Detecting unbalanced bids via an improved grading-based model

Gul Polat; Harun Turkoglu; Atilla Damci; Firat Dogu Akin

doi:10.2478/otmcj-2020-0004

Figures & Tables

Comparison of the ranking of bidders according to the previous model developed by Polat et al. (2019) and the current model.

Grade values for grading systems 6, 7, and 8

Comparison ratio	Grade	Comparison ratio	Grade
r ≤ 0.9	42	1.005 < r ≤ 1.010	20
0.900 < r ≤ 0.905	41	1.010 < r ≤ 1.015	19
0.905 < r ≤ 0.910	40	1.015 < r ≤ 1.020	18
0.910 < r ≤ 0.915	39	1.020 < r ≤ 1.025	17
0.915 < r ≤ 0.920	38	1.025 < r ≤ 1.030	16
0.920 < r ≤ 0.925	37	1.030 < r ≤ 1.035	15
0.925 < r ≤ 0.930	36	1.035 < r ≤ 1.040	14
0.930 < r ≤ 0.935	35	1.040 < r ≤ 1.045	13
0.935 < r ≤ 0.940	34	1.045 < r ≤ 1.050	12
0.940 < r ≤ 0.945	33	1.050 < r ≤ 1.055	11
0.945 < r ≤ 0.950	32	1.055 < r ≤ 1.060	10
0.950 < r ≤ 0.955	31	1.060 < r ≤ 1.065	9
0.955 < r ≤ 0.960	30	1.065 < r ≤ 1.070	8
0.960 < r ≤ 0.965	29	1.070 < r ≤ 1.075	7
0.965 < r ≤ 0.970	28	1.075 < r ≤ 1.080	6
0.970 < r ≤ 0.975	27	1.080 < r ≤ 1.085	5
0.975 < r ≤ 0.980	26	1.085 < r ≤ 1.090	4
0.980 < r ≤ 0.985	25	1.090 < r ≤ 1.095	3
0.985 < r ≤ 0.990	24	1.095 < r ≤ 1.100	2
0.990 < r ≤ 0.995	23	1.100 < r	1
0.995 < r ≤ 1.000	22
1.000 < r ≤ 1.005	21

Input data for illustrative example

Activity ID	Unit	Quantity	Unit prices (in TL [Turkish Liras])

			O	B ₁	B ₂	B ₃	B ₄	B ₅	B ₆	B ₇	B ₈
A₁	m³	700	14.38	14.75	13.07	15.50	15.56	14.92	13.64	14.88	14.66
A₂	m³	365	38.83	41.91	41.25	42.38	35.58	41.11	38.14	40.41	36.32
A₃	m³	850	2.84	3.08	2.59	2.96	2.63	2.98	2.84	2.86	2.68
A₄	m³	736	4.83	5.29	4.57	5.27	5.15	4.36	4.46	4.62	4.72
A₅	M	198	67.70	65.94	63.94	74.14	65.43	69.76	68.75	69.39	62.33
A₆	m³	59	31.88	29.82	28.96	29.66	29.41	33.12	29.21	28.89	29.34
A₇	m³	150	14.19	13.60	13.21	14.34	13.67	13.78	15.17	13.64	15.11
A₈	m³	90	29.19	26.97	28.68	29.95	31.42	30.40	31.12	29.52	30.38
A₉	m³	2000	178.63	170.44	183.53	173.77	166.04	189.94	187.99	175.84	169.66
A₁₀	M	1200	335.43	330.84	362.48	336.29	333.25	322.75	318.94	329.43	353.08
A₁₁	M	650	68.40	65.53	74.79	69.38	63.26	64.79	69.13	72.10	73.25
A₁₂	m³	350	52.20	51.26	47.00	54.89	56.72	47.53	54.14	52.51	56.04
A₁₃	m³	100	86.29	84.53	92.11	85.72	91.16	88.14	85.52	88.90	82.79
A₁₄	m³	360	121.63	112.82	133.19	131.99	130.73	122.52	128.27	111.87	124.88
A₁₅	M	36	29.19	29.64	28.97	30.16	27.98	28.77	31.89	29.44	27.92
A₁₆	M	40	33.40	35.59	34.05	32.36	36.04	35.12	36.57	32.56	36.23
A₁₇	m²	1000	22.18	20.98	23.41	20.95	23.78	22.35	23.19	23.00	20.95
A₁₈	m²	750	23.24	23.34	21.41	23.86	21.85	21.32	24.63	21.88	22.87
A₁₉	m²	635	31.39	32.96	31.66	29.76	30.56	32.36	28.90	29.47	33.33
A₂₀	m²	400	35.64	36.75	37.55	36.58	39.03	35.38	37.56	35.40	36.21
A₂₁	m²	348	38.05	39.78	38.77	39.28	35.44	35.79	39.19	39.63	35.08
A₂₂	m²	250	50.16	50.34	49.73	52.14	45.85	52.27	49.12	50.30	49.46
A₂₃	m²	100	26.56	26.26	27.36	26.88	25.07	24.98	27.50	24.59	27.82
A₂₄	m²	150	35.63	36.26	34.12	37.72	34.84	35.66	35.98	32.82	35.03
A₂₅	m²	75	23.61	24.87	21.25	21.81	24.29	23.15	23.41	24.72	24.89
A₂₆	m²	98	28.59	25.89	26.65	28.53	28.52	31.41	28.69	28.21	30.46
A₂₇	m²	50	27.29	27.41	25.95	29.84	26.82	28.77	25.32	25.65	24.73
A₂₈	m²	43	29.98	30.20	29.84	27.50	30.75	28.48	32.57	28.26	30.09
A₂₉	m²	66	44.61	45.92	47.46	44.67	40.65	48.92	42.76	43.53	41.53
A₃₀	m²	40	58.94	54.01	56.03	53.11	59.19	59.65	54.99	59.98	60.40
A₃₁	m²	40	39.54	43.20	42.80	39.07	37.86	38.69	42.66	41.16	39.66
A₃₂	m²	100	40.24	42.55	39.59	41.02	42.52	43.04	41.36	41.56	36.69
A₃₃	m²	450	1.94	1.75	2.08	2.01	1.94	2.00	1.99	2.01	1.75
A₃₄	m²	350	2.35	2.17	2.48	2.39	2.27	2.55	2.20	2.58	2.19
A₃₅	m²	40	16.91	15.70	15.29	15.72	16.19	15.85	15.66	16.05	17.10
A₃₆	m²	60	20.71	18.91	20.89	20.97	20.51	21.01	22.31	20.95	20.96
A₃₇	m²	50	14.68	15.50	14.91	13.82	13.55	13.29	14.37	14.57	13.84
A₃₈	m²	1000	27.71	26.86	27.56	26.32	29.55	26.55	26.78	27.64	28.43
A₃₉	m²	450	43.24	39.04	46.78	45.19	46.00	43.59	45.01	45.12	47.13
A₄₀	m²	900	32.39	34.31	29.90	34.25	33.58	32.77	29.28	31.71	29.34
A₄₁	m²	650	33.90	33.90	30.71	36.87	36.48	30.83	35.46	31.94	31.03
A₄₂	m²	100	6.29	6.84	5.71	6.33	5.92	5.68	5.97	6.86	6.02
A₄₃	m²	1000	1.29	1.29	1.31	1.23	1.40	1.36	1.22	1.19	1.18
A₄₄	m²	150	7.33	7.01	6.67	6.64	7.45	7.91	7.12	7.29	7.64
A₄₅	m²	2000	11.78	11.58	12.45	11.39	11.86	12.38	11.66	12.90	12.94
A₄₆	m²	1600	30.04	29.74	30.87	31.84	27.61	30.66	31.46	29.77	30.38
A₄₇	m²	2000	29.56	30.55	30.33	30.01	32.43	28.17	30.23	29.49	27.07
A₄₈	m³	600	4.59	4.65	4.72	4.72	4.68	4.50	4.27	4.87	4.15
A₄₉	m³	450	5.84	5.36	6.42	5.29	5.88	6.11	5.41	6.06	5.64
A₅₀	m²	750	4.83	5.29	4.61	4.97	5.18	4.77	4.79	4.86	5.21
A₅₁	m²	1600	115.81	107.85	117.90	125.97	116.49	107.78	122.21	120.78	120.28
A₅₂	m²	650	136.51	142.73	139.82	133.89	126.59	128.11	149.12	141.47	126.39
A₅₃	m²	650	88.36	89.02	81.44	91.52	92.22	93.89	89.25	79.90	81.71
A₅₄	m²	250	123.24	133.28	134.02	112.88	133.04	134.99	119.83	131.82	114.27
A₅₅	m²	690	50.34	48.72	47.31	53.42	49.00	46.54	53.07	51.53	45.89
A₅₆	m²	600	170.88	157.50	161.31	160.47	179.91	166.13	182.67	164.95	182.67
A₅₇	m²	350	319.38	338.86	338.76	344.12	339.48	325.54	350.95	306.97	302.08
A₅₈	m²	400	250.09	261.30	253.70	264.69	249.89	244.55	265.10	264.46	226.00
A₅₉	ton	1300	2096.56	2127.33	2152.31	1941.54	2089.57	2077.30	2026.49	1988.62	2045.57
A₆₀	ton	1650	2017.94	2140.37	2143.31	1877.71	1975.24	1998.95	1887.98	2160.53	1974.92
A₆₁	ton	350	1972.66	1871.37	1796.76	2120.92	2169.36	1789.12	2155.85	1837.37	1987.05
A₆₂	ton	1000	1939.23	1985.11	1832.36	1762.37	1999.50	2115.62	2044.00	1860.08	1918.36
A₆₃	ton	1150	1914.79	1914.13	1780.31	2038.14	1781.33	1987.31	1875.30	1810.11	1885.75
A₆₄	ton	200	3386.01	3642.50	3635.81	3425.98	3236.22	3658.23	3346.48	3591.23	3238.26
A₆₅	Kg	4000	8.64	9.39	8.07	8.58	7.87	8.65	9.13	8.38	7.97
A₆₆	m²	2000	9.59	9.16	10.29	10.06	9.74	10.16	9.55	8.82	10.51
A₆₇	m²	600	13.00	12.96	13.32	14.30	14.00	13.68	11.84	12.36	14.07
A₆₈	m²	150	5.23	5.62	5.34	5.53	5.32	5.06	4.91	5.17	5.45
A₆₉	m²	2000	15.65	14.26	16.26	14.72	16.25	15.96	14.87	15.75	16.47
A₇₀	m²	2000	18.56	19.20	16.81	18.13	19.78	18.95	17.37	17.73	18.78
A₇₁	m²	700	28.60	27.78	27.36	26.28	31.23	30.24	27.97	27.13	28.49
A₇₂	m²	2000	20.88	21.98	22.75	22.95	19.38	19.91	21.36	19.67	22.51

Final scores of bidders

Bidder ID	Grading system number								Final Score	Ranking

	1 (15%)	2 (10%)	3 (5%)	4 (10%)	5 (30%)	6 (5%	7 (5%)	8 (20%)
B₁	51.35	41.16	39.12	31.82	50.00	40.19	36.59	45.24	44.84	8
B₂	49.30	47.62	45.27	50.00	66.67	51.24	47.13	69.05	58.15	1
B₃	49.52	62.05	59.75	77.27	2.38	66.41	62.42	76.19	46.74	6
B₄	50.73	55.00	53.22	63.64	54.76	54.74	51.55	50.00	53.88	4
B₅	50.23	43.29	42.19	40.91	42.86	43.47	41.00	52.38	45.62	7
B₆	49.74	54.88	53.38	63.64	52.38	57.57	54.73	64.29	56.17	3
B₇	49.59	53.83	52.26	59.09	38.10	55.75	52.74	61.90	50.58	5
B₈	50.35	58.99	57.40	68.18	61.90	59.61	56.58	52.38	58.00	2

Detecting unbalanced bids via an improved grading-based model

Figures & Tables

Fig. 1

Grade values for grading systems 6, 7, and 8

Input data for illustrative example

Final scores of bidders

Paradigm

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