A Two-Stage Simulated Annealing Algorithm for the Many-to-Many Milk-Run Routing Problem with Pipeline Inventory Cost

Table 2

Results obtained for the three algorithms (TSSALSS, TSSA, and SA).

Instances	TSSALSS					TSSA							SA
	Average	Minimum	Std		NI	Average	Minimum	Std			Gap 1	NI	Average	Minimum	Std			Gap 1	NI
S1	304.901	297.15	4.41	1.73	30988	302.645	295.69	3.65	1.96	5	−0.74%	37414	303.769	298.92	2.46	3.12	6	−0.37%	56618
S2	456.536	449.86	3.98	1.88	30988	452.370	444.21	4.83	2.04	6	−0.91%	37414	455.791	448.72	4.04	3.16	7	−0.16%	56618
S3	602.408	585.28	8.14	5.67	72306	602.332	587.65	9.84	6.83	6	−0.01%	99770	598.319	584.15	7.82	8.89	4	−0.68%	152817
S4	879.412	848.56	18.20	5.70	72306	876.568	837.68	27.13	7.29	5	−0.32%	99770	875.906	846.73	19.89	8.61	6	−0.40%	152817
S5	501.301	493.02	5.18	3.59	51647	503.956	490.13	8.55	4.11	3	0.53%	74828	502.876	493.48	5.24	6.02	3	0.31%	114613
S6	629.063	612.58	10.24	3.43	51647	630.897	620.04	7.24	4.34	4	0.29%	74828	629.803	614.61	9.64	6.14	3	0.12%	114613
S7	934.877	902.45	19.29	4.05	92965	929.226	893.19	24.96	7.62	5	−0.60%	149655	936.248	906.73	20.39	13.16	2	0.15%	235956
S8	1239.98	1192.3	27.04	4.47	92965	1244.04	1217.4	19.98	7.31	3	0.33%	149655	1247.59	1216.6	20.09	13.82	3	0.61%	235956
M1	1788.32	1748.3	33.93	9.44	206589	1790.89	1768.9	12.69	19.35	1	0.14%	374138	1789.84	1760.8	15.76	34.67	2	0.08%	602942
M2	3056.33	2961.1	46.96	10.38	206589	3099.02	3067.3	20.22	19.58	0	1.40%	374138	3100.79	3047.8	36.31	36.12	1	1.45%	619767
M3	3362.66	3316.6	34.38	23.01	413178	3423.01	3371.1	32.18	47.55	0	1.79%	872990	3403.08	3351.0	37.11	83.74	1	1.20%	1446124
M4	4304.45	4244.3	42.61	24.32	413178	4400.65	4343.8	43.99	46.28	0	2.23%	872990	4393.82	4311.3	51.87	84.20	0	2.08%	1459131
M5	6668.53	6596.3	48.92	73.86	1239535	6757.88	6669.6	55.29	134.65	0	1.34%	2244830	6803.68	6673.4	80.34	233.27	0	2.03%	3810673
M6	10201.1	10107	60.24	76.35	1239535	10415.9	10338	86.07	135.77	0	2.11%	2244830	10426.8	10302	93.99	239.09	0	2.21%	3796910
M7	5933.78	5880.7	59.37	74.02	1239535	6025.07	5928.7	60.39	127.23	1	1.54%	2244830	6034.00	5941.9	62.11	226.57	0	1.69%	3796910
M8	9039.82	8905.8	84.22	79.19	1239535	9192.46	9040.1	122.74	137.51	0	1.69%	2244830	9212.56	9086.4	100.60	256.14	0	1.91%	3860891
M9	10582.9	10396	132.05	160.04	2582364	10790.7	10561	173.01	320.22	0	1.96%	4988511	10805.6	10536	222.69	570.52	0	2.10%	8804100
M10	13712.1	13523	137.71	184.77	2788953	14000.7	13810	151.68	395.58	0	2.10%	5237937	14005.5	13834	133.30	672.36	0	2.14%	9244305
L1	9829.9	9766.5	58.41	83.20	1342829	9972.3	9813.0	87.24	151.05	0	1.45%	2494256	10033.1	9917.0	88.39	275.78	0	2.07%	4327041
L2	18127.8	17930	119.90	203.29	2995542	18621.3	18342	186.38	411.13	0	2.72%	5487363	18809.6	18477	273.08	728.70	0	3.76%	9785545
L3	25307.3	25023	170.72	358.27	3098836	26132.2	25663	283.87	722.54	0	3.26%	5612075	26134.0	25733	209.27	1103.96	0	3.27%	10100378
L4	44704.2	44276	319.65	1532.21	8712249	46402.4	45235	730.92	3212.35	0	3.80%	16941776	46353.9	45637	503.28	5932.82	0	3.69%	30370067
L5	20877.3	20651	143.83	224.84	3098836	21468.2	21039	308.38	423.63	0	2.83%	5612075	21518.3	21356	273.78	743.19	0	3.07%	10100378
L6	39325.9	38912	251.02	824.93	8712249	40496.4	40076	296.43	1564.54	0	2.98%	16941776	40566.8	40233	219.51	2688.31	0	3.16%	30370067
L7	38951.6	38327	389.55	1675.24	10759079	40706.9	39124	1266.30	3973.80	0	4.51%	19527397	40560.1	39646	495.65	7432.02	0	4.13%	34207264
L8	77932.8	77134	472.58	5708.22	29953307				>10000			56492589				>10000			96608294
L9	21374.5	21195	144.58	259.16	3615309	21933.1	21573	271.82	488.21	0	2.61%	6235639	21954.4	21373	365.09	882.13	1	2.71%	11222642
L10	39113.6	38850	210.16	867.88	9801280	40401.4	39762	430.52	1631.88	0	3.29%	18244990	40463.4	39831	354.59	2982.57	0	3.45%	32706226
L11	54512.3	54081	373.65	1787.21	11680795	56645.6	54883	1122.00	4209.09	0	3.91%	20733929	57025.3	56219	617.77	8397.48	0	4.61%	35694937
L12	110389.7	109834	765.05	6045.78	34276626				>10000			71917382				>10000			121540613