emphasized the role of hybrid MCDM models in the sustainable evaluation of transport strategies, showing that multi-layered models can reflect both operational and strategic criteria 3. Performance Evaluation of SRTCs State Road Transport Corporations (SRTCs) are vital public sector undertakings that provide affordable and accessible mobility to millions of commuters across diverse geographic and socio- economic regions. Operating in varied terrains with different levels of infrastructure development and demand patterns, these organizations face numerous challenges such as aging fleets, escalating operational costs, increasing passenger expectations, and the imperative to maintain service reliability and safety. In such a dynamic and resource-constrained environment, systematic performance evaluation becomes crucial—not only for monitoring and enhancing operational efficiency but also for guiding strategic decisions, ensuring financial sustainability, and fulfilling public service mandates. To facilitate a structured and focused assessment, this study adopts the Core Performance Scorecard (CPS)—a data-driven framework that evaluates performance through three essential dimensions: Physical, Operational, and Financial. Each dimension includes key indicators that reflect the organization's internal strength, productivity, and cost efficiency. The Physical Performance dimension captures the readiness and health of the fleet through indicators such as Passengers Carried, Fleet Utilization, Average Fleet Operated, Average Age of Fleet, and Over-aged Vehicles. These variables offer insights into asset availability, capacity, and fleet condition. The Operational Performance dimension evaluates the effectiveness of service delivery and resource use through metrics such as Staff/Bus Ratio, Staff Productivity, Revenue Earning Kilometers, Fuel Efficiency, Occupancy Ratio, and Number of Accidents. Together, these indicators reflect how well human and physical resources are aligned with service output and safety. The Financial Performance dimension provides a deep dive into cost components that influence economic sustainability, including Staff Cost, Fuel & Lubricant Cost, Tyres & Tubes Cost, Spares Cost, Interest Cost, and Depreciation Cost. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 915 https://internationalpubls.com While the CPS framework provides a solid foundation for assessing individual performance components, deriving a consolidated performance ranking across multiple SRTCs requires a more analytical, multi-dimensional approach. To achieve this, the present study introduces an integrated Multi-Criteria Decision-Making (MCDM) methodology based on geometric similarity measures— namely, • RAPS (Ranking by Alternatives Perimeter Similarity). • RAMS (Ranking by Alternatives Median Similarity), • RATMI (Ranking the Alternatives using the Trace to Median Index) • MCRAT (Multi-Criteria Ranking of Alternatives using Trace) These innovative methods evaluate each SRTC's proximity to an ideal performance vector by considering the geometric characteristics of their performance across all criteria. Unlike traditional scoring or weighting methods, these similarity-based approaches maintain objectivity and ensure a more balanced and holistic evaluation by accounting for the multi-dimensional nature of performance data. By applying RAMS, RATMI, and RAPS to the CPS framework, this study develops a Comprehensive Performance Scorecard capable of ranking SRTCs not only based on individual performance indicators but also on their overall alignment with high-performing standards. This enables transport administrators and policymakers to identify relative strengths and weaknesses across SRTCs, benchmark performance, and make data-driven decisions for improvement. In summary, the integration of the Core Performance Scorecard with advanced MCDM techniques presents a powerful approach for evaluating the performance of SRTCs. It ensures that both the quantitative rigor of multi-criteria analysis and the practical relevance of operational metrics are brought together in a unified framework. This model supports the strategic goal of transforming public transport into a more efficient, cost-effective, and citizen-centric service, while fostering accountability, operational excellence, and long-term viability. The proposed methods are discussed in the following sections: The evaluation methodology involves a structured multi-step approach designed to rank alternatives (e.g., SRTCs) based on multiple criteria using geometric similarity-based MCDM methods. The process includes data preparation, normalization, weighted transformation, optimal alternative identification, and application of ranking techniques such as RATMI, RAPS and RAMS 3.1 Ranking of alternatives by geometric similarity based MCDM methods Step-1: Construction of the decision matrix. The problem is initially expressed in the form of a decision matrix X = [xij]m×n, where • A = [A1, A2, …, Am]: set of m alternatives. • C = [C1, C2, …, Cn]: set of n evaluation criteria. • xij: performance source of alternative Ai with respect to criterion Cj. Some criteria are to be maximized (Smax) and other minimized (Smin). Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 916 https://internationalpubls.com Step-2: Normalize the decsion matrix. Vector normaliztion method as discussed below is used. 2 1 ij ij m iji x r x = =  Step-3: Weighted normalization. The normalized matrix is converted into a weighted normalized matrix using the weights wj for each criterion. Weights may be derived from expert opinion or MCDM weighting methods. The transformation is performed as: ij = wj  rij where 1 1 n jj w = = . The weighted normalized matrix is denoted by V = [ij] Step-4: Determination of the optimal alternative. An optimal (ideal) alternative is constructed, represented as: * * * * 1 2, ,..., nV  =      where * j = max(ij) for benefit criteria and * j = min(ij) for cost criteria. Step-5: Decomposition of the optimal alternative. The optimal alternative vector V* is decomposed into two components: • Qk: Sub-vector for k criteria to be maximized. • Qh: Sub-vector for h criteria to be minimized. Such that: V* = [Qk,Qh] Step-6: Decomposition of alternatives. Similarly, each alternative Vi = [i1, i2, …, in] is decomposed into: Vi = [Gik, Gih] where Gik corresponds to maximization criteria, and Gih to minimization criteria. Step-7: Ranking methods. From this step forward, four distinct methods are used to rank alternatives: 3.1.1 Ranking by alternatives perimeter similarity (RAPS) Treating Qk and Qh as the legs of a right triangle, compute the perimeter: Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 917 https://internationalpubls.com 2 2* | | | | | | | |k h k hP Q Q Q Q= + + + For each alternative: 2 2| | | | | | | |i ik ih ik ihP G G G G= + + + * i i P PS P = Rank alternatives in descending order of PSi. 3.1.2 Ranking by alternatives median similarity (RAMS) Compute the median of the optimal alternative (hypothenuse of triangle divided by 2): 2 2| | | | * 2 k hQ Q M + = For each alternative: 2 2| | | | * , 2 ik ihG G M + = * i i M MS M = Rank alternatives in descending order of MSi. 3.1.3 Ranking using trace to median index (RATMI) This method combines MCRAT and RAMS through a weighted index: Ei =   tr(Ti) + (1 – )  MSi where   [0, 1] is the decision-maker’s preference for trace-based (MCRAT) versus median-based (RAMS) evaluation. Rank alternatives in descending order of Ei. 3.1.4 Multiple criteria ranking by alternative (MCRAT) MCRAT – Ranking by alternative traces. Construct: • Matrix : k h Q F Q   =     Optimal components • Matrix : ik i ih G G G   =     Alternative components Compute: T i iT F G= Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 918 https://internationalpubls.com tr (Ti) = Trace of Ti. Alternatives are ranked in descending order of tr(Tr). 3.2 Multi attributive ideal-real comparative analysis (MAIRCA) method The steps to implement multi-criteria decision-making according to the MAIRCA method are as follows [18]. Step-1: Building the initial matrix according to the following equation: 11 1 21 2 1 n n m mn x x x x X x x      =       (1) where m is the number of options; n is the number of criteria; xmn is the value of the n criterion in m. Step-2: Determining the priority for an indicator. When the decision maker is neutral, the role of the indicators is the same (no priority is given to any). Then the priority for the criteria is the same and is calculated as follows: 1 , jAP m = j = 1,2,…,n (2) Step-3: Calculating the quantities tpij according to the equation: 1 , jpij A jt P w= i = 1,2,…,m; j = 1,2,…,n (3) where wj is the weight of the j-th criterion. Step-4: Calculating the quantities trij according to the equations: ij i rij pij i i x x t t x x − + −  − =    −  if j is the criterion, the bigger the better (4) ij i rij pij i i x x t t x x + − +  − =    −  if j is the criterion, as small as better (5) Step-5: Calculating the quantities of gij according to the equation: gij = tpij – trij (6) Step-6: Summing the gj values according to the equation: 1 m i ij i Q g = =  (7) Ranking the options according to the principle that the one with the smallest Qi is the better. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 919 https://internationalpubls.com 4. Case Study 4.1 Data collection and preparation Secondary data is collected through reports on State Road Transport Organizations (SRTUs) covering 17 variables over three years. The data is presented in Table-1. Table-1: Data on factors of performance of SRTUs FACTORS 2018-19 2017-18 2016-17 Weights AVG STDEV AVG STDEV AVG STDEV Passengers Carried 7709.00 9916.17 7796.20 9742.04 7697.89 9473.97 0.207 Fleet Utilization 81.27 17.20 82.08 17.28 82.99 16.10 0.041 Average Fleet Operated 4616.38 4685.70 4631.10 4688.29 4533.48 4676.27 0.173 Avg Age of Fleet 7.05 2.32 6.52 2.38 6.89 2.12 0.036 Over aged vehicles 27.69 22.32 22.47 20.87 19.13 21.48 0.036 Staff/Bus Ratio 3.99 1.24 4.19 1.34 4.50 1.29 0.043 Staff Productivity 65.34 39.20 62.95 37.23 59.18 33.35 0.025 Revenue Earning Kms 5667.88 6162.43 5700.99 6159.98 5596.35 6142.43 0.114 Fuel Efficiency 4.33 1.10 4.31 1.09 4.35 1.08 0.014 Occupancy Ratio 80.80 21.94 77.66 15.28 74.44 14.58 0.066 Number of Accidents 502.71 751.48 528.14 724.77 504.10 670.31 0.084 Staff Cost 39.22 10.07 43.07 13.65 43.42 10.83 0.004 Fuel & Lubricant Cost 30.90 10.38 28.21 10.93 27.17 9.19 0.046 Tyres & Tubes Cost 1.24 0.65 1.26 0.69 1.42 0.90 0.008 Spares Cost 1.72 0.94 1.68 0.94 1.74 0.91 0.023 Interest Cost 5.32 14.34 5.73 13.70 5.61 13.46 0.033 Depreciation Cost 4.55 2.76 4.30 2.70 4.56 3.04 0.049 From 2016-17 to 2018-19, occupancy ratio and staff productivity improved, while fleet utilization and accident numbers showed concerning trends. The number of over-aged vehicles increased, indicating an aging fleet. Staff costs decreased, but fuel and maintenance costs fluctuated. High standard deviations in key metrics suggest performance inconsistency across regions. Overall, some efficiency gains are evident, but safety and fleet modernization need attention. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 920 https://internationalpubls.com 4. Results and Discussion 4.1 RAPS method Raps method is implemented as discussed in section 3.1.1 and the results are presented below. Table-2: Decision matrix (2018-19) SRTU Passengers Carried (Fl) Fleet Utilisation (F2) Average Fleet Operated (F3) Avg. Age of Fleet (F4) Over aged vehicles (F5) Staff/Bus Ratio (F6) Staff Productivity (F7) Revenue Earning Kms (F8) Fuel Efficiency (F9) Occupancy Ratio (F10) Number of Accidents (Fil) Staff Cost (F12) Fuel & Lubricant Cost (F13) Tyres & Tubes Cost (F14) Spares Cost (F15) Interest Cost (F16) Depreciation Cost (F17) SRTU 1 26020.85 99.71 11803 5.92 1.06 4.5 81.08 15762.74 5.2 77.75 1163 47.31 23.07 1.19 1.16 3.98 2.03 SRTU 2 185.31 49.77 639 5.37 24.17 2.71 19.33 245.83 3.79 87.08 71 45.66 26.78 1.84 0.82 9.78 8.94 SRTU 3 12775 84.12 5615 6.6 10.6 5.08 33.58 4152.85 3.74 71.39 286 52.95 28.4 0.6 3.5 1 5.41 SRTU 4 266 59.59 345 15 100 1.88 59.74 237.68 4.66 164 13 22.91 44.27 2.13 1.33 0 0 SRTU 5 11004.48 84.62 3295 9.2 51.39 6.35 25.93 2340.11 1.94 81.19 125 21.22 5.27 0 0.06 65.9 2.1 SRTU 6 7436.94 85.58 6882 5.41 32.68 4.99 76.92 11271.75 5.38 68.77 674 35.54 40.66 1.55 1.4 2.02 6.36 SRTU 7 43.24 57.42 294 10 27.6945 4.19 19.09 149.58 4.23 66.29 10 39.93 16.18 0.36 1.46 0 3.33 SRTU 8 10986.09 91.65 8045 5.26 37.6 4.4 75.22 10598.57 4.87 71.4 1018 40.92 38.06 1.42 2.5 0.57 5.68 SRTU 9 9524 80.08 4548 7.09 0 5.84 45.84 5546 4.12 84.44 1083 29.99 29.55 0.12 0.19 8.43 2.45 SRTU 10 24078.48 87.33 16414 7.1 6.18 5.42 54.8 20377.97 4.57 69.14 3310 41.77 33.5 1.76 1.57 0.02 3.03 SRTU 11 2.52 41.9346 26 8 49 3.56 30.66 24.73 5.01 63.66 3 63.88 21.8 1.85 3.43 0 6.18 SRTU 12 4945.75 86.33 4134 4.63 26 4.3 68.72 5160.9 5.25 58.53 323 46.9 35.74 1.67 1.31 0.48 5.94 SRTU 13 8205.2 94.4 4711 7.31 42.6 4.74 68.19 5890.17 5.12 64.27 449 46.14 36.7 1.55 1.5 0.49 4.32 SRTU 14 71.7 93.65 413 5.12 5 3.49 61.23 343.72 4.81 93.24 30 26.32 50.41 2.45 2.38 0 7.72 SRTU 15 0.28 100 1138 8 29 3.73 98.68 1529.65 4.69 100.05 112 32.89 33.1 0.67 0.83 0 2.15 SRTU 16 3106.89 71.73 3798 6.31 35.81 2.89 97.51 5437.74 5.03 87.49 187 41.34 22.45 1.1 1.33 3.43 2.46 SRTU 17 214 80.85 726 6.24 24.52 3.11 63.71 649.5 4.59 81 23 30.02 31.65 1.16 2.89 12.36 4.51 SRTU 18 35 605.75 99.76 10456 7.66 26.05 4.83 70.79 13088.44 1.94 73.12 772 39.91 23.66 1.02 2.34 3.18 2.92 SRTU 19 6015.69 97.77 11615 5.7 12.13 1.78 187.74 14497.28 5.23 68 751 35.59 28.55 1.48 2.69 0 3.87 SRTU 20 377.83 94.47 1264 7.5 29.3 2.58 114.22 1438.26 4.81 90.48 74 41.97 34.27 1.56 1.5 0 4.02 SRTU 21 1023 65.96 783 4.57 10.8 3.39 19.23 282 1.94 75.61 80 40.41 44.88 0.66 1.86 0 12.19 Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 921 https://internationalpubls.com Table-3: Normalized decision matrix SRTU Fl F2 F3 F4 F5 F6 F7 F8 F9 F10 Fil F12 F13 F14 F15 F16 F17 SRTU 1 0.4589 0.2622 0.3964 0.1745 0.0066 0.2356 0.2337 0.4162 0.2544 0.2030 0.2854 0.2554 0.1548 0.1857 0.1301 0.0580 0.0837 SRTU 2 0.0033 0.1309 0.0215 0.1583 0.1497 0.1419 0.0557 0.0065 0.1854 0.2273 0.0174 0.2464 0.1797 0.2871 0.0920 0.1426 0.3688 SRTU 3 0.2253 0.2212 0.1886 0.1946 0.0657 0.2659 0.0968 0.1097 0.1830 0.1864 0.0702 0.2858 0.1906 0.0936 0.3925 0.0146 0.2232 SRTU4 0.0047 0.1567 0.0116 0.4422 0.6194 0.0984 0.1722 0.0063 0.2280 0.4281 0.0032 0.1237 0.2971 0.3323 0.1492 0.0000 0.0000 SRTU 5 0.1941 0.2225 0.1107 0.2712 0.3183 0.3324 0.0747 0.0618 0.0949 0.2119 0.0307 0.1145 0.0354 0.0000 0.0067 0.9606 0.0866 SRTU 6 0.1312 0.2250 0.2311 0.1595 0.2024 0.2612 0.2217 0.2976 0.2632 0.1795 0.1654 0.1918 0.2728 0.2418 0.1570 0.0294 0.2623 SRTU 7 0.0008 0.1510 0.0099 0.2948 0.1715 0.2193 0.0550 0.0039 0.2070 0.1730 0.0025 0.2155 0.1086 0.0562 0.1637 0.0000 0.1374 SRTU 8 0.1938 0.2410 0.2702 0.1551 0.2329 0.2303 0.2168 0.2799 0.2383 0.1864 0.2498 0.2209 0.2554 0.2216 0.2804 0.0083 0.2343 SRTU 9 0.1680 0.2106 0.1527 0.2090 0.0000 0.3057 0.1321 0.1464 0.2016 0.2204 0.2658 0.1619 0.1983 0.0187 0.0213 0.1229 0.1011 SRTU 10 0.4247 0.2296 0.5512 0.2093 0.0383 0.2837 0.1579 0.5381 0.2236 0.1805 0.8124 0.2255 0.2248 0.2746 0.1761 0.0003 0.1250 SRTU 11 0.0000 0.1103 0.0009 0.2358 0.3035 0.1864 0.0884 0.0007 0.2451 0.1662 0.0007 0.3448 0.1463 0.2886 0.3847 0.0000 0.2549 SRTU 12 0.0872 0.2270 0.1388 0.1365 0.1610 0.2251 0.1980 0.1363 0.2569 0.1528 0.0793 0.2531 0.2398 0.2606 0.1469 0.0070 0.2450 SRTU 13 0.1447 0.2482 0.1582 0.2155 0.2639 0.2481 0.1965 0.1555 0.2505 0.1678 0.1102 0.2490 0.2463 0.2418 0.1682 0.0071 0.1782 SRTU 14 0.0013 0.2463 0.0139 0.1509 0.0310 0.1827 0.1765 0.0091 0.2354 0.2434 0.0074 0.1421 0.3383 0.3823 0.2669 0.0000 0.3184 SRTU 15 0.0000 0.2630 0.0382 0.2358 0.1796 0.1953 0.2844 0.0404 0.2295 0.2612 0.0275 0.1775 0.2221 0.1045 0.0931 0.0000 0.0887 SRTU 16 0.0548 0.1886 0.1275 0.1860 0.2218 0.1513 0.2810 0.1436 0.2461 0.2284 0.0459 0.2231 0.1506 0.1716 0.1492 0.0500 0.1015 SRTU 17 0.0038 0.2126 0.0244 0.1839 0.1519 0.1628 0.1836 0.0172 0.2246 0.2114 0.0056 0.1620 0.2124 0.1810 0.3241 0.1802 0.1860 SRTU 18 0.6280 0.2623 0.3511 0.2258 0.1613 0.2528 0.2040 0.3456 0.0949 0.1909 0.1895 0.2154 0.1588 0.1591 0.2624 0.0464 0.1204 SRTU 19 0.1061 0.2571 0.3901 0.1680 0.0751 0.0932 0.5411 0.3828 0.2559 0.1775 0.1843 0.1921 0.1916 0.2309 0.3017 0.0000 0.1596 SRTU 20 0.0067 0.2484 0.0424 0.2211 0.1815 0.1351 0.3292 0.0380 0.2354 0.2362 0.0182 0.2265 0.2300 0.2434 0.1682 0.0000 0.1658 SRTU 21 0.0180 0.1734 0.0263 0.1347 0.0669 0.1775 0.0554 0.0074 0.0949 0.1974 0.0196 0.2181 0.3012 0.1030 0.2086 0.0000 0.5028 Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 922 https://internationalpubls.com Table-4: Weighted normalized decision matrix SRTU F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 Fil F12 F13 F14 F15 F16 F17 SRTU 1 0.0950 0.0107 0.0686 0.0063 0.0002 0.0101 0.0058 0.0475 0.0036 0.0134 0.0240 0.0010 0.0071 0.0015 0.0030 0.0019 0.0041 SRTU 2 0.0007 0.0054 0.0037 0.0057 0.0054 0.0061 0.0014 0.0007 0.0026 0.0150 0.0015 0.0010 0.0083 0.0023 0.0021 0.0047 0.0181 SRTU 3 0.0466 0.0091 0.0326 0.0070 0.0024 0.0114 0.0024 0.0125 0.0026 0.0123 0.0059 0.0011 0.0088 0.0007 0.0090 0.0005 0.0109 SRTU4 0.0010 0.0064 0.0020 0.0159 0.0223 0.0042 0.0043 0.0007 0.0032 0.0283 0.0003 0.0005 0.0137 0.0027 0.0034 0.0000 0.0000 SRTU 5 0.0402 0.0091 0.0191 0.0098 0.0115 0.0143 0.0019 0.0070 0.0013 0.0140 0.0026 0.0005 0.0016 0.0000 0.0002 0.0317 0.0042 SRTU 6 0.0272 0.0092 0.0400 0.0057 0.0073 0.0112 0.0055 0.0339 0.0037 0.0118 0.0139 0.0008 0.0126 0.0019 0.0036 0.0010 0.0129 SRTU 7 0.0002 0.0062 0.0017 0.0106 0.0062 0.0094 0.0014 0.0005 0.0029 0.0114 0.0002 0.0009 0.0050 0.0004 0.0038 0.0000 0.0067 SRTU 8 0.0401 0.0099 0.0467 0.0056 0.0084 0.0099 0.0054 0.0319 0.0033 0.0123 0.0210 0.0009 0.0117 0.0018 0.0064 0.0003 0.0115 SRTU 9 0.0348 0.0086 0.0264 0.0075 0.0000 0.0131 0.0033 0.0167 0.0028 0.0145 0.0223 0.0006 0.0091 0.0001 0.0005 0.0041 0.0050 SRTU 10 0.0879 0.0094 0.0954 0.0075 0.0014 0.0122 0.0039 0.0613 0.0031 0.0119 0.0682 0.0009 0.0103 0.0022 0.0040 0.0000 0.0061 SRTU 11 0.0000 0.0045 0.0002 0.0085 0.0109 0.0080 0.0022 0.0001 0.0034 0.0110 0.0001 0.0014 0.0067 0.0023 0.0088 0.0000 0.0125 SRTU 12 0.0181 0.0093 0.0240 0.0049 0.0058 0.0097 0.0050 0.0155 0.0036 0.0101 0.0067 0.0010 0.0110 0.0021 0.0034 0.0002 0.0120 SRTU 13 0.0300 0.0102 0.0274 0.0078 0.0095 0.0107 0.0049 0.0177 0.0035 0.0111 0.0093 0.0010 0.0113 0.0019 0.0039 0.0002 0.0087 SRTU 14 0.0003 0.0101 0.0024 0.0054 0.0011 0.0079 0.0044 0.0010 0.0033 0.0161 0.0006 0.0006 0.0156 0.0031 0.0061 0.0000 0.0156 SRTU 15 0.0000 0.0108 0.0066 0.0085 0.0065 0.0084 0.0071 0.0046 0.0032 0.0172 0.0023 0.0007 0.0102 0.0008 0.0021 0.0000 0.0043 SRTU 16 0.0113 0.0077 0.0221 0.0067 0.0080 0.0065 0.0070 0.0164 0.0034 0.0151 0.0039 0.0009 0.0069 0.0014 0.0034 0.0017 0.0050 SRTU 17 0.0008 0.0087 0.0042 0.0066 0.0055 0.0070 0.0046 0.0020 0.0031 0.0140 0.0005 0.0006 0.0098 0.0014 0.0075 0.0059 0.0091 SRTU 18 0.1300 0.0108 0.0607 0.0081 0.0058 0.0109 0.0051 0.0394 0.0013 0.0126 0.0159 0.0009 0.0073 0.0013 0.0060 0.0015 0.0059 SRTU 19 0.0220 0.0105 0.0675 0.0060 0.0027 0.0040 0.0135 0.0436 0.0036 0.0117 0.0155 0.0008 0.0088 0.0018 0.0069 0.0000 0.0078 SRTU 2O 0.0014 0.0102 0.0073 0.0080 0.0065 0.0058 0.0082 0.0043 0.0033 0.0156 0.0015 0.0009 0.0106 0.0019 0.0039 0.0000 0.0081 SRTU 21 0.0037 0.0071 0.0045 0.0048 0.0024 0.0076 0.0014 0.0008 0.0013 0.0130 0.0016 0.0009 0.0139 0.0008 0.0048 0.0000 0.0246 Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 923 https://internationalpubls.com Table-5: Ranking by RAPS Method SRTU Pi Rank SRTU 1 0.6616 3 SRTU 2 0.1443 18 SRTU 3 0.3265 7 SRTU 4 0.2196 12 SRTU 5 0.3136 8 SRTU 6 0.3429 6 SRTU 7 0.1150 21 SRTU 8 0.3976 5 SRTU 9 0.2948 9 SRTU 10 0.8214 1 SRTU 11 0.1338 20 SRTU 12 0.2196 11 SRTU 13 0.2699 10 SRTU 14 0.1633 15 SRTU 15 0.1485 16 SRTU 16 0.1970 13 SRTU 17 0.1370 19 SRTU 18 0.7487 2 SRTU 19 0.4508 4 SRTU 20 0.1478 17 SRTU 21 0.1716 14 Ranking by RAM’s method: RAM’s method is implemented as discussed in section 3.1.2 and the results are presented below. Table-6: Ranking by RAM’s SRTU Mi Pi Rank SRTU 1 0.0654 0.6858 4 SRTU 2 0.0142 0.1488 19 SRTU 3 0.0322 0.3373 8 SRTU 4 0.0215 0.2253 13 SRTU 5 0.0307 0.3222 9 SRTU 6 0.0336 0.3517 7 SRTU 7 0.0113 0.1181 22 SRTU 8 0.0389 0.4079 6 SRTU 9 0.0289 0.3031 10 SRTU 10 0.0804 0.8431 2 SRTU 11 0.0132 0.1387 21 SRTU 12 0.0215 0.2253 12 SRTU 13 0.0264 0.2772 11 SRTU 14 0.0160 0.1676 16 SRTU 15 0.0146 0.1535 17 SRTU 16 0.0193 0.2021 14 SRTU 17 0.0134 0.1405 20 SRTU 18 0.0759 0.7957 3 SRTU 19 0.0444 0.4651 5 SRTU 20 0.0145 0.1519 18 SRTU 21 0.0171 0.1795 15 Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 924 https://internationalpubls.com Ranking by RATMI method: RATMI method is implemented as discussed in section 3.1.3 and the results are presented below. Table-7: Ranking by RATMI SRTU TRACE MSi Ei RANK SRTU 1 0.025475 0.3338 0.7831 3 SRTU 2 0.005454 0.0724 0.0424 18 SRTU 3 0.012571 0.1642 0.3024 7 SRTU 4 0.008392 0.1097 0.1480 12 SRTU 5 0.012048 0.1568 0.2815 8 SRTU 6 0.013127 0.1712 0.3223 6 SRTU 7 0.004411 0.0575 0.0000 21 SRTU 8 0.015213 0.1985 0.3998 5 SRTU 9 0.011334 0.1475 0.2552 9 SRTU 10 0.031331 0.4103 1.0000 1 SRTU 11 0.005012 0.0675 0.0284 20 SRTU 12 0.008392 0.1097 0.1480 11 SRTU 13 0.010369 0.1349 0.2196 10 SRTU 14 0.006217 0.0816 0.0684 15 SRTU 15 0.005718 0.0747 0.0489 16 SRTU 16 0.007553 0.0984 0.1160 13 SRTU 17 0.00524 0.0684 0.0310 19 SRTU 18 0.02865 0.3872 0.9346 2 SRTU 19 0.017005 0.2264 0.4787 4 SRTU 20 0.00568 0.0739 0.0466 17 SRTU 21 0.00635 0.0874 0.0848 14 Ranking by MCRAT method: MCRAT method is implemented as discussed in section 3.1.4 and the results are presented below. Table-8: Ranking by MCRAT SRTU TRACE Rank SRTU 1 0.0255 3 SRTU 2 0.0055 18 SRTU 3 0.0126 7 SRTU 4 0.0084 12 SRTU 5 0.0120 8 SRTU 6 0.0131 6 SRTU 7 0.0044 21 SRTU 8 0.0152 5 SRTU 9 0.0113 9 SRTU 10 0.0313 1 SRTU 11 0.0050 20 SRTU 12 0.0084 11 SRTU 13 0.0104 10 SRTU 14 0.0062 15 SRTU 15 0.0057 16 SRTU 16 0.0076 13 SRTU 17 0.0052 19 SRTU 18 0.0286 2 SRTU 19 0.0170 4 SRTU 20 0.0057 17 SRTU 21 0.0064 14 Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 925 https://internationalpubls.com MAIRCA method: Ranking by MAICRA method is implemented as discussed in section 3.2 and the results are presented below. Table-9: Real rating matrix in MAICRA SRTU C1 C2 C3 C4 C5 C6 C7 C8 C9 CIO C11 C12 C13 C14 C15 C16 C17 SRTU 1 0.0072 0.0019 0.0023 0.0015 0.0017 0.0012 0.0004 0.0042 0.0006 0.0006 0.0026 0.0001 0.0013 0.0002 0.0007 0.0015 0.0019 SRTU 2 0.0001 0.0003 0.0079 0.0016 0.0013 0.0004 0.0000 0.0001 0.0004 0.0009 0.0039 0.0001 0.0011 0.0001 0.0009 0.0013 0.0006 SRTU 3 0.0035 0.0014 0.0054 0.0014 0.0015 0.0015 0.0001 0.0011 0.0003 0.0004 0.0037 0.0000 0.0011 0.0003 0.0000 0.0015 0.0013 SRTU 4 0.0001 0.0006 0.0081 0.0000 0.0000 0.0000 0.0003 0.0001 0.0005 0.0031 0.0040 0.0002 0.0003 0.0000 0.0007 0.0016 0.0023 SRTU 5 0.0030 0.0014 0.0066 0.0010 0.0008 0.0020 0.0000 0.0006 0.0000 0.0007 0.0039 0.0002 0.0022 0.0004 0.0011 0.0000 0.0019 SRTU 6 0.0021 0.0015 0.0048 0.0016 0.0012 0.0014 0.0004 0.0030 0.0007 0.0003 0.0032 0.0001 0.0005 0.0001 0.0007 0.0015 0.0011 SRTU 7 0.0000 0.0005 0.0081 0.0008 0.0012 0.0011 0.0000 0.0000 0.0004 0.0002 0.0040 0.0001 0.0017 0.0003 0.0006 0.0016 0.0017 SRTU 8 0.0030 0.0017 0.0042 0.0016 0.0011 0.0012 0.0004 0.0028 0.0006 0.0004 0.0028 0.0001 0.0006 0.0002 0.0003 0.0016 0.0012 SRTU 9 0.0026 0.0013 0.0060 0.0013 0.0017 0.0018 0.0002 0.0015 0.0004 0.0008 0.0027 0.0002 0.0010 0.0004 0.0011 0.0014 0.0019 SRTU 10 0.0067 0.0015 0.0000 0.0013 0.0016 0.0016 0.0003 0.0054 0.0005 0.0003 0.0000 0.0001 0.0008 0.0001 0.0006 0.0016 0.0018 SRTU 11 0.0000 0.0000 0.0082 0.0012 0.0009 0.0008 0.0001 0.0000 0.0006 0.0002 0.0040 0.0000 0.0014 0.0001 0.0000 0.0016 0.0012 SRTU 12 0.0014 0.0015 0.0062 0.0017 0.0013 0.0011 0.0004 0.0014 0.0006 0.0000 0.0036 0.0001 0.0007 0.0001 0.0007 0.0016 0.0012 SRTU 13 0.0023 0.0018 0.0059 0.0013 0.0010 0.0013 0.0003 0.0016 0.0006 0.0002 0.0035 0.0001 0.0007 0.0001 0.0006 0.0016 0.0015 SRTU 14 0.0000 0.0017 0.0080 0.0016 0.0016 0.0008 0.0003 0.0001 0.0006 0.0010 0.0040 0.0002 0.0000 0.0000 0.0004 0.0016 0.0009 SRTU 15 0.0000 0.0020 0.0077 0.0012 0.0012 0.0009 0.0006 0.0004 0.0005 0.0012 0.0039 0.0001 0.0008 0.0003 0.0009 0.0016 0.0019 SRTU 16 0.0009 0.0010 0.0063 0.0014 0.0011 0.0005 0.0006 0.0014 0.0006 0.0009 0.0038 0.0001 0.0014 0.0002 0.0007 0.0015 0.0019 SRTU 17 0.0001 0.0013 0.0079 0.0014 0.0013 0.0006 0.0003 0.0002 0.0005 0.0007 0.0040 0.0002 0.0009 0.0002 0.0002 0.0013 0.0015 SRTU 18 0.0099 0.0019 0.0030 0.0012 0.0013 0.0014 0.0004 0.0035 0.0000 0.0004 0.0031 0.0001 0.0013 0.0002 0.0004 0.0015 0.0018 SRTU 19 0.0017 0.0019 0.0024 0.0015 0.0015 0.0000 0.0012 0.0039 0.0006 0.0003 0.0031 0.0001 0.0011 0.0002 0.0003 0.0016 0.0016 SRTU 20 0.0001 0.0018 0.0076 0.0012 0.0012 0.0004 0.0007 0.0004 0.0006 0.0010 0.0039 0.0001 0.0008 0.0001 0.0006 0.0016 0.0016 SRTU 21 0.0003 0.0008 0.0079 0.0017 0.0015 0.0007 0.0000 0.0001 0.0000 0.0005 0.0039 0.0001 0.0003 0.0003 0.0005 0.0016 0.0000 Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 926 https://internationalpubls.com Table-10: GAP matrix SRTU C1 C2 C3 C4 C5 C6 C7 C8 C9 CIO Cll C12 C13 C14 C15 C16 C17 SRTU 1 0.0027 0.0000 0.0059 0.0002 0.0000 0.0008 0.0008 0.0012 0.0000 0.0026 0.0014 0.0001 0.0009 0.0002 0.0004 0.0001 0.0004 SRTU 2 0.0098 0.0017 0.0003 0.0001 0.0004 0.0016 0.0012 0.0054 0.0003 0.0023 0.0001 0.0001 0.0010 0.0003 0.0002 0.0002 0.0017 SRTU 3 0.0063 0.0005 0.0028 0.0003 0.0002 0.0006 0.0011 0.0043 0.0003 0.0028 0.0003 0.0001 0.0011 0.0001 0.0011 0.0000 0.0010 SRTU 4 0.0098 0.0014 0.0002 0.0017 0.0017 0.0020 0.0009 0.0054 0.0001 0.0000 0.0000 0.0000 0.0019 0.0003 0.0004 0.0000 0.0000 SRTU 5 0.0068 0.0005 0.0016 0.0008 0.0009 0.0000 0.0011 0.0048 0.0007 0.0025 0.0001 0.0000 0.0000 0.0000 0.0000 0.0016 0.0004 SRTU 6 0.0078 0.0005 0.0034 0.0001 0.0006 0.0006 0.0008 0.0024 0.0000 0.0028 0.0008 0.0001 0.0017 0.0002 0.0004 0.0000 0.0012 SRTU 7 0.0098 0.0014 0.0001 0.0009 0.0005 0.0010 0.0012 0.0054 0.0002 0.0029 0.0000 0.0001 0.0005 0.0001 0.0004 0.0000 0.0006 SRTU 8 0.0068 0.0003 0.0040 0.0001 0.0006 0.0009 0.0008 0.0026 0.0001 0.0028 0.0012 0.0001 0.0016 0.0002 0.0008 0.0000 0.0011 SRTU 9 0.0072 0.0007 0.0023 0.0004 0.0000 0.0002 0.0010 0.0040 0.0002 0.0024 0.0013 0.0000 0.0012 0.0000 0.0000 0.0002 0.0005 SRTU 10 0.0032 0.0004 0.0082 0.0004 0.0001 0.0004 0.0009 0.0000 0.0002 0.0028 0.0040 0.0001 0.0014 0.0003 0.0005 0.0000 0.0006 SRTU 11 0.0099 0.0020 0.0000 0.0006 0.0008 0.0013 0.0011 0.0054 0.0001 0.0030 0.0000 0.0002 0.0008 0.0003 0.0011 0.0000 0.0012 SRTU 12 0.0085 0.0005 0.0021 0.0000 0.0004 0.0009 0.0008 0.0041 0.0000 0.0031 0.0004 0.0001 0.0015 0.0003 0.0004 0.0000 0.0011 SRTU 13 0.0076 0.0002 0.0024 0.0005 0.0007 0.0007 0.0008 0.0039 0.0001 0.0030 0.0005 0.0001 0.0015 0.0002 0.0005 0.0000 0.0008 SRTU 14 0.0098 0.0002 0.0002 0.0001 0.0001 0.0013 0.0009 0.0053 0.0001 0.0021 0.0000 0.0000 0.0022 0.0004 0.0007 0.0000 0.0015 SRTU 15 0.0099 0.0000 0.0006 0.0006 0.0005 0.0012 0.0006 0.0050 0.0001 0.0019 0.0001 0.0001 0.0014 0.0001 0.0002 0.0000 0.0004 SRTU 16 0.0090 0.0010 0.0019 0.0003 0.0006 0.0016 0.0006 0.0040 0.0001 0.0023 0.0002 0.0001 0.0008 0.0002 0.0004 0.0001 0.0005 SRTU 17 0.0098 0.0006 0.0004 0.0003 0.0004 0.0015 0.0009 0.0053 0.0002 0.0025 0.0000 0.0000 0.0013 0.0002 0.0009 0.0003 0.0009 SRTU 18 0.0000 0.0000 0.0052 0.0005 0.0004 0.0007 0.0008 0.0019 0.0007 0.0027 0.0009 0.0001 0.0009 0.0002 0.0007 0.0001 0.0006 SRTU 19 0.0082 0.0001 0.0058 0.0002 0.0002 0.0020 0.0000 0.0016 0.0000 0.0029 0.0009 0.0001 0.0011 0.0002 0.0008 0.0000 0.0007 SRTU 20 0.0098 0.0002 0.0006 0.0005 0.0005 0.0017 0.0005 0.0051 0.0001 0.0022 0.0001 0.0001 0.0014 0.0002 0.0005 0.0000 0.0008 SRTU 21 0.0096 0.0011 0.0004 0.0000 0.0002 0.0013 0.0012 0.0054 0.0007 0.0026 0.0001 0.0001 0.0019 0.0001 0.0006 0.0000 0.0023 1 Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 927 https://internationalpubls.com Table-11: Ranking by MAIRCA SRTU Total gap Rank SRTU 1 0.0176 2 SRTU 2 0.0268 19 SRTU 3 0.0231 6 SRTU 4 0.0258 18 SRTU 5 0.0218 4 SRTU 6 0.0236 10 SRTU 7 0.0252 16 SRTU 8 0.0240 11 SRTU 9 0.0216 3 SRTU 10 0.0235 8 SRTU 11 0.0276 21 SRTU 12 0.0242 13 SRTU 13 0.0235 7 SRTU 14 0.0250 15 SRTU 15 0.0226 5 SRTU 16 0.0235 9 SRTU 17 0.0253 17 SRTU 18 0.0165 1 SRTU 19 0.0249 14 SRTU 20 0.0242 12 SRTU 21 0.0276 20 Table-12: Comparison of ranks for FY 2018-19 SRTU RAP's RAM's RATMI MCRAT MAIRCA SRTU 1 3 4 3 3 2 SRTU 2 18 19 18 18 19 SRTU 3 7 8 7 7 6 SRTU 4 12 13 12 12 18 SRTU 5 8 9 8 8 4 SRTU 6 6 7 6 6 10 SRTU 7 21 22 21 21 16 SRTU 8 5 6 5 5 11 SRTU 9 9 10 9 9 3 SRTU 10 1 2 1 1 8 SRTU 11 20 21 20 20 21 SRTU 12 11 12 11 11 13 SRTU 13 10 11 10 10 7 SRTU 14 15 16 15 15 15 SRTU 15 16 17 16 16 5 SRTU 16 13 14 13 13 9 SRTU 17 19 20 19 19 17 SRTU 18 2 3 2 2 1 SRTU 19 4 5 4 4 14 SRTU 20 17 18 17 17 12 SRTU 21 14 15 14 14 20 Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 928 https://internationalpubls.com For the financial Year 2018-19, RAPs, RAMs, RATMI, and MCRAT methods provide nearly identical rankings, suggesting high agreement. MAIRCA diverges notably, reordering several SRTUs significantly. SRTU10 and SRTU18 consistently rank high across all methods, while SRTU2, SRTU7, and SRTU11 remain among the lowest. MAIRCA’s variability may stem from a different evaluation logic as discussed in section 3.2. Similarly ranking of SRTUs for the financial year 2017-18 and 2016-17 are determined and presented in the following table. Table-13: Ranking of SRTUs for the FY 2017-18 SRTU RAP's RAM's RATMI MCRAT MAIRCA SRTU 1 3 4 3 3 2 SRTU 2 18 19 18 18 21 SRTU 3 7 7 6 6 5 SRTU 4 12 14 13 13 18 SRTU 5 8 10 9 9 3 SRTU 6 6 9 8 8 9 SRTU 7 21 22 21 21 13 SRTU 8 5 6 5 5 12 SRTU 9 9 8 7 7 4 SRTU 10 1 2 1 1 8 SRTU 11 20 21 20 20 19 SRTU 12 11 13 12 12 14 SRTU 13 10 11 10 10 11 SRTU 14 15 16 15 15 15 SRTU 15 16 18 17 17 7 SRTU 16 13 12 11 11 6 SRTU 17 19 20 19 19 17 SRTU 18 2 3 2 2 1 SRTU 19 4 5 4 4 16 SRTU 20 17 17 16 16 10 SRTU 21 14 15 14 14 20 For the financial year 2017-18, RAP's, RAM's, RATMI, and MCRAT produce near-identical rankings, showing strong consistency. MAIRCA shows noticeable deviations, reshuffling several SRTUs significantly. SRTU18 and SRTU10 rank consistently at the top, while SRTU2, SRTU11, and SRTU17 remain bottom performers. MAIRCA tends to reward certain SRTUs (e.g., SRTU5, SRTU15) differently. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 929 https://internationalpubls.com Table-14: Ranking of SRTUs for the FY 2016-17 SRTU RAP’s RAM's RATMI MCRAT MAIRCA SRTU 1 3 4 3 3 2 SRTU 2 18 15 14 16 21 SRTU 3 7 6 5 5 6 SRTU 4 12 14 13 13 18 SRTU 5 8 10 9 9 3 SRTU 6 6 9 8 8 9 SRTU 7 21 22 21 21 19 SRTU 8 5 7 6 6 13 SRTU 9 9 8 7 7 5 SRTU 10 1 2 1 1 8 SRTU 11 20 20 19 19 16 SRTU 12 11 12 11 11 14 SRTU 13 10 11 10 10 11 SRTU 14 15 17 16 14 17 SRTU 15 16 18 17 17 7 SRTU 16 13 13 12 12 4 SRTU 17 19 21 20 20 15 SRTU 18 2 3 2 2 1 SRTU 19 4 5 4 4 12 SRTU 20 17 19 18 18 10 SRTU 21 14 16 15 15 20 For the financial year 2016-17, RAP’s, RAM’s, RATMI, and MCRAT display high consistency in rankings. MAIRCA significantly reorders several SRTUs, promoting some (like SRTU5, SRTU15) and demoting others (like SRTU2, SRTU19). SRTU18 and SRTU10 are consistently top ranked, while SRTU2, SRTU7, and SRTU11 stay at the bottom. The variation in MAIRCA suggests it applies a different scoring logic compared to the others. ANOVA (Analysis of Variance): ANOVA is conducted to know the signification factors that are causing variation in the ranking Table-15: ANOVA Source DF SS MS F P METHOD 4 50.4 12.6 2.47 0.045 SRTU 20 10079.87 503.99 98.73 0 FY 2 0 0 0 1 Error 288 1470.13 5.1 Total 314 11600.4 S = .25934 R-Sq = 87.33% R-Sq(adj) = 86.18% The analysis shows that the METHOD factor has a small but statistically significant effect on the response variable at a significance level of α = 0.05, indicating that the choice of method does influence the outcome to some extent. The SRTU factor is highly significant (P < 0.001) and explains the Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 930 https://internationalpubls.com majority of the variability in the response, making it the most influential factor in the model. On the other hand, the FY factor is not significant and has no impact on the response, as indicated by its zero sum of squares and an F-value of 0. The residual or unexplained variability is captured under the Error term, and the relatively low mean square error (MS = 5.1) suggests that the model fits the data well. Overview of the model fit: • R-Sq (R²) = 87.33%: This means that 87.33% of the total variation in the response variable is explained by the model (i.e., by METHOD, SRTU, and FY). • R-Sq(adj) = 86.18%: This is the adjusted R², which accounts for the number of predictors. It’s slightly lower than R², indicating the model is still a good fit but slightly penalizes the number of predictors. The findings across three financial years (2016–17 to 2018–19) consistently reveal strong agreement among the geometric similarity-based methods—RAPs, RAMs, RATMI, and MCRAT— demonstrating their robustness and reliability for evaluating the relative performance of SRTUs. These methods yield nearly identical rankings, reinforcing their internal consistency and methodological harmony. However, the MAIRCA method consistently deviates, reshuffling rankings and offering a distinct perspective on performance evaluation. This divergence can be attributed to its unique ideal-real comparative logic, which appears to emphasize different performance characteristics than the geometric methods. For instance, MAIRCA elevates SRTUs like SRTU5 and SRTU15 while demoting consistently low performers such as SRTU2 and SRTU7 more drastically. Statistical analysis further substantiates the credibility of the model. The SRTU factor emerged as the most influential with high significance (P < 0.001), explaining the majority of the variance in the rankings. The METHOD factor, though statistically significant at α = 0.05, contributes to a smaller portion of the variability, suggesting that while the choice of method affects rankings, it does so marginally compared to the inherent differences among SRTUs. The FY factor, on the other hand, showed no significant impact, indicating performance rankings are relatively stable across the years analyzed. The model’s high explanatory power (R² = 87.33%, R²(adj) = 86.18%) and low mean square error (MS = 5.1) confirm a strong model fit, supporting the reliability of the results and the applied MCDM framework. 5. CONCLUDING REMARKS This study highlights the effectiveness of geometric similarity-based MCDM methods—RAPs, RAMs, RATMI, and MCRAT—in evaluating the multidimensional performance of State Road Transport Undertakings (SRTUs). The consistency observed among these methods across three financial years underscores their reliability and robustness in ranking alternatives. In contrast, the MAIRCA method demonstrated a distinct ranking pattern, often promoting or demoting specific SRTUs differently. While this divergence suggests a different underlying logic, it also provides an alternative perspective that may reveal additional insights into the strengths and weaknesses of the transport units. Notably, SRTU18 and SRTU10 emerged as consistent top performers, whereas SRTU2, SRTU7, and SRTU11 Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 931 https://internationalpubls.com frequently ranked among the lowest across all methods. The statistical analysis confirms that while the choice of method has a modest but significant effect on rankings, the most influential factor is the inherent performance differences among the SRTUs. Overall, the proposed framework offers a robust tool for transport administrators to benchmark performance and identify areas needing strategic intervention. Developing hybrid MCDM models that combine geometric methods with fuzzy logic or objective rating methods could improve decision-making under uncertainty. Additionally, conducting a weight sensitivity analysis could help understand how different performance criteria influence rankings and address any potential biases. References [1] Gwilliam, K. M. (2003). Urban transport in developing countries. Transport Reviews, 23(2), 197–216. [2] Pucher, J., Korattyswaroopam, N., & Ittyerah, N. (2005). The crisis of public transport in India: Overwhelming needs but limited resources. Journal of Public Transportation, 8(1), 1–20. [3] Tiwari, G., & Jain, D. (2012). Accessibility and safety indicators for all road users: Case study Delhi BRT. Journal of Transport Geography, 22, 87–95. [4] Kale, R. H., & Godbole, A. A. (2014). Performance Evaluation of MSRTC Using DEA. International Journal of Engineering and Management Research, 4(4), 52–56. [5] Kaplan, R. S., & Norton, D. P. (1992). The Balanced Scorecard: Measures That Drive Performance. Harvard Business Review, 70(1), 71–79. [6] Bhattacharya, A., & Sharma, M. (2011). Operational benchmarking in Indian SRTCs using DEA. Journal of Public Transportation, 14(1), 111–129. [7] Ramasamy, R., & Ramanathan, R. (2015). Multi-criteria decision-making in public transport: An application of fuzzy AHP. Journal of Transport Literature, 9(1), 8–13. [8] Hwang, C. L., & Yoon, K. (1981). Multiple Attribute Decision Making: Methods and Applications. Springer-Verlag. [9] Saaty, T. L. (1980). The Analytic Hierarchy Process. McGraw-Hill. [10] Petrović, G., & Stanujkic, D. (2020). A novel approach for multi-criteria decision-making based on geometric similarities. Operational Research in Engineering Sciences: Theory and Applications, 3(2), 123–135. [11] Jaiswal, R. K., & Sharma, A. (2013). Performance benchmarking of Indian public road transport using DEA. International Journal of Transport Economics, 40(1), 101–117. [12] Ghosh, M. (2011). Productivity growth and efficiency measurement in Indian bus transport: An application of SFA. Indian Economic Review, 46(2), 179–202. [13] Ramírez-Nafarrate, A., Llamazares, B., & Méndez, J. A. (2014). Evaluating public transport systems using TOPSIS and entropy-based weighting. Journal of Public Transportation, 17(4), 79–97. [14] Duleba, S., & Mishina, T. (2017). Promoting sustainable public transport: Ranking of public preferences in Bratislava. Transportation Research Part D, 50, 284–297. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 932 https://internationalpubls.com [15] Zolfani, S. H., & Saparauskas, J. (2013). New application of SWARA method in prioritizing sustainability assessment indicators of energy system. Inzinerine Ekonomika-Engineering Economics, 24(5), 408–416. [16] Stanujkic, D., & Zavadskas, E. K. (2019). A novel approach for multi-criteria decision-making based on the evaluation of distances. Symmetry, 11(9), 1114. [17] Petrović, G., Stanujkic, D., & Savic, Z. (2020). Ranking of alternatives using new geometric similarity-based MCDM methods. Decision Making: Applications in Management and Engineering, 3(1), 99–118.