A Three-Stage Saving-Based Heuristic for Vehicle Routing Problem with Time Windows and Stochastic Travel Times

Table 3

Average results for each instance set under three variance levels.

Instance set	Results of best-known VRPTW solutions		Results of TSH			Gap	Variance level
	BKS expected total cost	Reliability	TSH expected total cost	Reliability
c1	831.83	0.999	830.85	0.999	0.369	0.12%	The relatively low variances
c2	601.37	0.997	603.34	1.000	0.025	−0.32%
r1	1363.81	0.962	1351.26	0.985	0.383	0.90%
r2	1072.93	0.983	1028.65	0.998	0.323	4.14%
rc1	1651.61	0.952	1601.59	0.978	0.338	3.19%
rc2	1269.20	0.980	1215.64	0.998	0.313	4.37%
Avg.	1131.79	0.979	1105.22	0.9929	0.292	2.07%
c1	1332.58	0.980	1062.00	0.993	0.419	24.17%	The medium variances
c2	653.11	0.996	630.26	1.000	0.300	3.62%
r1	3009.56	0.892	1640.47	0.985	0.413	81.73%
r2	2083.48	0.954	1138.65	0.998	0.336	80.16%
rc1	3959.32	0.881	2016.18	0.980	0.375	91.06%
rc2	2630.62	0.945	1312.55	0.998	0.344	97.50%
Avg.	2278.11	0.941	1300.02	0.9923	0.364	63.04%
c1	2580.59	0.961	1091.76	0.993	0.425	132.27%	The relatively high variances
c2	757.45	0.995	660.64	1.000	0.450	14.89%
r1	5630.55	0.863	1656.88	0.986	0.421	238.48%
r2	4493.30	0.930	1156.05	0.998	0.327	280.99%
rc1	7279.30	0.854	2108.23	0.977	0.338	238.74%
rc2	5920.61	0.916	1356.47	0.998	0.363	319.61%
Avg.	4443.63	0.920	1338.34	0.9920	0.387	204.16%