RANKING OF INSTRUCTORS IN A BRAZILIAN AIR FORCE SCHOOL USING THE AHP AND TOPSIS METHODS

Silva, Carlos Eduardo José da; Salles-Neto, Luiz Leduino de; Santos, Marcos dos

doi:10.1590/0101-7438.2023.043.00274249

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APPLICATIONS TO THE PUBLIC SECTOR SPECIAL ISSUE ARTICLES • Pesqui. Oper. 44 • 2024 • https://doi.org/10.1590/0101-7438.2023.043.00274249 copy

RANKING OF INSTRUCTORS IN A BRAZILIAN AIR FORCE SCHOOL USING THE AHP AND TOPSIS METHODS

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

The selection process for instructors at the Brazilian Air Force Officers Improvement School (EAOAR) needs improvement to provide clearer guidance to the Commandant. This article aims to streamline and enhance the process by making it more efficient, less subjective, and more reliable. Researchers employed the Analytic Hierarchy Process (AHP) to determine criteria weights and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) to rank candidates. They used Three Decision Methods (3DM) Software Web (v.1) for efficient calculations. Results showed that candidates closer to the Positive Ideal Solution (PIS) received favorable indications, while those closer to the Negative Ideal Solution (NIS) faced rejections. The AHP-TOPSIS hybrid approach successfully ranked candidates and expedited the process. Moreover, this approach has broader applications, including assessing candidates for international missions in the Brazilian Navy and Army, and evaluating employee performance in any organization. Future research could explore classification methods like the ELECTRE-TRI.

Keywords:
AHP-TOPSIS methods; Brazilian Air Force; personnel selection

Authors	Document title
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Nong & Ha (2021NONG N & HA D. 2021. Application of MCDM methods to qualified personnel selection in distribution science: Case of logistics companies. Journal of Distribution Science, 19(8): 25-35.)	Application of MCDM methods to Qualified Personnel Selection in Distribution Science: Case of Logistics Companies
Petridis et al. (2021PETRIDIS K, DROGALAS G & ZOGRAFIDOU E. 2021. Internal auditor selection using a TOPSIS/non-linear programming model. Annals of Operations Research, 296(1-2): 539.)	Internal auditor selection using a TOPSIS/non-linear programming model
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Intensity of Importance	Definition	Explanation
1	Equal Importance	Two factors contribute equally to the objective.
3	Moderate Importance	Experience and judgement slightly favour one factor over another.
5	Strong Importance	Experience and judgement strongly favour one factor over another.
7	Very Strong Importance	One factor is strongly favoured and its dominance demonstrated in practice.
9	Extreme Importance	The evidence favouring one factor over another is of the highest possible validity.
2, 4, 6, 8	Intermediate Values	When compromise is needed in assigning importance between two adjacent values.

Criteria	Description	Goal
MFINC	Final average of the courses taken, ranging from 0.000 to10.000.	Maximize
NOTCC	Grade for the oral presentation of the course completion work, ranging from 0.000 to 10.000.	Maximize
AIOTG	Subjective evaluation of the Instructor Guiding Group Work (IOTG), expressed in a verbal scale, in which: 1- I do not indicate; 2- Neutral; and 3- I Indicate.	Maximize
AOTCC	Advisor’s subjective assessment of the course completion work, expressed on a verbal scale, in which: 1- I do not indicate; 2- Neutral; and 3- I Indicate.	Maximize
COHOR	Horizontal concept, in which each student evaluates his peers in the class, expressed in a verbal scale, in which: 1- I do not indicate; 2- Neutral; and 3- Indico. The performance in this criterion is measured by the sum of the evaluations received.	Maximize
AAPSI	Evaluation carried out by the School’s Psychopedagogical Advisory, expressed in a verbal scale, in which: 1- I do not indicate; 2- Neutral; and 3- I indicate.	Maximize

Alternatives		S₁	S₂	S₃	S₄	S₅	S₆	S₇	S₈	S₉	S₁₀	S₁₁	S₁₂	S₁₃	S₁₄
Criteria (Max)	MFINC	9,817	9,810	9,807	9,805	9,792	9,779	9,775	9,753	9,746	9,745	9,743	9,738	9,736	9,735
	NOTCC	9,920	9,710	10,000	9,710	10,000	10,000	9,660	10,000	10,000	9,860	9,850	10,000	9,850	10,000
	AIOTG	3	3	3	3	3	3	3	3	3	3	3	3	1	3
	AOTCC	3	3	3	3	3	3	3	3	3	3	3	3	3	3
	COHOR	797	550	739	348	162	235	444	275	241	327	297	238	105	159
	AAPSI	2	2	3	3	2	2	2	2	3	2	2	1	1	2
Alternatives		S ₁₅	S ₁₆	S ₁₇	S ₁₈	S ₁₉	S ₂₀	S ₂₁	S ₂₂	S ₂₃	S ₂₄	S ₂₅	S ₂₆	S ₂₇	S ₂₈
Criteria (Max)	MFINC	9,724	9,721	9,717	9,716	9,711	9,708	9,704	9,702	9,702	9,692	9,691	9,679	9,678	9,676
	NOTCC	9,700	9,820	9,860	9,540	9,880	9,810	9,860	9,620	9,790	9,310	9,930	9,630	9,370	10,000
	AIOTG	2	3	3	3	3	3	3	3	3	3	2	3	3	3
	AOTCC	3	3	3	1	3	3	3	3	1	3	3	2	3	3
	COHOR	188	249	206	102	334	144	138	151	132	144	165	150	144	560
	AAPSI	2	2	2	2	2	3	2	2	2	2	2	2	2	3
Alternatives		S ₂₉	S ₃₀	S ₃₁	S ₃₂	S ₃₃	S ₃₄	S ₃₅	S ₃₆	S ₃₇	S ₃₈	S ₃₉	S ₄₀	S ₄₁	S ₄₂
Criteria (Max)	MFINC	9,670	9,667	9,665	9,662	9,624	9,616	9,613	9,611	9,609	9,609	9,592	9,582	9,573	9,571
	NOTCC	9,860	9,500	9,640	9,760	9,810	9,910	10,000	10,000	9,700	10,000	9,810	9,450	9,540	9,620
	AIOTG	3	3	3	3	3	3	3	3	1	3	3	3	3	3
	AOTCC	3	3	3	3	3	3	3	3	3	2	3	3	3	3
	COHOR	292	430	134	393	110	166	480	327	417	196	167	170	197	313
	AAPSI	3	2	2	2	2	2	2	2	2	2	2	2	3	3
Alternatives		S ₄₃	S ₄₄	S ₄₅	S ₄₆	S ₄₇	S ₄₈	S ₄₉	S ₅₀	S ₅₁	S ₅₂	S ₅₃	S ₅₄	S ₅₅	S ₅₆
Criteria (Max)	MFINC	9,562	9,555	9,552	9,549	9,548	9,538	9,530	9,503	9,478	9,459	9,411	9,401	9,393	9,341
	NOTCC	10,000	9,480	9,490	9,760	9,770	9,880	10,000	10,000	10,000	9,880	9,840	9,810	10,000	10,000
	AIOTG	3	3	3	3	1	2	3	2	3	3	3	3	3	3
	AOTCC	3	3	2	3	1	3	3	3	3	3	2	1	3	2
	COHOR	356	250	168	320	135	138	120	192	319	139	153	153	159	189
	AAPSI	2	2	2	2	2	3	2	3	2	3	2	2	2	2
Alternatives		S ₅₇	S ₅₈	S ₅₉	S ₆₀	S ₆₁	S ₆₂	S ₆₃	S ₆₄	S ₆₅	S ₆₆	S ₆₇
Criteria (Max)	MFINC	9,335	9,319	9,308	9,306	9,262	9,245	9,226	9,218	9,197	9,176	9,101
	NOTCC	9,880	10,000	10,000	10,000	10,000	9,810	9,890	9,820	10,000	9,880	10,000
	AIOTG	3	3	1	1	3	3	3	1	3	3	3
	AOTCC	1	3	2	1	3	1	3	3	2	3	2
	COHOR	117	212	104	98	189	283	147	127	192	195	115
	AAPSI	2	2	2	2	2	3	1	2	3	3	2

DM1							DM2
	MFDC	NTCC	IOTG	OTCC	COHO	APSI		MFDC	NTCC	IOTG	OTCC	COHO	APSI
MFDC	1	6	6	6	3	4	MFDC	1	1/3	1/5	1/5	1/3	1/7
NTCC	1/6	1	1	1/6	4	4	NTCC	3	1	1	1	4	1/5
IOTG	1/6	1	1	4	4	4	IOTG	5	1	1	1	4	1/3
OTCC	1/6	6	1/4	1	1/4	1/4	OTCC	5	1	1	1	2	1/7
COHO	1/3	1/4	1/4	4	1	1/7	COHO	3	1/4	1/4	1/2	1	1/5
APSI	1/4	1/4	1/4	4	7	1	APSI	7	5	3	7	5	1
DM3							DM4
	MFDC	NTCC	IOTG	OTCC	COHO	APSI		MFDC	NTCC	IOTG	OTCC	COHO	APSI
MFDC	1	1/5	1/5	1/5	1/5	1/4	MFDC	1	1	1/4	1/4	1/2	1/7
NTCC	5	1	1	1	5	3	NTCC	1	1	1/4	1/4	1/4	1/7
IOTG	5	1	1	5	1	4	IOTG	4	4	1	1	1	1
OTCC	5	1	1/5	1	1/5	1/4	OTCC	4	4	1	1	1	1
COHO	5	1/5	1	5	1	4	COHO	2	4	1	1	1	1/4
APSI	4	1/3	1/4	4	1/4	1	APSI	7	7	1	1	4	1
DM5							DM6
	MFDC	NTCC	IOTG	OTCC	COHO	APSI		MFDC	NTCC	IOTG	OTCC	COHO	APSI
MFDC	1	1/6	1/6	1/6	1	3	MFDC	1	1	1	9	9	9
NTCC	6	1	1/6	3	5	4	NTCC	1	1	1	9	9	9
IOTG	6	6	1	5	4	4	IOTG	1	1	1	9	9	9
OTCC	6	1/3	1/5	1	3	3	OTCC	1/9	1/9	1/9	1	9	9
COHO	1	1/5	1/4	1/3	1	1	COHO	1/9	1/9	1/9	1/9	1	1
APSI	1/3	1/4	1/4	1/3	1	1	APSI	1/9	1/9	1/9	1/9	1	1
DM7							Aggregate preferences
	MFDC	NTCC	IOTG	OTCC	COHO	APSI		MFDC	NTCC	IOTG	OTCC	COHO	APSI
MFDC	1	1/9	1/9	1/2	1/7	1/9	MFDC	1	0,3333	0,1771	0,2924	0,2877	0,1314
NTCC	9	1	1	9	3	1	NTCC	3,0000	1	0,6300	1,3104	1,4422	0,3057
IOTG	9	1	1	9	5	2	IOTG	5,6462	1,5874	1	2,0801	2,7144	0,8736
OTCC	2	1/9	1/9	1	1/9	1/9	OTCC	3,4200	0,7631	0,4807	1	0,6057	0,2513
COHO	7	1/3	1/5	9	1	1	COHO	3,4760	0,6934	0,3684	1,6510	1	0,3684
APSI	9	1	1/2	9	1	1	APSI	7,6117	3,2711	1,1447	3,9791	2,7144	1

	MFDC	NTCC	IOTG	OTCC	COHO	APSI	Priority	λ _Max	CI	RI	CR
MFDC	0,0414	0,0436	0,0466	0,0284	0,0328	0,0448	0,0396	6,0954	0,0191	1,24	0,0154
NTCC	0,1242	0,1307	0,1657	0,1271	0,1646	0,1043	0,1361
IOTG	0,2338	0,2075	0,2631	0,2017	0,3097	0,2981	0,2523
OTCC	0,1416	0,0998	0,1265	0,0970	0,0691	0,0858	0,1033
COHO	0,1439	0,0907	0,0969	0,1601	0,1141	0,1257	0,1219
APSI	0,3151	0,4277	0,3012	0,3858	0,3097	0,3413	0,3468

	D+	D-	ξ		D+	D-	ξ		D+	D-	ξ
S1	0.0191	0.0481	0.7156	S13	0.0574	0.0092	0.1385	S25	0.0402	0.0241	0.3750
S2	0.0232	0.0388	0.6257	S14	0.0390	0.0306	0.4398	S26	0.0397	0.0295	0.4264
S3	0.0031	0.0565	0.9481	S15	0.0392	0.0243	0.3830	S27	0.0397	0.0305	0.4346
S4	0.0239	0.0469	0.6622	S16	0.0349	0.0315	0.4743	S28	0.0126	0.0513	0.8024
S5	0.0389	0.0306	0.4409	S17	0.0368	0.0310	0.4568	S29	0.0269	0.0462	0.6317
S6	0.0355	0.0313	0.4685	S18	0.0427	0.0290	0.4047	S30	0.0274	0.0352	0.5626
S7	0.0268	0.0356	0.5701	S19	0.0312	0.0329	0.5135	S31	0.0402	0.0305	0.4315
S8	0.0337	0.0319	0.4857	S20	0.0348	0.0450	0.5642	S32	0.0288	0.0343	0.5433
S9	0.0296	0.0456	0.6064	S21	0.0400	0.0305	0.4329	S33	0.0413	0.0304	0.4244
S10	0.0315	0.0328	0.5100	S22	0.0394	0.0306	0.4370	S34	0.0387	0.0307	0.4422
S11	0.0328	0.0322	0.4957	S23	0.0413	0.0291	0.4132	S35	0.0255	0.0366	0.5894
S12	0.0485	0.0248	0.3389	S24	0.0397	0.0305	0.4346	S36	0.0315	0.0328	0.5101
S37	0.0354	0.0272	0.4345	S49	0.0408	0.0305	0.4274	S61	0.0376	0.0308	0.4504
S38	0.0376	0.0299	0.4427	S50	0.0340	0.0411	0.5473	S62	0.0289	0.0451	0.6097
S39	0.0386	0.0307	0.4425	S51	0.0318	0.0326	0.5062	S63	0.0516	0.0238	0.3160
S40	0.0385	0.0307	0.4434	S52	0.0351	0.0450	0.5623	S64	0.0460	0.0213	0.3163
S41	0.0320	0.0453	0.5861	S53	0.0395	0.0295	0.4275	S65	0.0326	0.0446	0.5778
S42	0.0258	0.0464	0.6428	S54	0.0403	0.0292	0.4197	S66	0.0321	0.0453	0.5853
S43	0.0303	0.0334	0.5245	S55	0.0390	0.0306	0.4398	S67	0.0413	0.0294	0.4158
S44	0.0349	0.0315	0.4745	S56	0.0379	0.0298	0.4401
S45	0.0389	0.0296	0.4324	S57	0.0420	0.0290	0.4089
S46	0.0318	0.0327	0.5066	S58	0.0366	0.0310	0.4592
S47	0.0466	0.0192	0.2923	S59	0.0472	0.0197	0.2946
S48	0.0368	0.0409	0.5265	S60	0.0481	0.0192	0.2849

	Alternative	ξ		Alternative	ξ		Alternative	ξ
1º	S3	0.9481	24º	S10	0.5100	47º	S21	0.4329
2º	S28	0.8024	25º	S46	0.5066	48º	S45	0.4324
3º	S1	0.7156	26º	S51	0,5062	49º	S31	0.4315
4º	S4	0.6622	27º	S11	0,4957	50º	S53	0.4275
5º	S42	0.6428	28º	S8	0.4857	51º	S49	0.4274
6º	S29	0.6317	29º	S44	0.4745	52º	S26	0.4264
7º	S2	0.6257	30º	S16	0.4743	53º	S33	0.4244
8º	S62	0.6097	31º	S6	0.4685	54º	S54	0.4197
9º	S9	0.6064	32º	S58	0.4592	55º	S67	0.4158
10º	S35	0.5894	33º	S17	0.4568	56º	S23	0.4132
11º	S41	0.5861	34º	S61	0.4504	57º	S57	0.4089
12º	S66	0.5853	35º	S40	0.4434	58º	S18	0.4047
13º	S65	0.5778	36º	S38	0.4427	59º	S15	0.3830
14º	S7	0.5701	37º	S39	0.4425	60º	S25	0.3750
15º	S20	0.5642	38º	S34	0.4422	61º	S12	0.3389
16º	S30	0.5626	39º	S5	0.4409	62º	S64	0.3163
17º	S52	0.5623	40º	S56	0.4401	63º	S63	0.3160
18º	S50	0.5473	41º	S14	0.4398	64º	S59	0.2946
19º	S32	0.5433	42º	S55	0.4398	65º	S47	0.2923
20º	S48	0.5265	43º	S22	0.4370	66º	S60	0.2849
21º	S43	0.5245	44º	S27	0.4346	67º	S13	0.1385
22º	S19	0.5135	45º	S24	0.4346
23º	S36	0.5101	46º	S37	0.4345

	Alternative	Appointed?		Alternative	Appointed?		Alternative	Appointed?
1º	S3	Yes	24º	S10	Yes	47º	S21	No
2º	S28	Yes	25º	S46	Yes	48º	S45	Yes
3º	S1	Yes	26º	S51	Yes	49º	S31	Yes
4º	S4	Yes	27º	S11	Yes	50º	S53	Yes
5º	S42	Yes	28º	S8	No	51º	S49	Yes
6º	S29	Yes	29º	S44	Yes	52º	S26	No
7º	S2	Yes	30º	S16	Yes	53º	S33	Yes
8º	S62	Yes	31º	S6	Yes	54º	S54	Yes
9º	S9	Yes	32º	S58	Yes	55º	S67	Yes
10º	S35	No	33º	S17	Yes	56º	S23	Yes
11º	S41	Yes	34º	S61	Yes	57º	S57	No
12º	S66	Yes	35º	S40	Yes	58º	S18	No
13º	S65	Yes	36º	S38	Yes	59º	S15	Yes
14º	S7	Yes	37º	S39	Yes	60º	S25	Yes
15º	S20	Yes	38º	S34	Yes	61º	S12	Yes
16º	S30	Yes	39º	S5	Yes	62º	S64	No
17º	S52	Yes	40º	S56	Yes	63º	S63	No
18º	S50	Yes	41º	S14	Yes	64º	S59	No
19º	S32	No	42º	S55	Yes	65º	S47	No
20º	S48	Yes	43º	S22	Yes	66º	S60	No
21º	S43	No	44º	S27	No	67º	S13	No
22º	S19	Yes	45º	S24	Yes
23º	S36	Yes	46º	S37	Yes

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Matrix order	1	2	3	4	5	6	7	. . .	14	15
RI	0.00	0.00	0.58	0.90	1.12	1.24	1.32	...	1.57	1.59