# AHP-RAPS Approach for Evaluating the Productivity of Engineering Departments at a Public University

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Motivation of the Study

#### 1.2. Structure of the Study

## 2. Background of the MCDM Techniques

#### Overview of MCDM Techniques Used in the Educational Sector

## 3. The AHP-RAPS Approach for Evaluating the Productivity of Engineering Departments

#### 3.1. Analytical Hierarchy Process (AHP)

#### 3.2. Ranking Alternatives by Perimeter Similarity (RAPS)

## 4. Application and Results

## 5. Discussion

#### Comparative Analysis of Different MCDM Methods

## 6. Sensitivity Analysis

#### 6.1. Case 1

#### 6.2. Case 2

#### 6.3. Case 3

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Yap, J.Y.L.; Ho, C.C.; Ting, C.-Y. A systematic review of the applications of multi-criteria decision-making methods in site selection problems. Built Environ. Proj. Asset Manag.
**2019**, 9, 548–563. [Google Scholar] [CrossRef] - Fofan, A.C.; de Oliveira, L.A.B.; de Melo, F.J.C.; de Jerônimo, T.B.; de Medeiros, D.D. An Integrated Methodology Using PROMETHEE and Kano’s Model to Rank Strategic Decisions. Eng. Manag. J.
**2019**, 31, 270–283. [Google Scholar] [CrossRef] - Ozsahin, D.U.; Denker, A.; Kibarer, A.G.; Kaba, S. Evaluation of stage IV brain cancer treatment techniques. In Applications of Multi-Criteria Decision-Making Theories in Healthcare and Biomedical Engineering; Elsevier: Amsterdam, The Netherlands, 2021; pp. 59–69. [Google Scholar]
- Chen, C.-H. A new multi-criteria assessment model combining GRA techniques with intuitionistic fuzzy entropy-based TOPSIS method for sustainable building materials supplier selection. Sustainability
**2019**, 11, 2265. [Google Scholar] [CrossRef] [Green Version] - Ibrahim, A.; Surya, R.A. The implementation of simple additive weighting (SAW) method in decision support system for the best school selection in Jambi. J. Phys. Conf. Ser.
**2019**, 1338, 12054. [Google Scholar] [CrossRef] [Green Version] - Kraujalienė, L. Comparative analysis of multicriteria decision-making methods evaluating the efficiency of technology transfer. Bus. Manag. Educ.
**2019**, 17, 72–93. [Google Scholar] [CrossRef] - Kabassi, K. Comparing Multi-Criteria Decision Making Models for Evaluating Environmental Education Programs. Sustainability
**2021**, 13, 11220. [Google Scholar] [CrossRef] - Miç, P.; Antmen, Z.F. A Decision-Making Model Based on TOPSIS, WASPAS, and MULTIMOORA Methods for University Location Selection Problem. SAGE Open
**2021**, 11, 21582440211040116. [Google Scholar] [CrossRef] - Thakkar, J.J. Multi-Criteria Decision Making; Springer: Berlin/Heidelberg, Germany, 2021; Volume 336. [Google Scholar]
- Karunathilake, H.; Bakhtavar, E.; Chhipi-Shrestha, G.; Mian, H.R.; Hewage, K.; Sadiq, R. Decision making for risk management: A multi-criteria perspective. In Methods in chemical Process Safety; Elsevier: Amsterdam, The Netherlands, 2020; Volume 4, pp. 239–287. [Google Scholar]
- Vásquez, J.A.; Escobar, J.W.; Manotas, D.F. AHP–TOPSIS Methodology for Stock Portfolio Investments. Risks
**2021**, 10, 4. [Google Scholar] [CrossRef] - De Almeida, A.T.; Cavalcante, C.A.V.; Alencar, M.H.; Ferreira, R.J.P.; de Almeida-Filho, A.T.; Garcez, T.V. Multicriteria and Multiobjective Models for Risk, Reliability and Maintenance Decision Analysis; Springer: Berlin/Heidelberg, Germany, 2015; Volume 231. [Google Scholar]
- Su, W.; Zhang, L.; Zhang, C.; Zeng, S.; Liu, W.A. Heterogeneous Information-Based Multi-Attribute Decision Making Framework for Teaching Model Evaluation in Economic Statistics. Systems
**2022**, 10, 86. [Google Scholar] [CrossRef] - Syed Hassan, S.A.H.; Tan, S.C.; Yusof, K.M. MCDM for engineering education: Literature review and research issues. In Engineering Education for a Smart Society; Spring: Berlin/Heidelberg, Germany, 2016; pp. 204–214. [Google Scholar]
- Jongbloed, B.; Vossensteyn, H. Keeping up performances: An international survey of performance-based funding in higher education. J. High. Educ. Policy Manag.
**2001**, 23, 127–145. [Google Scholar] [CrossRef] - Buzzigoli, L.; Giusti, A.; Viviani, A. The evaluation of university departments. A case study for Firenze. Int. Adv. Econ. Res.
**2010**, 16, 24–38. [Google Scholar] [CrossRef] - Urošević, K.; Gligorić, Z.; Miljanović, I.; Beljić, C.; Gligorić, M. Novel methods in multiple criteria decision-making process (Mcrat and raps)—Application in the mining industry. Mathematics
**2021**, 9, 1980. [Google Scholar] [CrossRef] - Marqués, A.I.; García, V.; Sánchez, J.S. Ranking-based MCDM models in financial management applications: Analysis and emerging challenges. Prog. Artif. Intell.
**2020**, 9, 171–193. [Google Scholar] [CrossRef] - Akram, M.; Ilyas, F.; Garg, H. Multi-criteria group decision making based on ELECTRE I method in Pythagorean fuzzy information. Soft Comput.
**2020**, 24, 3425–3453. [Google Scholar] [CrossRef] - Komsiyah, S.; Wongso, R.; Pratiwi, S.W. Applications of the fuzzy ELECTRE method for decision support systems of cement vendor selection. Procedia Comput. Sci.
**2019**, 157, 479–488. [Google Scholar] [CrossRef] - Sembiring, B.S.B.; Zarlis, M.; Agusnady, A.; Qowidho, T. Comparison of SMART and SAW Methods in Decision Making. J. Phys. Conf. Ser.
**2019**, 1255, 12095. [Google Scholar] [CrossRef] - Shahsavar, S.; Jafari Rad, A.; Afzal, P.; Nezafati, N.; Akhavan Aghdam, M. Prospecting for polymetallic mineralization using step-wise weight assessment ratio analysis (SWARA) and fractal modeling in Aghkand Area, NW Iran. Arab. J. Geosci.
**2019**, 12, 248. [Google Scholar] [CrossRef] - Saaty, T.L. The Analytic Hierarchy Process: Decision Making in Complex Environments BT—Quantitative Assessment in Arms Control: Mathematical Modeling and Simulation in the Analysis of Arms Control Problems; Avenhaus, R., Huber, R.K., Eds.; Springer: Boston, MA, USA, 1984; pp. 285–308. [Google Scholar]
- Pakkar, M.S. A hierarchical aggregation approach for indicators based on data envelopment analysis and analytic hierarchy process. Systems
**2016**, 4, 6. [Google Scholar] [CrossRef] [Green Version] - Sari, F.; Kandemir, İ.; Ceylan, D.A.; Gül, A. Using AHP and PROMETHEE multi-criteria decision making methods to define suitable apiary locations. J. Apic. Res.
**2020**, 59, 546–557. [Google Scholar] [CrossRef] - Issa, U.; Saeed, F.; Miky, Y.; Alqurashi, M.; Osman, E. Hybrid AHP-Fuzzy TOPSIS Approach for Selecting Deep Excavation Support System. Buildings
**2022**, 12, 295. [Google Scholar] [CrossRef] - Rezaei, J. Best-worst Multi-criteria Decision-making Method. Omega
**2015**, 53, 49–57. [Google Scholar] [CrossRef] - Van de Kaa, G.; Fens, T.; Rezaei, J.; Kaynak, D.; Hatun, Z.; Tsilimeni-Archangelidi, A. Realizing smart meter connectivity: Analyzing the competing technologies Power line communication, mobile telephony, and radio frequency using the best worst method. Renew. Sustain. Energy Rev.
**2019**, 103, 320–327. [Google Scholar] [CrossRef] - Khan, S.A.; Ojiako, U.; Marshall, A.; Dalalah, D.; Ceylan, S.; Ali Shabani, N.N.; Al Sharqawi, S.I. The Critical Risk Factors that Influence Production-oriented Projects in the United Arab Emirates: A ‘Best-worst Method’(BWM) Analysis. Eng. Manag. J.
**2022**, 1–17. [Google Scholar] [CrossRef] - Mi, X.; Tang, M.; Liao, H.; Shen, W.; Lev, B. The state-of-the-art survey on integrations and applications of the best worst method in decision making: Why, what, what for and what’s next? Omega
**2019**, 87, 205–225. [Google Scholar] [CrossRef] - Akram, M.; Al-Kenani, A.N.; Alcantud, J.C.R. Group decision-making based on the VIKOR method with trapezoidal bipolar fuzzy information. Symmetry
**2019**, 11, 1313. [Google Scholar] [CrossRef] [Green Version] - Yu, P.-L. A class of solutions for group decision problems. Manag. Sci.
**1973**, 19, 936–946. [Google Scholar] [CrossRef] - Arslan, A.E.; Arslan, O.; Kandemir, S.Y. AHP–TOPSIS hybrid decision-making analysis: Simav integrated system case study. J. Therm. Anal. Calorim.
**2021**, 145, 1191–1202. [Google Scholar] [CrossRef] - Taylan, O.; Bafail, A.O.; Abdulaal, R.M.S.; Kabli, M.R. Construction projects selection and risk assessment by fuzzy AHP and fuzzy TOPSIS methodologies. Appl. Soft Comput.
**2014**, 17, 105–116. [Google Scholar] [CrossRef] - Hwang, C.-L.; Yoon, K. Multiple Attribute Decision Making, 1st ed.; Springer: Berlin/Heidelberg, Germany, 1981. [Google Scholar]
- Ishak, A.; Akmaliah, V. Analytical Hierarchy Process and PROMETHEE as Decision Making Tool: A Review. IOP Conf. Ser. Mater. Sci. Eng.
**2019**, 505, 12085. [Google Scholar] [CrossRef] [Green Version] - Julong, D. Introduction to grey system theory. J. Grey Syst.
**1989**, 1, 1–24. [Google Scholar] - Supçiller, A.A.; Bayramoğlu, S. Wind farm location selection with interval grey numbers based I-GRA and grey EDAS methods. J. Fac. Eng. Archit. Gazi Univ.
**2020**, 35, 1847–1860. [Google Scholar] - Brauers, W.K.; Zavadskas, E.K. The MOORA method and its application to privatization in a transition economy. Control Cybern.
**2006**, 35, 445–469. [Google Scholar] - Moradian, M.; Modanloo, V.; Aghaiee, S. Comparative analysis of multi criteria decision making techniques for material selection of brake booster valve body. J. Traffic Transp. Eng.
**2019**, 6, 526–534. [Google Scholar] [CrossRef] - Zavadskas, E.K.; Kaklauskas, A. Pastatų sistemotechninis įvertinimas [eng. Systemic-technical assessment of buildings]. Vilnius Tech.
**1996**, 4. [Google Scholar] - Krishankumar, R.; Garg, H.; Arun, K.; Saha, A.; Ravichandran, K.S.; Kar, S. An integrated decision-making COPRAS approach to probabilistic hesitant fuzzy set information. Complex Intell. Syst.
**2021**, 7, 2281–2298. [Google Scholar] [CrossRef] - Kusnady, D. Implementation of Computer-Based Systems in Efficient Credit Acceptance Decisions Applying the Addi-tive Ratio Assessment (ARAS) Method. J. Phys. Conf. Ser.
**2019**, 1424, 12018. [Google Scholar] - Zulqarnain, R.M.; Xin, X.L.; Saeed, M.; Ahmad, N.; Dayan, F.; Ahmad, B. Recruitment of medical staff in health department by using TOPSIS method. Int. J. Pharm. Sci. Rev. Res.
**2020**, 62, 1–7. [Google Scholar] - Hafezalkotob, A.; Hafezalkotob, A.; Liao, H.; Herrera, F. An overview of MULTIMOORA for multi-criteria decision-making: Theory, developments, applications, and challenges. Inf. Fusion
**2019**, 51, 145–177. [Google Scholar] [CrossRef] - Tuan, N.A.; Hue, T.T.; Lien, L.T.; Thao, T.D.; Quyet, N.D.; Van, L.H.; Anh, L.T. A new integrated MCDM approach for lecturers’ research productivity evaluation. Decis. Sci. Lett.
**2020**, 9, 355–364. [Google Scholar] [CrossRef] - Turan, H. Assessment factors affecting e-learning using fuzzy analytic hierarchy process and SWARA. Int. J. Eng. Educ.
**2018**, 34, 915–923. [Google Scholar] - Biswas, T.K.; Chaki, S.; Das, M.C. MCDM technique application to the selection of an Indian institute of technology. Oper. Res. Eng. Sci. Theory Appl.
**2019**, 2, 65–76. [Google Scholar] [CrossRef] - Kazan, H.; Karaman, E.; Akçalı, B.Y.; Şişmanoğlu, E. Assessment of teog examination success: Topsis multi-criteria decision-making method practice. Procedia-Soc. Behav. Sci.
**2015**, 195, 915–924. [Google Scholar] [CrossRef] [Green Version] - Koltharkar, P.; Eldhose, K.K.; Sridharan, R. Application of fuzzy TOPSIS for the prioritization of students’ requirements in higher education institutions: A case study: A multi-criteria decision making approach. In Proceedings of the 2020 International Conference on System, Computation, Automation and Networking (ICSCAN), Pondicherry, India, 30 November 2020; pp. 1–7. [Google Scholar]
- Mohammed, H.J.; Kasim, M.M.; Shaharanee, I.N. Evaluation of E-learning approaches using AHP-TOPSIS technique. J. Telecommun. Electron. Comput. Eng.
**2018**, 10, 7–10. [Google Scholar] - Shekhovtsov, A.; Sałabun, W. A comparative case study of the VIKOR and TOPSIS rankings similarity. Procedia Comput. Sci.
**2020**, 176, 3730–3740. [Google Scholar] [CrossRef] - Perdana, A.; Budiman, A. College Ranking Analysis Using VIKOR Method. J. Comput. Netw. Archit. High Perform. Comput.
**2021**, 3, 241–248. [Google Scholar] [CrossRef] - Ayouni, S.; Menzli, L.J.; Hajjej, F.; Maddeh, M.; Al-Otaibi, S. Fuzzy Vikor application for learning management systems evaluation in higher education. Int. J. Inf. Commun. Technol. Educ.
**2021**, 17, 17–35. [Google Scholar] [CrossRef] - Monalisa, R.; Kusnawi, K. Decision support system of model teacher selection using PROMETHEE method. In Proceedings of the 2017 International Conference on Innovative and Creative Information Technology (ICITech), Salatiga, Indonesia, 2–4 November 2017; pp. 1–8. [Google Scholar]
- Hanifatulqolbi, D.; Ismail, I.E.; Hammad, J.; Al-Hooti, M.H. Decision support system for considering the best teacher performance using MOORA method. J. Phys. Conf. Ser.
**2019**, 1193, 12018. [Google Scholar] [CrossRef] - Alinezhad, A.; Khalili, J. New Methods and Applications in Multiple Attribute Decision Making (MADM); Springer: Berlin/Heidelberg, Germany, 2019; Volume 277. [Google Scholar]
- Bhushan, N.; Rai, K. Strategic Decision Making. In Strategic Decision Making; Springer: London, UK, 2004. [Google Scholar]
- Saaty, T.L. The analytic hierarchy and analytic network measurement processes: Applications to decisions under Risk. Eur. J. Pure Appl. Math.
**2008**, 1, 122–196. [Google Scholar] [CrossRef]

Criteria/Sub-Criteria | Feature |
---|---|

Research and Scientific Productivity (C1) | Max |

Total number of book chapters produced (C11) | Max |

Total number of publications in Scopus (C12) | Max |

Total number of proceeding papers (C13) | Max |

Graduate Programs (C2) | Max |

Total number of executives programs (C21) | Max |

Total number of M.S. programs (C22) | Max |

Total number of Ph.D. programs (C23) | Max |

Resources (C3) | Max |

Total number of full professors (C31) | Max |

Total number of associate professors (C32) | Max |

Total number of assistant professors (C33) | Max |

Total number of lecturers (C34) | Max |

Total number of labs available (C35) | Max |

Capacity (C4) | Max |

Total number of students accepted in B.S. program (C41) | Max |

Total number of students accepted in M.S. program (C42) | Max |

Total number of students accepted in Ph.D. program (C43) | Max |

Verbal Judgment | Numeric Value |
---|---|

Extremely important | 9 |

8 | |

Very strongly more important | 7 |

6 | |

Strongly more important | 5 |

4 | |

Moderately more important | 3 |

2 | |

Equally important | 1 |

Criteria No. | C1 | C2 | C3 | C4 | Weights |
---|---|---|---|---|---|

C1 | 1 | 9 | 8 | 7 | 0.70 |

C2 | 1/9 | 1 | 1/3 | 1/3 | 0.05 |

C3 | 1/8 | 3 | 1 | 1 | 0.12 |

C4 | 1/7 | 3 | 1 | 1 | 0.13 |

Consistency ratio = 8% |

Criteria No. | C11 | C12 | C13 | Weights |
---|---|---|---|---|

C11 | 1 | 1 | 6 | 0.44 |

C12 | 1 | 1 | 8 | 0.49 |

C13 | 1/6 | 1/8 | 1 | 0.07 |

Consistency ratio = 1% |

Criteria No. | C21 | C22 | C23 | Weights |
---|---|---|---|---|

C21 | 1 | 6 | 4 | 0.71 |

C22 | 1/6 | 1 | 1 | 0.13 |

C23 | 1/4 | 1 | 1 | 0.16 |

Consistency ratio = 3% |

Criteria No. | C31 | C32 | C33 | C34 | C35 | Weights |
---|---|---|---|---|---|---|

C31 | 1 | 3 | 4 | 5 | 8 | 0.35 |

C32 | 1/3 | 1 | 1 | 2 | 4 | 0.15 |

C33 | 2 | 3 | 1 | 3 | 3 | 0.35 |

C34 | 1/5 | 1/2 | 1/3 | 1 | 2 | 0.09 |

C35 | 1/8 | 1/4 | 1/3 | 1/2 | 1 | 0.06 |

Consistency ratio = 3% |

Criteria No. | C41 | C42 | C43 | Weights |
---|---|---|---|---|

C41 | 1 | 5 | 7 | 0.73 |

C42 | 1/5 | 1 | 3 | 0.19 |

C43 | 1/7 | 1/3 | 1 | 0.08 |

Consistency ratio = 10% |

Criteria/Sub-Criteria | Level-One Weight | Level-Two Weight | Overall Weight |
---|---|---|---|

Research and Scientific Productivity | 0.70 | 0.70 | |

Total number of book chapters produced | 0.21 | 0.15 | |

Total number of publications in Scopus | 0.72 | 0.50 | |

Total number of proceeding papers | 0.07 | 0.05 | |

Graduate Programs | 0.05 | 0.05 | |

Total number of executives programs | 0.71 | 0.04 | |

Total number of M.S. programs | 0.13 | 0.01 | |

Total number of Ph.D. programs | 0.16 | 0.01 | |

Resources | 0.12 | 0.12 | |

Total number of full professors | 0.35 | 0.04 | |

Total number of associate professors | 0.15 | 0.02 | |

Total number of assistant professors | 0.35 | 0.04 | |

Total number of lecturers | 0.09 | 0.01 | |

Total number of labs available | 0.06 | 0.01 | |

Capacity | 0.13 | 0.13 | |

Total number of students accepted into B.S. program | 0.73 | 0.10 | |

Total number of students accepted into M.S. program | 0.19 | 0.02 | |

Total number of students accepted into Ph.D. program | 0.08 | 0.01 |

Alternatives | Criteria | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

C11 | C12 | C13 | C21 | C22 | C23 | C31 | C32 | C33 | C34 | C35 | C41 | C42 | C43 | |

Weights | ||||||||||||||

0.15 | 0.50 | 0.05 | 0.04 | 0.01 | 0.01 | 0.04 | 0.02 | 0.04 | 0.01 | 0.01 | 0.10 | 0.02 | 0.01 | |

2019 | ||||||||||||||

A1 | 0 | 19 | 11 | 0 | 1 | 1 | 6 | 3 | 5 | 1 | 16 | 384 | 0 | 0 |

A2 | 1 | 29 | 2 | 0 | 1 | 1 | 7 | 7 | 4 | 3 | 17 | 183 | 2 | 1 |

A3 | 0 | 7 | 0 | 0 | 2 | 1 | 14 | 7 | 13 | 0 | 32 | 237 | 11 | 0 |

A4 | 0 | 170 | 39 | 0 | 4 | 1 | 17 | 15 | 35 | 6 | 31 | 400 | 41 | 7 |

A5 | 3 | 30 | 4 | 1 | 3 | 1 | 9 | 13 | 24 | 6 | 7 | 496 | 67 | 0 |

A6 | 0 | 41 | 2 | 0 | 2 | 1 | 15 | 15 | 13 | 0 | 24 | 330 | 17 | 0 |

A7 | 0 | 4 | 0 | 0 | 2 | 1 | 4 | 4 | 2 | 1 | 5 | 63 | 0 | 1 |

A8 | 0 | 10 | 2 | 0 | 1 | 0 | 4 | 6 | 13 | 0 | 10 | 54 | 3 | 0 |

2020 | ||||||||||||||

A1 | 0 | 19 | 4 | 0 | 1 | 1 | 6 | 3 | 5 | 1 | 16 | 379 | 7 | 3 |

A2 | 2 | 28 | 0 | 0 | 1 | 1 | 7 | 7 | 4 | 3 | 17 | 160 | 8 | 3 |

A3 | 0 | 8 | 3 | 0 | 2 | 1 | 14 | 7 | 13 | 0 | 32 | 182 | 13 | 2 |

A4 | 0 | 230 | 170 | 0 | 4 | 1 | 17 | 15 | 35 | 6 | 31 | 401 | 58 | 6 |

A5 | 1 | 32 | 5 | 1 | 3 | 1 | 9 | 13 | 24 | 6 | 7 | 507 | 98 | 0 |

A6 | 0 | 93 | 0 | 0 | 2 | 1 | 15 | 15 | 13 | 0 | 24 | 355 | 29 | 7 |

A7 | 0 | 5 | 0 | 0 | 2 | 1 | 4 | 4 | 2 | 1 | 5 | 62 | 1 | 1 |

A8 | 0 | 31 | 2 | 0 | 1 | 0 | 4 | 6 | 13 | 0 | 10 | 49 | 2 | 0 |

2021 | ||||||||||||||

A1 | 0 | 26 | 4 | 0 | 1 | 1 | 4 | 2 | 4 | 1 | 16 | 164 | 2 | 0 |

A2 | 0 | 48 | 0 | 0 | 1 | 1 | 7 | 8 | 10 | 0 | 17 | 142 | 3 | 0 |

A3 | 0 | 4 | 0 | 0 | 2 | 1 | 11 | 12 | 17 | 0 | 32 | 143 | 7 | 0 |

A4 | 1 | 289 | 26 | 0 | 4 | 1 | 16 | 29 | 31 | 3 | 31 | 426 | 26 | 12 |

A5 | 0 | 57 | 4 | 1 | 3 | 1 | 9 | 11 | 18 | 5 | 7 | 498 | 92 | 0 |

A6 | 1 | 163 | 2 | 0 | 2 | 1 | 13 | 11 | 24 | 0 | 24 | 553 | 11 | 2 |

A7 | 0 | 10 | 0 | 0 | 2 | 1 | 2 | 2 | 6 | 1 | 5 | 64 | 1 | 0 |

A8 | 0 | 57 | 0 | 0 | 1 | 0 | 6 | 8 | 12 | 2 | 10 | 45 | 4 | 0 |

2019 | |||||
---|---|---|---|---|---|

Alternatives | Q | P | PS_{i} | Final Rank | |

0.5395 | 0.0000 | 1.08 | |||

A1 | 0.0985 | 0.0000 | 0.20 | 0.183 | 5 |

A2 | 0.1081 | 0.0000 | 0.22 | 0.200 | 4 |

A3 | 0.0658 | 0.0000 | 0.13 | 0.122 | 6 |

A4 | 0.5131 | 0.0000 | 1.03 | 0.951 | 1 |

A5 | 0.2099 | 0.0000 | 0.42 | 0.389 | 2 |

A6 | 0.1451 | 0.0000 | 0.29 | 0.269 | 3 |

A7 | 0.0235 | 0.0000 | 0.05 | 0.044 | 8 |

A8 | 0.0372 | 0.0000 | 0.07 | 0.069 | 7 |

2020 | |||||

A1 | 0.0877 | 0.0000 | 0.18 | 0.163 | 5 |

A2 | 0.1666 | 0.0000 | 0.33 | 0.309 | 3 |

A3 | 0.0568 | 0.0000 | 0.11 | 0.105 | 7 |

A4 | 0.5128 | 0.0000 | 1.03 | 0.950 | 1 |

A5 | 0.1557 | 0.0000 | 0.31 | 0.288 | 4 |

A6 | 0.2190 | 0.0000 | 0.44 | 0.406 | 2 |

A7 | 0.0229 | 0.0000 | 0.05 | 0.042 | 8 |

A8 | 0.0709 | 0.0000 | 0.14 | 0.131 | 6 |

2021 | |||||

A1 | 0.0568 | 0.0000 | 0.11 | 0.105 | 6 |

A2 | 0.0905 | 0.0000 | 0.18 | 0.168 | 5 |

A3 | 0.0474 | 0.0000 | 0.09 | 0.088 | 7 |

A4 | 0.5339 | 0.0000 | 1.07 | 0.989 | 1 |

A5 | 0.1458 | 0.0000 | 0.29 | 0.270 | 3 |

A6 | 0.3381 | 0.0000 | 0.68 | 0.627 | 2 |

A7 | 0.0255 | 0.0000 | 0.05 | 0.047 | 8 |

A8 | 0.1016 | 0.0000 | 0.20 | 0.188 | 4 |

Alternatives | AHP-RAPS | AHP-TOPSIS | AHP-MOORA | AHP-VIKOR V = 0.5 |
---|---|---|---|---|

2019 | ||||

A1 | 5 | 5 | 5 | 5 |

A2 | 4 | 4 | 4 | 4 |

A3 | 6 | 6 | 6 | 6 |

A4 | 1 | 1 | 1 | 1 |

A5 | 2 | 2 | 2 | 2 |

A6 | 3 | 3 | 3 | 3 |

A7 | 8 | 8 | 8 | 8 |

A8 | 7 | 7 | 7 | 7 |

2020 | ||||

A1 | 5 | 6 | 6 | 5 |

A2 | 3 | 3 | 3 | 4 |

A3 | 7 | 7 | 7 | 7 |

A4 | 1 | 1 | 1 | 1 |

A5 | 4 | 4 | 4 | 3 |

A6 | 2 | 2 | 2 | 2 |

A7 | 8 | 8 | 8 | 8 |

A8 | 6 | 5 | 5 | 6 |

2021 | ||||

A1 | 6 | 6 | 6 | 6 |

A2 | 5 | 5 | 5 | 5 |

A3 | 7 | 7 | 7 | 7 |

A4 | 1 | 1 | 1 | 1 |

A5 | 3 | 3 | 3 | 3 |

A6 | 2 | 2 | 2 | 2 |

A7 | 8 | 8 | 8 | 8 |

A8 | 4 | 4 | 3 | 4 |

Alternatives | Original | Case 1 | Case 2 | Case 3 |
---|---|---|---|---|

2019 | ||||

A1 | 5 | 3 | 4 | 5 |

A2 | 4 | 5 | 5 | 4 |

A3 | 6 | 6 | 6 | 6 |

A4 | 1 | 1 | 1 | 1 |

A5 | 2 | 2 | 2 | 2 |

A6 | 3 | 4 | 3 | 3 |

A7 | 8 | 8 | 8 | 7 |

A8 | 7 | 7 | 7 | 8 |

2020 | ||||

A1 | 5 | 5 | 5 | 5 |

A2 | 3 | 2 | 3 | 3 |

A3 | 7 | 6 | 6 | 6 |

A4 | 1 | 1 | 1 | 1 |

A5 | 4 | 3 | 2 | 4 |

A6 | 2 | 4 | 4 | 2 |

A7 | 8 | 8 | 8 | 7 |

A8 | 6 | 7 | 7 | 8 |

2021 | ||||

A1 | 6 | 4 | 7 | 7 |

A2 | 5 | 6 | 5 | 5 |

A3 | 7 | 7 | 6 | 6 |

A4 | 1 | 1 | 1 | 1 |

A5 | 3 | 3 | 2 | 3 |

A6 | 2 | 2 | 3 | 2 |

A7 | 8 | 8 | 8 | 8 |

A8 | 4 | 5 | 4 | 4 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Bafail, O.A.; Abdulaal, R.M.S.; Kabli, M.R.
AHP-RAPS Approach for Evaluating the Productivity of Engineering Departments at a Public University. *Systems* **2022**, *10*, 107.
https://doi.org/10.3390/systems10040107

**AMA Style**

Bafail OA, Abdulaal RMS, Kabli MR.
AHP-RAPS Approach for Evaluating the Productivity of Engineering Departments at a Public University. *Systems*. 2022; 10(4):107.
https://doi.org/10.3390/systems10040107

**Chicago/Turabian Style**

Bafail, Omer A., Reda M. S. Abdulaal, and Mohammad R. Kabli.
2022. "AHP-RAPS Approach for Evaluating the Productivity of Engineering Departments at a Public University" *Systems* 10, no. 4: 107.
https://doi.org/10.3390/systems10040107