Page - 108 - in Algorithms for Scheduling Problems

Algorithms 2018,11, 55 5.2. Results andAnalysis InTables 4and5, the results are summarized. Thegrey cells include thebest solutionvalues foundbydifferentdispatching rules (DR-1 toDR-6) configurations. These solutionvalues canbe comparedwith theoptimalvaluesgeneratedbyMIPmodel. The tworightmost columnscompare thecomputational timefor theMIPmodelandheuristicalgorithm. Since thecomputationtimeof the algorithmisnotsignificantlyaffectedbythechoiceofdispatchingrule, thecomputationtimeisvery similar forall sixdifferentconfigurations,andthereforeonlyonecomputation timevalueperscenario ispresented inTables4and5. Table4.Computational results for1htimehorizon. Scenario TFD+3j ObjectiveFunction(hh:mm:ss) ComputationalTime (hh:mm:ss) Category: ID Optimal Results DispatchingRules (DR) MIPModel Heuristic Algorithm1 2 3 4 5 6 1:1 0:01:03 00:01:14 00:01:14 00:01:14 00:15:22 00:15:22 00:24:05 00:00:04 00:00:06 1:2 0:00:00 00:00:00 00:00:00 00:00:00 00:00:00 00:00:00 01:16:47 00:00:04 00:00:05 1:3 0:00:00 00:02:09 00:02:09 00:02:09 00:36:33 00:36:33 00:26:32 00:00:04 00:00:03 1:4 0:01:02 00:02:28 00:02:28 00:02:28 00:12:40 00:12:40 00:08:11 00:00:06 00:00:06 1:5 0:07:01 00:16:15 00:16:15 00:16:15 00:19:49 00:19:49 00:13:14 00:00:05 00:00:03 1:6 0:00:23 00:05:46 00:05:46 00:05:46 00:05:46 00:05:46 00:05:46 00:00:04 00:00:03 1:7 0:05:05 00:06:24 00:06:24 00:06:24 00:06:24 00:06:24 00:14:45 00:00:04 00:00:05 1:8 0:01:34 00:12:01 00:12:01 00:12:01 00:12:01 00:12:01 00:13:40 00:00:04 00:00:06 1:9 0:00:00 00:14:01 00:14:01 00:14:01 00:13:02 00:13:02 00:14:01 00:00:04 00:00:03 1:10 0:00:00 00:01:18 00:01:18 00:00:00 00:00:00 00:00:00 00:01:33 00:00:04 00:00:05 2:1 0:05:24 00:45:37 00:45:37 00:06:42 00:06:42 00:06:42 00:08:16 00:00:04 00:00:06 2:2 0:02:43 00:03:29 00:39:53 00:03:29 00:03:29 00:03:29 01:06:56 00:00:05 00:00:05 2:3 0:01:01 00:01:47 00:20:06 00:20:06 00:01:47 00:01:47 00:20:14 00:00:03 00:00:03 2:4 0:15:12 00:22:12 00:22:50 00:22:50 00:22:12 00:22:12 00:55:54 00:00:05 00:00:05 2:5 0:42:09 00:43:24 00:58:03 00:58:03 01:05:08 01:05:08 00:59:16 00:00:04 00:00:03 2:6 0:01:24 00:02:44 00:02:44 00:02:44 00:02:44 00:02:44 00:02:44 00:00:06 00:00:04 2:7 0:05:27 00:08:09 00:08:09 00:08:09 00:08:09 00:08:09 00:09:43 00:00:04 00:00:10 2:8 0:21:12 00:43:37 00:38:42 00:38:42 00:43:37 00:43:37 00:40:16 00:00:06 00:00:06 2:9 0:00:00 00:00:00 00:00:00 00:00:00 00:00:00 00:00:00 00:00:00 00:00:05 00:00:03 2:10 0:00:08 00:05:09 00:05:09 00:05:09 00:05:09 00:05:09 00:06:43 00:00:04 00:00:06 3:1 0:01:00 00:01:00 00:01:00 00:01:00 00:01:00 00:01:00 00:25:05 00:00:04 00:00:06 3:2 0:00:00 00:00:00 00:00:00 00:00:00 00:00:19 00:00:19 00:25:54 00:00:04 00:00:06 3:3 0:00:00 00:03:49 00:21:38 01:05:52 00:01:17 00:15:40 00:54:14 00:00:05 00:00:03 3:4 0:12:21 00:16:59 00:20:13 00:20:13 00:16:59 00:16:59 00:20:22 00:00:07 00:00:06 3:5 0:05:20 00:05:25 00:57:34 00:15:58 00:05:25 00:05:25 00:16:12 00:00:03 00:00:03 3:6 0:00:00 00:21:04 00:21:04 00:21:04 00:23:12 00:23:12 00:28:42 00:00:05 00:00:03 3:7 0:00:09 00:07:42 00:14:11 00:14:11 00:14:11 00:14:11 00:15:45 00:00:10 00:00:05 3:8 0:00:00 00:00:00 00:05:06 00:05:06 00:00:00 00:00:00 00:07:54 00:00:04 00:00:05 3:9 0:00:00 00:00:00 00:00:41 00:00:41 00:00:00 00:00:00 00:00:00 00:00:04 00:00:04 3:10 0:00:00 00:04:53 00:04:53 00:03:35 00:01:04 00:01:04 00:02:38 00:00:03 00:00:05 Table5.Thecomputational results for1.5h timehorizon(hh:mm:ss). Scenario TFD+3j ObjectiveFunction ComputationalTime Category: ID Optimal Results DispatchingRules (DR) MIPModel Heuristic Algorithm1 2 3 4 5 6 1:1 0:01:03 00:01:14 00:01:14 00:01:14 00:45:13 00:45:13 00:46:56 00:00:12 00:00:20 1:2 0:00:00 00:00:00 00:00:00 00:00:00 00:12:09 00:12:09 05:09:54 00:00:10 00:00:15 1:3 0:00:00 00:02:09 00:02:09 00:02:09 01:34:59 01:34:59 00:25:21 00:00:11 00:00:10 1:4 0:00:00 00:01:27 00:01:27 00:01:27 01:38:16 01:38:16 00:51:24 00:00:13 00:00:16 1:5 0:02:08 00:10:23 00:10:23 00:10:23 00:24:07 00:24:07 00:12:14 00:00:07 00:00:09 1:6 0:00:23 00:05:46 00:05:46 00:05:46 00:05:46 00:05:46 00:05:46 00:00:12 00:00:10 1:7 0:05:05 00:06:24 00:06:24 00:06:24 00:06:24 00:06:24 00:14:45 00:00:11 00:00:18 1:8 0:01:34 00:12:01 00:12:01 00:12:01 00:12:01 00:12:01 00:13:40 00:00:12 00:00:17 1:9 0:00:00 00:13:00 00:13:00 00:13:00 00:13:16 00:13:16 00:38:13 00:00:07 00:00:10 1:10 0:00:00 00:01:18 00:01:18 00:00:00 00:00:00 00:00:00 00:01:33 00:00:11 00:00:16 2:1 0:03:36 00:45:37 00:45:37 00:04:31 00:17:11 00:17:11 00:14:16 00:00:11 00:00:17 2:2 0:00:00 00:00:23 01:21:00 00:00:23 00:00:23 00:00:23 04:36:13 00:00:12 00:00:15 2:3 0:02:40 00:29:31 00:32:58 00:32:58 00:39:25 00:39:25 00:33:46 00:00:07 00:00:09 2:4 0:26:34 00:43:50 01:11:40 01:11:40 00:43:50 00:43:50 01:57:35 00:00:16 00:00:15 2:5 1:11:44 01:17:47 01:40:09 01:40:09 01:41:32 01:41:32 01:35:29 00:00:12 00:00:08 2:6 0:01:24 00:02:44 00:02:44 00:02:44 00:02:44 00:02:44 00:02:44 00:00:11 00:00:09 108