bus_driver_scheduling_flow_sat.py

# Copyright 2010-2018 Google LLC
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""This model implements a bus driver scheduling problem.

Constraints:
- max driving time per driver <= 9h
- max working time per driver <= 12h
- min working time per driver >= 6.5h (soft)
- 30 min break after each 4h of driving time per driver
- 10 min preparation time before the first shift
- 15 min cleaning time after the last shift
- 2 min waiting time after each shift for passenger boarding and alighting
"""
from __future__ import print_function

import argparse
import collections
import math

from ortools.sat.python import cp_model

PARSER = argparse.ArgumentParser()
PARSER.add_argument(
    '--instance', default=1, type=int, help='Instance number (1..3).')
PARSER.add_argument(
    '--output_proto',
    default="",
    help='Output file to write the cp_model'
    'proto to.')
PARSER.add_argument('--params', default="", help='Sat solver parameters.')

SAMPLE_SHIFTS_SMALL = [
    #
    # column description:
    # - shift id
    # - shift start time as hh:mm string (for logging and readability purposes)
    # - shift end time as hh:mm string (for logging and readability purposes)
    # - shift start minute
    # - shift end minute
    # - shift duration in minutes
    #
    [0, '05:18', '06:00', 318, 360, 42],
    [1, '05:26', '06:08', 326, 368, 42],
    [2, '05:40', '05:56', 340, 356, 16],
    [3, '06:06', '06:51', 366, 411, 45],
    [4, '06:40', '07:52', 400, 472, 72],
    [5, '06:42', '07:13', 402, 433, 31],
    [6, '06:48', '08:15', 408, 495, 87],
    [7, '06:59', '08:07', 419, 487, 68],
    [8, '07:20', '07:36', 440, 456, 16],
    [9, '07:35', '08:22', 455, 502, 47],
    [10, '07:50', '08:55', 470, 535, 65],
    [11, '08:00', '09:05', 480, 545, 65],
    [12, '08:00', '08:35', 480, 515, 35],
    [13, '08:11', '09:41', 491, 581, 90],
    [14, '08:28', '08:50', 508, 530, 22],
    [15, '08:35', '08:45', 515, 525, 10],
    [16, '08:40', '08:50', 520, 530, 10],
    [17, '09:03', '10:28', 543, 628, 85],
    [18, '09:23', '09:49', 563, 589, 26],
    [19, '09:30', '09:40', 570, 580, 10],
    [20, '09:57', '10:20', 597, 620, 23],
    [21, '10:09', '11:03', 609, 663, 54],
    [22, '10:20', '10:30', 620, 630, 10],
    [23, '11:00', '11:10', 660, 670, 10],
    [24, '11:45', '12:24', 705, 744, 39],
    [25, '12:18', '13:00', 738, 780, 42],
    [26, '13:18', '14:44', 798, 884, 86],
    [27, '13:53', '14:49', 833, 889, 56],
    [28, '14:03', '14:50', 843, 890, 47],
    [29, '14:28', '15:15', 868, 915, 47],
    [30, '14:30', '15:41', 870, 941, 71],
    [31, '14:48', '15:35', 888, 935, 47],
    [32, '15:03', '15:50', 903, 950, 47],
    [33, '15:28', '16:54', 928, 1014, 86],
    [34, '15:38', '16:25', 938, 985, 47],
    [35, '15:40', '15:56', 940, 956, 16],
    [36, '15:58', '16:45', 958, 1005, 47],
    [37, '16:04', '17:30', 964, 1050, 86],
    [38, '16:28', '17:15', 988, 1035, 47],
    [39, '16:36', '17:21', 996, 1041, 45],
    [40, '16:50', '17:00', 1010, 1020, 10],
    [41, '16:54', '18:20', 1014, 1100, 86],
    [42, '17:01', '17:13', 1021, 1033, 12],
    [43, '17:19', '18:31', 1039, 1111, 72],
    [44, '17:23', '18:10', 1043, 1090, 47],
    [45, '17:34', '18:15', 1054, 1095, 41],
    [46, '18:04', '19:29', 1084, 1169, 85],
    [47, '18:34', '19:58', 1114, 1198, 84],
    [48, '19:56', '20:34', 1196, 1234, 38],
    [49, '20:05', '20:48', 1205, 1248, 43]
]  # yapf:disable

SAMPLE_SHIFTS_MEDIUM = [
    [0, '04:30', '04:53', 270, 293, 23],
    [1, '04:46', '04:56', 286, 296, 10],
    [2, '04:52', '05:56', 292, 356, 64],
    [3, '04:53', '05:23', 293, 323, 30],
    [4, '05:07', '05:44', 307, 344, 37],
    [5, '05:10', '06:06', 310, 366, 56],
    [6, '05:18', '06:03', 318, 363, 45],
    [7, '05:30', '05:40', 330, 340, 10],
    [8, '05:30', '05:40', 330, 340, 10],
    [9, '05:33', '06:15', 333, 375, 42],
    [10, '05:40', '05:50', 340, 350, 10],
    [11, '05:43', '06:08', 343, 368, 25],
    [12, '05:54', '07:20', 354, 440, 86],
    [13, '06:04', '06:37', 364, 397, 33],
    [14, '06:13', '06:58', 373, 418, 45],
    [15, '06:14', '07:40', 374, 460, 86],
    [16, '06:15', '07:15', 375, 435, 60],
    [17, '06:16', '06:26', 376, 386, 10],
    [18, '06:17', '06:34', 377, 394, 17],
    [19, '06:20', '06:36', 380, 396, 16],
    [20, '06:22', '07:06', 382, 426, 44],
    [21, '06:24', '07:50', 384, 470, 86],
    [22, '06:27', '06:44', 387, 404, 17],
    [23, '06:30', '06:40', 390, 400, 10],
    [24, '06:31', '06:43', 391, 403, 12],
    [25, '06:33', '07:53', 393, 473, 80],
    [26, '06:34', '07:09', 394, 429, 35],
    [27, '06:40', '06:56', 400, 416, 16],
    [28, '06:44', '07:17', 404, 437, 33],
    [29, '06:46', '06:58', 406, 418, 12],
    [30, '06:49', '07:43', 409, 463, 54],
    [31, '06:50', '07:05', 410, 425, 15],
    [32, '06:52', '07:36', 412, 456, 44],
    [33, '06:54', '07:27', 414, 447, 33],
    [34, '06:56', '08:23', 416, 503, 87],
    [35, '07:04', '07:44', 424, 464, 40],
    [36, '07:11', '08:36', 431, 516, 85],
    [37, '07:17', '07:35', 437, 455, 18],
    [38, '07:22', '08:06', 442, 486, 44],
    [39, '07:27', '08:15', 447, 495, 48],
    [40, '07:35', '07:45', 455, 465, 10],
    [41, '07:43', '08:08', 463, 488, 25],
    [42, '07:50', '08:37', 470, 517, 47],
    [43, '07:58', '08:45', 478, 525, 47],
    [44, '08:00', '08:35', 480, 515, 35],
    [45, '08:06', '08:51', 486, 531, 45],
    [46, '08:10', '08:45', 490, 525, 35],
    [47, '08:15', '08:30', 495, 510, 15],
    [48, '08:16', '09:00', 496, 540, 44],
    [49, '08:18', '09:16', 498, 556, 58],
    [50, '08:20', '08:36', 500, 516, 16],
    [51, '08:27', '09:07', 507, 547, 40],
    [52, '08:30', '08:45', 510, 525, 15],
    [53, '08:35', '09:15', 515, 555, 40],
    [54, '08:46', '09:30', 526, 570, 44],
    [55, '08:51', '09:17', 531, 557, 26],
    [56, '08:55', '09:15', 535, 555, 20],
    [57, '08:58', '09:38', 538, 578, 40],
    [58, '09:00', '09:35', 540, 575, 35],
    [59, '09:00', '09:16', 540, 556, 16],
    [60, '09:20', '09:36', 560, 576, 16],
    [61, '09:31', '09:43', 571, 583, 12],
    [62, '09:33', '10:15', 573, 615, 42],
    [63, '09:54', '10:05', 594, 605, 11],
    [64, '10:11', '10:38', 611, 638, 27],
    [65, '10:18', '11:00', 618, 660, 42],
    [66, '10:21', '10:47', 621, 647, 26],
    [67, '10:25', '11:04', 625, 664, 39],
    [68, '10:26', '11:08', 626, 668, 42],
    [69, '10:44', '12:11', 644, 731, 87],
    [70, '11:00', '11:16', 660, 676, 16],
    [71, '11:15', '11:54', 675, 714, 39],
    [72, '11:16', '11:28', 676, 688, 12],
    [73, '11:20', '11:30', 680, 690, 10],
    [74, '11:21', '11:47', 681, 707, 26],
    [75, '11:25', '12:04', 685, 724, 39],
    [76, '11:34', '11:45', 694, 705, 11],
    [77, '11:35', '12:14', 695, 734, 39],
    [78, '11:41', '12:23', 701, 743, 42],
    [79, '11:44', '12:35', 704, 755, 51],
    [80, '11:46', '11:58', 706, 718, 12],
    [81, '12:00', '12:10', 720, 730, 10],
    [82, '12:04', '12:15', 724, 735, 11],
    [83, '12:04', '13:04', 724, 784, 60],
    [84, '12:11', '12:38', 731, 758, 27],
    [85, '12:15', '12:54', 735, 774, 39],
    [86, '12:25', '13:10', 745, 790, 45],
    [87, '12:30', '12:40', 750, 760, 10],
    [88, '12:34', '13:58', 754, 838, 84],
    [89, '12:38', '13:25', 758, 805, 47],
    [90, '12:48', '13:35', 768, 815, 47],
    [91, '13:00', '13:16', 780, 796, 16],
    [92, '13:05', '13:44', 785, 824, 39],
    [93, '13:08', '13:55', 788, 835, 47],
    [94, '13:14', '14:38', 794, 878, 84],
    [95, '13:23', '13:49', 803, 829, 26],
    [96, '13:25', '14:04', 805, 844, 39],
    [97, '13:28', '14:54', 808, 894, 86],
    [98, '13:31', '13:43', 811, 823, 12],
    [99, '13:34', '14:58', 814, 898, 84],
    [100, '13:38', '14:25', 818, 865, 47],
    [101, '13:38', '15:04', 818, 904, 86],
    [102, '13:39', '14:33', 819, 873, 54],
    [103, '13:40', '13:50', 820, 830, 10],
    [104, '13:43', '14:10', 823, 850, 27],
    [105, '13:48', '14:35', 828, 875, 47],
    [106, '13:48', '14:35', 828, 875, 47],
    [107, '13:53', '14:40', 833, 880, 47],
    [108, '13:58', '15:24', 838, 924, 86],
    [109, '13:58', '14:25', 838, 865, 27],
    [110, '14:00', '14:16', 840, 856, 16],
    [111, '14:13', '15:00', 853, 900, 47],
    [112, '14:20', '15:31', 860, 931, 71],
    [113, '14:25', '15:02', 865, 902, 37],
    [114, '14:34', '14:45', 874, 885, 11],
    [115, '14:40', '15:51', 880, 951, 71],
    [116, '14:40', '14:56', 880, 896, 16],
    [117, '14:46', '14:58', 886, 898, 12],
    [118, '14:49', '15:43', 889, 943, 54],
    [119, '14:52', '15:21', 892, 921, 29],
    [120, '14:58', '16:24', 898, 984, 86],
    [121, '14:59', '15:53', 899, 953, 54],
    [122, '15:00', '15:10', 900, 910, 10],
    [123, '15:00', '15:35', 900, 935, 35],
    [124, '15:08', '15:45', 908, 945, 37],
    [125, '15:12', '15:36', 912, 936, 24],
    [126, '15:18', '16:05', 918, 965, 47],
    [127, '15:24', '16:05', 924, 965, 41],
    [128, '15:31', '15:43', 931, 943, 12],
    [129, '15:35', '15:54', 935, 954, 19],
    [130, '15:36', '16:21', 936, 981, 45],
    [131, '15:39', '16:33', 939, 993, 54],
    [132, '15:48', '16:35', 948, 995, 47],
    [133, '15:50', '17:01', 950, 1021, 71],
    [134, '16:03', '16:50', 963, 1010, 47],
    [135, '16:18', '17:44', 978, 1064, 86],
    [136, '16:24', '17:05', 984, 1025, 41],
    [137, '16:28', '17:15', 988, 1035, 47],
    [138, '16:34', '17:15', 994, 1035, 41],
    [139, '16:38', '17:25', 998, 1045, 47],
    [140, '16:40', '16:56', 1000, 1016, 16],
    [141, '16:45', '17:04', 1005, 1024, 19],
    [142, '16:52', '17:36', 1012, 1056, 44],
    [143, '16:58', '17:45', 1018, 1065, 47],
    [144, '17:04', '18:30', 1024, 1110, 86],
    [145, '17:04', '17:45', 1024, 1065, 41],
    [146, '17:09', '18:03', 1029, 1083, 54],
    [147, '17:18', '18:44', 1038, 1124, 86],
    [148, '17:28', '18:15', 1048, 1095, 47],
    [149, '17:29', '18:41', 1049, 1121, 72],
    [150, '17:36', '18:21', 1056, 1101, 45],
    [151, '17:38', '18:25', 1058, 1105, 47],
    [152, '17:40', '17:56', 1060, 1076, 16],
    [153, '17:45', '18:04', 1065, 1084, 19],
    [154, '17:46', '17:58', 1066, 1078, 12],
    [155, '17:48', '18:35', 1068, 1115, 47],
    [156, '17:49', '18:43', 1069, 1123, 54],
    [157, '17:55', '18:14', 1075, 1094, 19],
    [158, '17:58', '18:45', 1078, 1125, 47],
    [159, '18:00', '19:11', 1080, 1151, 71],
    [160, '18:04', '18:45', 1084, 1125, 41],
    [161, '18:09', '19:03', 1089, 1143, 54],
    [162, '18:13', '19:00', 1093, 1140, 47],
    [163, '18:13', '18:40', 1093, 1120, 27],
    [164, '18:19', '19:13', 1099, 1153, 54],
    [165, '18:28', '19:25', 1108, 1165, 57],
    [166, '18:48', '19:28', 1128, 1168, 40],
    [167, '19:03', '19:45', 1143, 1185, 42],
    [168, '19:20', '19:36', 1160, 1176, 16],
    [169, '19:21', '19:31', 1161, 1171, 10],
    [170, '19:25', '20:04', 1165, 1204, 39],
    [171, '19:26', '20:08', 1166, 1208, 42],
    [172, '19:30', '19:40', 1170, 1180, 10],
    [173, '19:44', '20:33', 1184, 1233, 49],
    [174, '19:48', '21:09', 1188, 1269, 81],
    [175, '19:53', '21:02', 1193, 1262, 69],
    [176, '20:04', '20:29', 1204, 1229, 25],
    [177, '20:17', '21:03', 1217, 1263, 46],
    [178, '20:20', '20:57', 1220, 1257, 37],
    [179, '20:29', '21:18', 1229, 1278, 49],
    [180, '20:35', '21:54', 1235, 1314, 79],
    [181, '20:40', '20:50', 1240, 1250, 10],
    [182, '20:47', '21:42', 1247, 1302, 55],
    [183, '21:00', '21:10', 1260, 1270, 10],
    [184, '21:07', '21:44', 1267, 1304, 37],
    [185, '21:14', '22:03', 1274, 1323, 49],
    [186, '21:39', '21:55', 1299, 1315, 16],
    [187, '21:40', '22:17', 1300, 1337, 37],
    [188, '21:40', '21:50', 1300, 1310, 10],
    [189, '21:48', '22:03', 1308, 1323, 15],
    [190, '22:17', '23:03', 1337, 1383, 46],
    [191, '22:43', '23:08', 1363, 1388, 25],
    [192, '23:35', '01:05', 1415, 1505, 90],
    [193, '23:46', '00:01', 1426, 1441, 15],
    [194, '23:47', '00:33', 1427, 1473, 46],
    [195, '23:52', '00:24', 1432, 1464, 32],
    [196, '23:58', '00:38', 1438, 1478, 40],
    [197, '00:02', '00:12', 1442, 1452, 10],
    [198, '00:07', '00:39', 1447, 1479, 32],
    [199, '00:25', '01:12', 1465, 1512, 47]
]  # yapf:disable

SAMPLE_SHIFTS_LARGE = [
    [0, '04:18', '05:00', 258, 300, 42],
    [1, '04:27', '05:08', 267, 308, 41],
    [2, '04:29', '05:26', 269, 326, 57],
    [3, '04:29', '04:55', 269, 295, 26],
    [4, '04:30', '04:53', 270, 293, 23],
    [5, '04:30', '04:51', 270, 291, 21],
    [6, '04:31', '04:53', 271, 293, 22],
    [7, '04:33', '05:15', 273, 315, 42],
    [8, '04:34', '04:44', 274, 284, 10],
    [9, '04:34', '05:03', 274, 303, 29],
    [10, '04:35', '04:50', 275, 290, 15],
    [11, '04:36', '04:46', 276, 286, 10],
    [12, '04:37', '05:18', 277, 318, 41],
    [13, '04:41', '05:13', 281, 313, 32],
    [14, '04:42', '05:23', 282, 323, 41],
    [15, '04:43', '04:53', 283, 293, 10],
    [16, '04:44', '05:45', 284, 345, 61],
    [17, '04:45', '05:11', 285, 311, 26],
    [18, '04:46', '05:01', 286, 301, 15],
    [19, '04:46', '04:56', 286, 296, 10],
    [20, '04:47', '05:14', 287, 314, 27],
    [21, '04:48', '05:30', 288, 330, 42],
    [22, '04:49', '05:41', 289, 341, 52],
    [23, '04:49', '05:18', 289, 318, 29],
    [24, '04:50', '05:33', 290, 333, 43],
    [25, '04:52', '05:56', 292, 356, 64],
    [26, '04:52', '05:07', 292, 307, 15],
    [27, '04:53', '05:19', 293, 319, 26],
    [28, '04:53', '05:23', 293, 323, 30],
    [29, '04:55', '05:27', 295, 327, 32],
    [30, '04:57', '05:38', 297, 338, 41],
    [31, '05:00', '06:00', 300, 360, 60],
    [32, '05:00', '05:54', 300, 354, 54],
    [33, '05:01', '05:33', 301, 333, 32],
    [34, '05:01', '05:26', 301, 326, 25],
    [35, '05:02', '05:29', 302, 329, 27],
    [36, '05:02', '05:12', 302, 312, 10],
    [37, '05:03', '05:45', 303, 345, 42],
    [38, '05:03', '05:18', 303, 318, 15],
    [39, '05:03', '06:28', 303, 388, 85],
    [40, '05:03', '05:13', 303, 313, 10],
    [41, '05:04', '06:24', 304, 384, 80],
    [42, '05:07', '05:44', 307, 344, 37],
    [43, '05:08', '05:48', 308, 348, 40],
    [44, '05:10', '06:06', 310, 366, 56],
    [45, '05:11', '05:37', 311, 337, 26],
    [46, '05:11', '05:53', 311, 353, 42],
    [47, '05:13', '06:15', 313, 375, 62],
    [48, '05:13', '05:38', 313, 338, 25],
    [49, '05:16', '05:44', 316, 344, 28],
    [50, '05:17', '05:27', 317, 327, 10],
    [51, '05:18', '06:40', 318, 400, 82],
    [52, '05:18', '06:03', 318, 363, 45],
    [53, '05:18', '06:11', 318, 371, 53],
    [54, '05:18', '06:00', 318, 360, 42],
    [55, '05:19', '06:34', 319, 394, 75],
    [56, '05:20', '06:17', 320, 377, 57],
    [57, '05:22', '05:59', 322, 359, 37],
    [58, '05:24', '05:48', 324, 348, 24],
    [59, '05:25', '05:40', 325, 340, 15],
    [60, '05:26', '06:08', 326, 368, 42],
    [61, '05:27', '06:30', 327, 390, 63],
    [62, '05:27', '05:54', 327, 354, 27],
    [63, '05:28', '05:53', 328, 353, 25],
    [64, '05:29', '05:44', 329, 344, 15],
    [65, '05:30', '05:40', 330, 340, 10],
    [66, '05:30', '05:40', 330, 340, 10],
    [67, '05:30', '05:40', 330, 340, 10],
    [68, '05:32', '06:53', 332, 413, 81],
    [69, '05:33', '07:00', 333, 420, 87],
    [70, '05:33', '06:15', 333, 375, 42],
    [71, '05:33', '05:47', 333, 347, 14],
    [72, '05:37', '06:13', 337, 373, 36],
    [73, '05:37', '06:05', 337, 365, 28],
    [74, '05:38', '06:33', 338, 393, 55],
    [75, '05:38', '06:04', 338, 364, 26],
    [76, '05:38', '06:18', 338, 378, 40],
    [77, '05:39', '05:54', 339, 354, 15],
    [78, '05:40', '05:56', 340, 356, 16],
    [79, '05:40', '06:41', 340, 401, 61],
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    [1125, '18:59', '19:53', 1139, 1193, 54],
    [1126, '18:59', '19:50', 1139, 1190, 51],
    [1127, '18:59', '19:53', 1139, 1193, 54],
    [1128, '19:00', '19:16', 1140, 1156, 16],
    [1129, '19:00', '19:10', 1140, 1150, 10],
    [1130, '19:00', '19:16', 1140, 1156, 16],
    [1131, '19:01', '19:13', 1141, 1153, 12],
    [1132, '19:03', '20:26', 1143, 1226, 83],
    [1133, '19:03', '19:45', 1143, 1185, 42],
    [1134, '19:05', '19:44', 1145, 1184, 39],
    [1135, '19:05', '19:25', 1145, 1165, 20],
    [1136, '19:08', '20:15', 1148, 1215, 67],
    [1137, '19:08', '19:35', 1148, 1175, 27],
    [1138, '19:09', '19:49', 1149, 1189, 40],
    [1139, '19:09', '20:03', 1149, 1203, 54],
    [1140, '19:10', '19:20', 1150, 1160, 10],
    [1141, '19:10', '19:20', 1150, 1160, 10],
    [1142, '19:11', '19:53', 1151, 1193, 42],
    [1143, '19:14', '20:26', 1154, 1226, 72],
    [1144, '19:14', '19:35', 1154, 1175, 21],
    [1145, '19:14', '19:24', 1154, 1164, 10],
    [1146, '19:14', '20:05', 1154, 1205, 51],
    [1147, '19:15', '19:30', 1155, 1170, 15],
    [1148, '19:15', '19:54', 1155, 1194, 39],
    [1149, '19:18', '20:39', 1158, 1239, 81],
    [1150, '19:18', '20:00', 1158, 1200, 42],
    [1151, '19:19', '20:14', 1159, 1214, 55],
    [1152, '19:20', '19:30', 1160, 1170, 10],
    [1153, '19:20', '19:36', 1160, 1176, 16],
    [1154, '19:21', '19:31', 1161, 1171, 10],
    [1155, '19:23', '20:30', 1163, 1230, 67],
    [1156, '19:23', '19:35', 1163, 1175, 12],
    [1157, '19:24', '19:45', 1164, 1185, 21],
    [1158, '19:24', '19:45', 1164, 1185, 21],
    [1159, '19:25', '20:04', 1165, 1204, 39],
    [1160, '19:26', '20:08', 1166, 1208, 42],
    [1161, '19:29', '20:02', 1169, 1202, 33],
    [1162, '19:29', '20:18', 1169, 1218, 49],
    [1163, '19:29', '20:41', 1169, 1241, 72],
    [1164, '19:30', '19:40', 1170, 1180, 10],
    [1165, '19:33', '20:54', 1173, 1254, 81],
    [1166, '19:33', '20:17', 1173, 1217, 44],
    [1167, '19:34', '19:55', 1174, 1195, 21],
    [1168, '19:35', '20:14', 1175, 1214, 39],
    [1169, '19:38', '20:05', 1178, 1205, 27],
    [1170, '19:38', '20:45', 1178, 1245, 67],
    [1171, '19:39', '20:12', 1179, 1212, 33],
    [1172, '19:40', '19:50', 1180, 1190, 10],
    [1173, '19:40', '19:56', 1180, 1196, 16],
    [1174, '19:41', '20:27', 1181, 1227, 46],
    [1175, '19:43', '19:55', 1183, 1195, 12],
    [1176, '19:44', '20:05', 1184, 1205, 21],
    [1177, '19:44', '20:33', 1184, 1233, 49],
    [1178, '19:44', '21:00', 1184, 1260, 76],
    [1179, '19:45', '20:24', 1185, 1224, 39],
    [1180, '19:48', '20:37', 1188, 1237, 49],
    [1181, '19:48', '21:09', 1188, 1269, 81],
    [1182, '19:50', '20:00', 1190, 1200, 10],
    [1183, '19:52', '20:29', 1192, 1229, 37],
    [1184, '19:53', '20:08', 1193, 1208, 15],
    [1185, '19:53', '21:02', 1193, 1262, 69],
    [1186, '19:53', '20:20', 1193, 1220, 27],
    [1187, '19:54', '20:19', 1194, 1219, 25],
    [1188, '19:55', '20:34', 1195, 1234, 39],
    [1189, '19:56', '20:34', 1196, 1234, 38],
    [1190, '19:59', '20:48', 1199, 1248, 49],
    [1191, '19:59', '21:20', 1199, 1280, 81],
    [1192, '20:00', '20:16', 1200, 1216, 16],
    [1193, '20:00', '20:10', 1200, 1210, 10],
    [1194, '20:03', '20:42', 1203, 1242, 39],
    [1195, '20:03', '21:24', 1203, 1284, 81],
    [1196, '20:04', '20:29', 1204, 1229, 25],
    [1197, '20:05', '20:48', 1205, 1248, 43],
    [1198, '20:07', '20:44', 1207, 1244, 37],
    [1199, '20:08', '20:40', 1208, 1240, 32],
    [1200, '20:08', '20:35', 1208, 1235, 27],
    [1201, '20:10', '20:20', 1210, 1220, 10],
    [1202, '20:10', '20:22', 1210, 1222, 12],
    [1203, '20:11', '20:47', 1211, 1247, 36],
    [1204, '20:14', '21:04', 1214, 1264, 50],
    [1205, '20:14', '21:03', 1214, 1263, 49],
    [1206, '20:17', '21:03', 1217, 1263, 46],
    [1207, '20:18', '21:39', 1218, 1299, 81],
    [1208, '20:20', '20:30', 1220, 1230, 10],
    [1209, '20:20', '20:57', 1220, 1257, 37],
    [1210, '20:20', '20:36', 1220, 1236, 16],
    [1211, '20:22', '20:59', 1222, 1259, 37],
    [1212, '20:22', '20:42', 1222, 1242, 20],
    [1213, '20:24', '20:49', 1224, 1249, 25],
    [1214, '20:27', '21:22', 1227, 1282, 55],
    [1215, '20:29', '21:18', 1229, 1278, 49],
    [1216, '20:30', '21:07', 1230, 1267, 37],
    [1217, '20:30', '20:40', 1230, 1240, 10],
    [1218, '20:30', '20:40', 1230, 1240, 10],
    [1219, '20:30', '21:40', 1230, 1300, 70],
    [1220, '20:32', '21:18', 1232, 1278, 46],
    [1221, '20:35', '21:54', 1235, 1314, 79],
    [1222, '20:37', '21:14', 1237, 1274, 37],
    [1223, '20:38', '21:08', 1238, 1268, 30],
    [1224, '20:40', '20:50', 1240, 1250, 10],
    [1225, '20:40', '21:17', 1240, 1277, 37],
    [1226, '20:40', '20:56', 1240, 1256, 16],
    [1227, '20:44', '21:33', 1244, 1293, 49],
    [1228, '20:47', '21:33', 1247, 1293, 46],
    [1229, '20:47', '21:42', 1247, 1302, 55],
    [1230, '20:50', '21:00', 1250, 1260, 10],
    [1231, '20:50', '22:00', 1250, 1320, 70],
    [1232, '20:50', '22:09', 1250, 1329, 79],
    [1233, '20:50', '21:27', 1250, 1287, 37],
    [1234, '20:52', '21:29', 1252, 1289, 37],
    [1235, '20:53', '21:20', 1253, 1280, 27],
    [1236, '20:56', '21:11', 1256, 1271, 15],
    [1237, '20:59', '21:48', 1259, 1308, 49],
    [1238, '21:00', '21:10', 1260, 1270, 10],
    [1239, '21:00', '21:37', 1260, 1297, 37],
    [1240, '21:02', '21:48', 1262, 1308, 46],
    [1241, '21:05', '22:24', 1265, 1344, 79],
    [1242, '21:07', '21:44', 1267, 1304, 37],
    [1243, '21:07', '22:02', 1267, 1322, 55],
    [1244, '21:08', '21:38', 1268, 1298, 30],
    [1245, '21:10', '22:25', 1270, 1345, 75],
    [1246, '21:10', '21:20', 1270, 1280, 10],
    [1247, '21:10', '21:47', 1270, 1307, 37],
    [1248, '21:14', '22:03', 1274, 1323, 49],
    [1249, '21:17', '22:03', 1277, 1323, 46],
    [1250, '21:20', '22:18', 1280, 1338, 58],
    [1251, '21:20', '21:57', 1280, 1317, 37],
    [1252, '21:20', '21:30', 1280, 1290, 10],
    [1253, '21:22', '21:59', 1282, 1319, 37],
    [1254, '21:24', '21:49', 1284, 1309, 25],
    [1255, '21:27', '22:21', 1287, 1341, 54],
    [1256, '21:30', '22:07', 1290, 1327, 37],
    [1257, '21:30', '22:20', 1290, 1340, 50],
    [1258, '21:30', '21:40', 1290, 1300, 10],
    [1259, '21:32', '22:18', 1292, 1338, 46],
    [1260, '21:32', '22:01', 1292, 1321, 29],
    [1261, '21:35', '22:54', 1295, 1374, 79],
    [1262, '21:37', '22:14', 1297, 1334, 37],
    [1263, '21:39', '21:55', 1299, 1315, 16],
    [1264, '21:40', '22:17', 1300, 1337, 37],
    [1265, '21:40', '21:50', 1300, 1310, 10],
    [1266, '21:41', '22:08', 1301, 1328, 27],
    [1267, '21:47', '22:16', 1307, 1336, 29],
    [1268, '21:47', '22:51', 1307, 1371, 64],
    [1269, '21:47', '22:33', 1307, 1353, 46],
    [1270, '21:48', '22:03', 1308, 1323, 15],
    [1271, '21:50', '22:55', 1310, 1375, 65],
    [1272, '21:50', '22:27', 1310, 1347, 37],
    [1273, '21:50', '22:00', 1310, 1320, 10],
    [1274, '21:52', '22:29', 1312, 1349, 37],
    [1275, '21:53', '22:19', 1313, 1339, 26],
    [1276, '22:00', '22:38', 1320, 1358, 38],
    [1277, '22:00', '22:10', 1320, 1330, 10],
    [1278, '22:02', '22:12', 1322, 1332, 10],
    [1279, '22:02', '22:48', 1322, 1368, 46],
    [1280, '22:04', '22:31', 1324, 1351, 27],
    [1281, '22:05', '23:24', 1325, 1404, 79],
    [1282, '22:07', '22:44', 1327, 1364, 37],
    [1283, '22:07', '22:39', 1327, 1359, 32],
    [1284, '22:09', '22:25', 1329, 1345, 16],
    [1285, '22:10', '23:25', 1330, 1405, 75],
    [1286, '22:13', '22:38', 1333, 1358, 25],
    [1287, '22:13', '22:53', 1333, 1373, 40],
    [1288, '22:17', '22:27', 1337, 1347, 10],
    [1289, '22:17', '23:03', 1337, 1383, 46],
    [1290, '22:19', '22:46', 1339, 1366, 27],
    [1291, '22:22', '22:59', 1342, 1379, 37],
    [1292, '22:24', '22:48', 1344, 1368, 24],
    [1293, '22:27', '22:52', 1347, 1372, 25],
    [1294, '22:27', '23:21', 1347, 1401, 54],
    [1295, '22:28', '23:08', 1348, 1388, 40],
    [1296, '22:30', '23:17', 1350, 1397, 47],
    [1297, '22:32', '22:42', 1352, 1362, 10],
    [1298, '22:32', '23:11', 1352, 1391, 39],
    [1299, '22:34', '23:01', 1354, 1381, 27],
    [1300, '22:35', '23:54', 1355, 1434, 79],
    [1301, '22:37', '23:14', 1357, 1394, 37],
    [1302, '22:43', '23:23', 1363, 1403, 40],
    [1303, '22:43', '23:08', 1363, 1388, 25],
    [1304, '22:47', '23:33', 1367, 1413, 46],
    [1305, '22:47', '22:57', 1367, 1377, 10],
    [1306, '22:49', '23:16', 1369, 1396, 27],
    [1307, '22:52', '23:29', 1372, 1409, 37],
    [1308, '22:53', '23:15', 1373, 1395, 22],
    [1309, '22:55', '23:55', 1375, 1435, 60],
    [1310, '22:57', '23:51', 1377, 1431, 54],
    [1311, '22:58', '23:38', 1378, 1418, 40],
    [1312, '23:02', '23:41', 1382, 1421, 39],
    [1313, '23:02', '23:12', 1382, 1392, 10],
    [1314, '23:04', '23:31', 1384, 1411, 27],
    [1315, '23:05', '00:24', 1385, 1464, 79],
    [1316, '23:07', '23:44', 1387, 1424, 37],
    [1317, '23:13', '23:53', 1393, 1433, 40],
    [1318, '23:13', '23:38', 1393, 1418, 25],
    [1319, '23:17', '00:03', 1397, 1443, 46],
    [1320, '23:17', '23:27', 1397, 1407, 10],
    [1321, '23:19', '23:46', 1399, 1426, 27],
    [1322, '23:22', '23:59', 1402, 1439, 37],
    [1323, '23:25', '00:25', 1405, 1465, 60],
    [1324, '23:27', '00:21', 1407, 1461, 54],
    [1325, '23:28', '00:08', 1408, 1448, 40],
    [1326, '23:32', '23:42', 1412, 1422, 10],
    [1327, '23:34', '00:01', 1414, 1441, 27],
    [1328, '23:35', '01:05', 1415, 1505, 90],
    [1329, '23:37', '00:09', 1417, 1449, 32],
    [1330, '23:43', '00:23', 1423, 1463, 40],
    [1331, '23:43', '00:08', 1423, 1448, 25],
    [1332, '23:46', '00:01', 1426, 1441, 15],
    [1333, '23:47', '23:57', 1427, 1437, 10],
    [1334, '23:47', '00:33', 1427, 1473, 46],
    [1335, '23:52', '00:24', 1432, 1464, 32],
    [1336, '23:55', '00:49', 1435, 1489, 54],
    [1337, '23:57', '00:57', 1437, 1497, 60],
    [1338, '23:58', '00:38', 1438, 1478, 40],
    [1339, '00:02', '00:12', 1442, 1452, 10],
    [1340, '00:07', '00:39', 1447, 1479, 32],
    [1341, '00:13', '00:38', 1453, 1478, 25],
    [1342, '00:13', '00:51', 1453, 1491, 38],
    [1343, '00:15', '01:14', 1455, 1514, 59],
    [1344, '00:17', '01:23', 1457, 1523, 66],
    [1345, '00:23', '00:33', 1463, 1473, 10],
    [1346, '00:24', '00:40', 1464, 1480, 16],
    [1347, '00:25', '01:12', 1465, 1512, 47],
    [1348, '00:28', '01:07', 1468, 1507, 39],
    [1349, '00:33', '01:05', 1473, 1505, 32],
    [1350, '00:43', '01:21', 1483, 1521, 38],
    [1351, '00:44', '00:54', 1484, 1494, 10],
    [1352, '00:47', '01:09', 1487, 1509, 22],
    [1353, '00:47', '01:26', 1487, 1526, 39],
    [1354, '00:54', '01:04', 1494, 1504, 10],
    [1355, '00:57', '01:07', 1497, 1507, 10]
]  # yapf:disable


def find_minimum_number_of_drivers(shifts, params):
    """Minimize the number of needed drivers."""

    num_shifts = len(shifts)

    # All durations are in minutes.
    max_driving_time = 540  # 8 hours.
    max_driving_time_without_pauses = 240  # 4 hours
    min_pause_after_4h = 30
    min_delay_between_shifts = 2
    max_working_time = 720
    min_working_time = 390  # 6.5 hours
    extra_time = 10 + 25

    # Computed data.
    total_driving_time = sum(shift[5] for shift in shifts)
    min_num_drivers = int(
        math.ceil(total_driving_time * 1.0 / max_driving_time))
    min_start_time = min(shift[3] for shift in shifts)
    max_end_time = max(shift[4] for shift in shifts)

    print('Bus driver scheduling')
    print('  num shifts =', num_shifts)
    print('  total driving time =', total_driving_time, 'minutes')
    print('  min num drivers =', min_num_drivers)
    print('  min start time =', min_start_time)
    print('  max end time =', max_end_time)

    # We are going to build a flow from a the start of the day to the end
    # of the day.
    #
    # Along the path, we will accumulate driving time, accrued time since the
    # last break, and total working time.

    model = cp_model.CpModel()    

    # Per node info
    driving_time = {}
    working_time = {}
    no_break_driving_time = {}

    incoming_literals = collections.defaultdict(list)
    outgoing_literals = collections.defaultdict(list)
    outgoing_source_literals = []
    incoming_sink_literals = []

    # Create all the shift variables before iterating on the transitions
    # between these shifts.
    for shift in range(num_shifts):
        driving_time[shift] = model.NewIntVar(0, max_driving_time, 'dt_%i' % shift)
        no_break_driving_time[shift] = model.NewIntVar(
            0, max_driving_time_without_pauses, 'nbdt_%i' % shift)
        working_time[shift] = model.NewIntVar(
            0, max_working_time, 'wt_%i' % shift)

    for shift in range(num_shifts):
        duration = shifts[shift][5]

        # Arc from source to shift.
        #    - set the working time of the driver
        #    - increase driving time and driving time since the last break
        source_lit = model.NewBoolVar('from source to %i' % shift)
        outgoing_source_literals.append(source_lit)
        incoming_literals[shift].append(source_lit)
        model.Add(driving_time[shift] == duration).OnlyEnforceIf(source_lit)
        model.Add(no_break_driving_time[shift] == duration).OnlyEnforceIf(
            source_lit)
        model.Add(working_time[shift] == duration + extra_time).OnlyEnforceIf(
            source_lit)

        # Arc from shift to sink
        #     - checks that working time is greater than min_working_time
        sink_lit = model.NewBoolVar('from %i to sink' % shift)
        outgoing_literals[shift].append(sink_lit)
        incoming_sink_literals.append(sink_lit)
        #model.Add(working_time[shift] >= min_working_time).OnlyEnforceIf(sink_lit)
        #model.Add(working_time[shift] < min_working_time).OnlyEnforceIf(sink_lit.Not())

        for other in range(num_shifts):
            delay = shifts[other][3] - shifts[shift][4]
            if delay < min_delay_between_shifts:
                continue
            other_duration = shifts[other][5]
            lit = model.NewBoolVar('from %i to %i' % (shift, other))

            # Increase driving time
            model.Add(driving_time[other] ==
                      driving_time[shift] + other_duration).OnlyEnforceIf(lit)

            # Increase no_break_driving or reset it to 0 depending on the delay
            if delay >= min_pause_after_4h:
                model.Add(no_break_driving_time[other] ==
                          other_duration).OnlyEnforceIf(lit)
            else:
                model.Add(
                    no_break_driving_time[other] ==
                    no_break_driving_time[shift] + other_duration).OnlyEnforceIf(lit)

            # Increase working time
            model.Add(working_time[other] == working_time[shift] + delay +
                      other_duration).OnlyEnforceIf(lit)

            # Add arc
            outgoing_literals[shift].append(lit)
            incoming_literals[other].append(lit)

    # Create dag constraint.
    for shift in range(num_shifts):
        model.Add(sum(outgoing_literals[shift]) == 1)
        model.Add(sum(incoming_literals[shift]) == 1)

    # Num drivers
    num_drivers = model.NewIntVar(min_num_drivers, min_num_drivers * 3, 'num_drivers')
    model.Add(sum(incoming_sink_literals) == num_drivers)
    model.Add(sum(outgoing_source_literals) == num_drivers)

    model.Minimize(num_drivers)      

    # Solve model.
    solver = cp_model.CpSolver()
    solver.parameters.log_search_progress = True
    solver.parameters.num_search_workers = 8
    status = solver.Solve(model)

    if status != cp_model.OPTIMAL and status != cp_model.FEASIBLE:
        return -1

    # Display solution
    optimal_num_drivers = int(solver.ObjectiveValue())
    print('minimal number of drivers =', optimal_num_drivers)
    return optimal_num_drivers


def main(args):
    """Optimize the bus driver allocation in two passes."""
    print('----------- first pass: minimize the number of drivers')
    shifts = []
    if args.instance == 1:
        shifts = SAMPLE_SHIFTS_SMALL
    elif args.instance == 2:
        shifts = SAMPLE_SHIFTS_MEDIUM
    elif args.instance == 3:
        shifts = SAMPLE_SHIFTS_LARGE
    num_drivers = find_minimum_number_of_drivers(shifts, args.params)

    print('----------- second pass: minimize the sum of working times')
    #bus_driver_scheduling(False, num_drivers)


if __name__ == '__main__':
    main(PARSER.parse_args())