Distribution-Free Model for Ambulance Location Problem with Ambiguous Demand

Table 4

Computational results on instances with data generated from uniform distribution.

Sampling approach			MIP-DF1			MIP-DF2			Sampling approach			MIP-DF1			MIP-DF2			Sampling approach			MIP-DF1			MIP-DF2
CT	Obj	Sel (%)	CT	Obj	Sel (%)	CT	Obj	Sel (%)	CT	Obj	Sel (%)	CT	Obj	Sel (%)	CT	Obj	Sel (%)	CT	Obj	Sel (%)	CT	Obj	Sel (%)	CT	Obj	Sel (%)
1	(2,6)	2.7	89	73.17	0.1	149	99.06	0.1	107	92.22	2.8	96	73.73	0.1	155	99.33	0.1	107	91.67	2.7	106	75.85	0.1	185	99.87	0.1	107	91.28
2	(4,12)	4.7	169	74.23	0.0	291	99.19	0.0	207	91.22	5.8	181	74.38	0.1	303	99.97	0.1	207	93.63	5.0	199	77.02	0.0	363	99.82	0.0	207	93.38
3	(6,18)	7.2	258	75.06	0.1	438	99.76	0.1	312	91.06	7.5	279	80.82	0.1	456	99.96	0.1	312	93.69	7.8	304	83.37	0.1	546	99.97	0.1	312	93.57
4	(8,24)	9.9	314	79.56	0.1	553	99.93	0.1	385	92.06	11.1	338	82.02	0.1	577	99.99	0.1	385	96.02	11.2	366	84.92	0.1	697	99.94	0.1	385	96.20
5	(10,30)	13.2	415	84.06	0.1	722	98.96	0.1	512	94.06	14.3	441	83.22	0.2	752	99.83	0.1	512	96.92	14.2	476	86.09	0.1	902	99.93	0.1	512	96.92
6	(12,36)	17.0	475	82.49	0.2	843	98.70	0.1	591	93.67	18.1	504	82.51	0.1	879	99.82	0.1	591	96.08	18.9	535	87.26	0.1	1059	99.97	0.1	591	96.09
7	(14,42)	21.5	573	81.11	0.2	1006	98.49	0.2	712	96.06	24.3	609	82.17	0.2	1048	99.53	0.2	712	95.89	23.3	644	86.08	0.2	1258	99.92	0.2	712	95.82
8	(16,48)	24.8	686	75.32	0.2	1185	98.96	0.2	849	97.25	28.4	727	83.07	0.2	1233	99.49	0.2	849	96.13	28.1	768	90.63	0.2	1473	99.99	0.3	849	96.22
9	(18,54)	31.3	691	83.53	0.3	1236	99.74	0.4	858	97.09	35.1	731	83.97	0.3	1290	99.88	0.3	858	97.65	35.2	760	89.06	0.3	1560	99.94	0.3	858	97.58
10	(20,60)	37.2	794	81.74	0.3	1409	98.87	0.3	989	96.57	42.8	843	84.89	0.3	1469	99.47	0.3	989	97.73	43.2	892	90.04	0.3	1769	99.97	0.3	989	97.38
11	(22,66)	45.1	830	80.72	0.4	1493	99.49	0.3	1031	97.58	51.8	880	83.28	0.4	1559	99.82	0.3	1031	97.23	51.6	930	89.67	0.5	1889	99.95	0.3	1031	97.27
12	(24,72)	54.3	1025	79.70	0.4	1771	99.27	0.4	1267	98.35	60.1	1083	84.82	0.5	1843	99.49	0.4	1267	97.76	63.7	1146	90.14	0.4	2203	99.93	0.4	1267	97.77
13	(26,78)	63.1	1026	81.42	0.5	1819	98.98	0.4	1274	97.82	74.3	1087	86.78	0.5	1897	99.36	0.4	1274	97.78	76.5	1146	90.23	0.4	2287	99.97	0.5	1273	98.37
14	(28,84)	78.2	1101	79.03	0.5	1949	98.69	0.8	1361	98.04	87.8	1165	87.90	0.5	2033	99.35	0.7	1361	98.89	87.0	1227	90.56	0.5	2453	99.98	0.6	1361	98.08
15	(30,90)	90.7	1091	80.98	0.6	1997	99.15	0.6	1367	96.29	101.8	1155	83.29	0.6	2087	99.81	0.6	1367	98.07	102.0	1225	89.86	0.6	2537	99.99	0.8	1367	98.17
16	(32,96)	106.2	1160	87.98	0.7	2123	99.44	0.7	1449	97.87	118.3	1229	83.83	0.7	2219	99.88	0.6	1449	98.49	119.3	1300	91.05	0.6	2698	99.98	0.6	1449	98.15
17	(34,102)	120.2	1298	75.72	0.7	2328	99.69	0.7	1614	98.21	137.7	1374	88.60	0.8	2430	99.97	0.7	1614	98.24	126.0	1452	90.85	0.7	2940	99.99	0.8	1614	98.18
18	(36,108)	139.4	1408	81.21	0.8	2509	99.47	0.8	1752	98.09	154.4	1492	89.28	0.8	2617	99.83	0.8	1752	97.99	154.8	1580	91.73	0.8	3156	99.99	0.8	1752	98.09
19	(38,114)	161.8	1508	81.70	0.9	2676	98.99	1.1	1877	97.42	176.0	1598	91.30	0.9	2790	99.34	0.8	1877	99.08	175.5	1688	91.86	0.9	3360	99.99	0.9	1877	98.72
20	(40,120)	220.6	1628	77.19	1.0	2869	99.89	1.0	2029	98.73	200.7	1732	87.53	1.1	2990	99.97	0.9	2029	98.79	190.4	1827	91.38	1.0	3590	99.98	0.9	2029	98.75
21	(42,126)	278.0	1622	83.54	1.0	2900	99.78	1.0	2017	97.32	260.9	1718	88.54	1.0	3026	98.76	1.0	2017	98.18	267.0	1812	90.89	1.2	3655	99.99	1.0	2017	98.48
22	(44,132)	318.9	1735	84.94	1.1	3088	99.85	1.5	2165	98.57	297.0	1840	89.22	1.2	3220	99.25	1.2	2165	98.86	287.3	1952	92.06	1.1	3880	99.99	1.1	2165	98.50
23	(46,138)	363.0	1937	81.41	1.2	3372	98.93	1.3	2406	97.96	322.2	2048	89.37	1.2	3510	99.34	1.4	2406	99.06	346.1	2170	89.89	1.2	4199	100.00	1.2	2406	98.09
24	(48,144)	422.6	1968	82.26	1.3	3461	99.32	1.3	2453	98.14	367.4	2085	88.46	1.3	3605	99.56	1.5	2453	99.12	355.6	2211	93.00	1.3	4326	99.99	1.3	2453	98.19
25	(50,150)	472.7	1919	81.11	1.4	3456	99.99	1.5	2407	96.29	401.9	2037	86.99	1.4	3606	99.99	1.4	2407	98.57	425.7	2161	92.59	1.5	4356	99.95	1.4	2407	98.19
26	(52,156)	530.0	1906	80.96	1.5	3484	98.78	1.7	2392	96.58	449.5	2021	89.52	1.4	3640	99.99	1.5	2392	95.68	448.6	2142	91.82	1.5	4420	99.99	1.5	2392	98.54
27	(54,162)	591.3	2096	83.87	1.6	3751	98.46	1.7	2617	97.61	511.7	2221	90.45	1.6	3913	99.98	1.7	2617	95.44	483.0	2355	93.46	1.8	4723	99.99	1.6	2617	98.93
28	(56,168)	631.0	2110	77.58	1.7	3819	99.33	1.9	2643	98.29	577.7	2234	91.57	1.8	3987	99.98	1.8	2643	95.26	555.0	2365	90.45	1.8	4827	99.99	1.7	2643	98.31
29	(58,174)	678.0	2175	79.98	1.8	3937	98.98	1.8	2720	97.14	630.3	2307	90.22	2.0	4111	99.69	1.9	2720	96.23	618.9	2444	91.28	1.9	4981	100.00	1.9	2720	99.14
30	(60,180)	759.3	2384	83.21	1.9	4240	99.67	2.0	2979	98.41	679.1	2527	89.78	1.9	4419	99.79	2.3	2979	97.21	687.8	2679	91.43	2.1	5316	99.99	2.0	2979	98.69
31	(62,186)	822.0	2281	76.04	2.0	4157	99.84	2.1	2856	97.96	773.4	2416	89.34	2.1	4343	99.97	2.1	2856	96.79	746.6	2557	91.58	2.2	5273	99.99	2.3	2856	99.02
32	(64,192)	876.6	2517	83.78	2.1	4489	99.32	2.5	3145	97.29	827.6	2671	82.96	2.3	4680	99.77	2.4	3145	98.25	789.7	2822	90.89	2.4	5640	99.99	2.2	3145	98.91
33	(66,198)	1012.3	2532	78.06	2.3	4555	99.67	2.3	3169	96.15	901.0	2682	89.47	2.4	4752	99.89	2.4	3169	97.03	905.1	2835	91.57	2.4	5742	99.98	2.4	3169	98.67
34	(68,204)	1101.0	2535	79.34	2.4	4602	99.99	2.9	3174	96.31	989.8	2685	88.58	3.0	4806	99.98	2.8	3174	97.62	986.3	2844	92.36	2.6	5824	99.99	2.5	3174	98.89
35	(70,210)	1166.6	2714	80.62	2.5	4862	99.86	2.9	3391	97.87	1066.6	2875	91.37	2.6	5072	99.99	2.9	3391	97.16	1082.2	3043	93.15	2.6	6122	99.99	2.9	3391	99.23
36	(72,216)	1201.1	2827	81.04	2.6	5047	99.91	2.8	3535	97.98	1246.5	2984	90.16	2.8	5263	99.99	2.8	3535	98.78	1166.7	3169	92.53	3.0	6343	99.99	2.9	3535	98.96
37	(74,222)	1143.7	2826	82.28	2.8	5096	99.33	2.9	3543	98.84	1358.2	3098	88.95	2.9	5318	99.99	3.2	3543	98.88	1265.4	3178	91.39	2.9	6427	100.00	3.1	3543	98.93
38	(76,228)	1243.5	2839	81.52	2.9	5161	98.97	2.9	3565	97.88	1397.6	3103	89.26	2.9	5388	99.99	3.1	3565	97.24	1383.7	3185	92.55	3.3	6528	100.00	3.1	3565	98.95
39	(78,234)	1464.3	2945	84.12	3.1	5331	99.98	3.2	3695	98.76	1479.4	3210	90.05	3.1	5565	99.99	3.4	3695	97.13	1456.1	3313	90.81	3.4	6735	100.00	3.3	3695	98.78
40	(80,240)	1604.2	2975	85.10	3.2	5414	99.57	3.6	3734	97.96	1626.3	3346	89.99	3.5	5654	99.99	3.5	3734	98.06	1586.9	3343	92.48	3.5	6854	100.00	3.5	3734	98.73
Average		448.2	1584.6	80.67	1.2	2839.7	99.36	1.3	1978.7	96.82	437.9	1691.3	86.54	1.3	2962.6	99.75	1.3	1978.7	97.21	429.5	1778.8	89.85	1.3	3577.4	99.97	1.3	1978.7	97.75