Lines Matching refs:n
16 "Licensed under the Apache License, Version 2.0 (the \"License\");\n",
17 "you may not use this file except in compliance with the License.\n",
18 "You may obtain a copy of the License at\n",
19 "\n",
20 " http://www.apache.org/licenses/LICENSE-2.0\n",
21 "\n",
22 "Unless required by applicable law or agreed to in writing, software\n",
23 "distributed under the License is distributed on an \"AS IS\" BASIS,\n",
24 "WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
25 "See the License for the specific language governing permissions and\n",
26 "limitations under the License.\n"
42 "<table align=\"left\">\n",
43 "<td>\n",
44 …aw.githubusercontent.com/google/or-tools/master/tools/colab_32px.png\"/>Run in Google Colab</a>\n",
45 "</td>\n",
46 "<td>\n",
47 …githubusercontent.com/google/or-tools/master/tools/github_32px.png\"/>View source on GitHub</a>\n",
48 "</td>\n",
77 "#!/usr/bin/env python3\n",
78 "# Copyright 2010-2021 Google LLC\n",
79 "# Licensed under the Apache License, Version 2.0 (the \"License\");\n",
80 "# you may not use this file except in compliance with the License.\n",
81 "# You may obtain a copy of the License at\n",
82 "#\n",
83 "# http://www.apache.org/licenses/LICENSE-2.0\n",
84 "#\n",
85 "# Unless required by applicable law or agreed to in writing, software\n",
86 "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
87 "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
88 "# See the License for the specific language governing permissions and\n",
89 "# limitations under the License.\n",
90 "\"\"\"This model implements a bus driver scheduling problem.\n",
91 "\n",
92 "Constraints:\n",
93 "- max driving time per driver <= 9h\n",
94 "- max working time per driver <= 12h\n",
95 "- min working time per driver >= 6.5h (soft)\n",
96 "- 30 min break after each 4h of driving time per driver\n",
97 "- 10 min preparation time before the first shift\n",
98 "- 15 min cleaning time after the last shift\n",
99 "- 2 min waiting time after each shift for passenger boarding and alighting\n",
100 "\"\"\"\n",
101 "\n",
102 "import collections\n",
103 "import math\n",
104 "\n",
105 "from absl import app\n",
106 "from absl import flags\n",
107 "from google.protobuf import text_format\n",
108 "from ortools.sat.python import cp_model\n",
109 "\n",
110 "FLAGS = flags.FLAGS\n",
111 "\n",
112 "flags.DEFINE_string('output_proto', '',\n",
113 " 'Output file to write the cp_model proto to.')\n",
114 "flags.DEFINE_string('params', 'num_search_workers:8,log_search_progress:true',\n",
115 " 'Sat solver parameters.')\n",
116 "flags.DEFINE_integer('instance', 1, 'Instance to select (1, 2, 3).', 1, 3)\n",
117 "\n",
118 "SAMPLE_SHIFTS_SMALL = [\n",
119 " #\n",
120 " # column description:\n",
121 " # - shift id\n",
122 " # - shift start time as hh:mm string (for logging and readability purposes)\n",
123 " # - shift end time as hh:mm string (for logging and readability purposes)\n",
124 " # - shift start minute\n",
125 " # - shift end minute\n",
126 " # - shift duration in minutes\n",
127 " #\n",
128 " [0, '05:18', '06:00', 318, 360, 42],\n",
129 " [1, '05:26', '06:08', 326, 368, 42],\n",
130 " [2, '05:40', '05:56', 340, 356, 16],\n",
131 " [3, '06:06', '06:51', 366, 411, 45],\n",
132 " [4, '06:40', '07:52', 400, 472, 72],\n",
133 " [5, '06:42', '07:13', 402, 433, 31],\n",
134 " [6, '06:48', '08:15', 408, 495, 87],\n",
135 " [7, '06:59', '08:07', 419, 487, 68],\n",
136 " [8, '07:20', '07:36', 440, 456, 16],\n",
137 " [9, '07:35', '08:22', 455, 502, 47],\n",
138 " [10, '07:50', '08:55', 470, 535, 65],\n",
139 " [11, '08:00', '09:05', 480, 545, 65],\n",
140 " [12, '08:00', '08:35', 480, 515, 35],\n",
141 " [13, '08:11', '09:41', 491, 581, 90],\n",
142 " [14, '08:28', '08:50', 508, 530, 22],\n",
143 " [15, '08:35', '08:45', 515, 525, 10],\n",
144 " [16, '08:40', '08:50', 520, 530, 10],\n",
145 " [17, '09:03', '10:28', 543, 628, 85],\n",
146 " [18, '09:23', '09:49', 563, 589, 26],\n",
147 " [19, '09:30', '09:40', 570, 580, 10],\n",
148 " [20, '09:57', '10:20', 597, 620, 23],\n",
149 " [21, '10:09', '11:03', 609, 663, 54],\n",
150 " [22, '10:20', '10:30', 620, 630, 10],\n",
151 " [23, '11:00', '11:10', 660, 670, 10],\n",
152 " [24, '11:45', '12:24', 705, 744, 39],\n",
153 " [25, '12:18', '13:00', 738, 780, 42],\n",
154 " [26, '13:18', '14:44', 798, 884, 86],\n",
155 " [27, '13:53', '14:49', 833, 889, 56],\n",
156 " [28, '14:03', '14:50', 843, 890, 47],\n",
157 " [29, '14:28', '15:15', 868, 915, 47],\n",
158 " [30, '14:30', '15:41', 870, 941, 71],\n",
159 " [31, '14:48', '15:35', 888, 935, 47],\n",
160 " [32, '15:03', '15:50', 903, 950, 47],\n",
161 " [33, '15:28', '16:54', 928, 1014, 86],\n",
162 " [34, '15:38', '16:25', 938, 985, 47],\n",
163 " [35, '15:40', '15:56', 940, 956, 16],\n",
164 " [36, '15:58', '16:45', 958, 1005, 47],\n",
165 " [37, '16:04', '17:30', 964, 1050, 86],\n",
166 " [38, '16:28', '17:15', 988, 1035, 47],\n",
167 " [39, '16:36', '17:21', 996, 1041, 45],\n",
168 " [40, '16:50', '17:00', 1010, 1020, 10],\n",
169 " [41, '16:54', '18:20', 1014, 1100, 86],\n",
170 " [42, '17:01', '17:13', 1021, 1033, 12],\n",
171 " [43, '17:19', '18:31', 1039, 1111, 72],\n",
172 " [44, '17:23', '18:10', 1043, 1090, 47],\n",
173 " [45, '17:34', '18:15', 1054, 1095, 41],\n",
174 " [46, '18:04', '19:29', 1084, 1169, 85],\n",
175 " [47, '18:34', '19:58', 1114, 1198, 84],\n",
176 " [48, '19:56', '20:34', 1196, 1234, 38],\n",
177 " [49, '20:05', '20:48', 1205, 1248, 43]\n",
178 "] # yapf:disable\n",
179 "\n",
180 "SAMPLE_SHIFTS_MEDIUM = [\n",
181 " [0, '04:30', '04:53', 270, 293, 23],\n",
182 " [1, '04:46', '04:56', 286, 296, 10],\n",
183 " [2, '04:52', '05:56', 292, 356, 64],\n",
184 " [3, '04:53', '05:23', 293, 323, 30],\n",
185 " [4, '05:07', '05:44', 307, 344, 37],\n",
186 " [5, '05:10', '06:06', 310, 366, 56],\n",
187 " [6, '05:18', '06:03', 318, 363, 45],\n",
188 " [7, '05:30', '05:40', 330, 340, 10],\n",
189 " [8, '05:30', '05:40', 330, 340, 10],\n",
190 " [9, '05:33', '06:15', 333, 375, 42],\n",
191 " [10, '05:40', '05:50', 340, 350, 10],\n",
192 " [11, '05:43', '06:08', 343, 368, 25],\n",
193 " [12, '05:54', '07:20', 354, 440, 86],\n",
194 " [13, '06:04', '06:37', 364, 397, 33],\n",
195 " [14, '06:13', '06:58', 373, 418, 45],\n",
196 " [15, '06:14', '07:40', 374, 460, 86],\n",
197 " [16, '06:15', '07:15', 375, 435, 60],\n",
198 " [17, '06:16', '06:26', 376, 386, 10],\n",
199 " [18, '06:17', '06:34', 377, 394, 17],\n",
200 " [19, '06:20', '06:36', 380, 396, 16],\n",
201 " [20, '06:22', '07:06', 382, 426, 44],\n",
202 " [21, '06:24', '07:50', 384, 470, 86],\n",
203 " [22, '06:27', '06:44', 387, 404, 17],\n",
204 " [23, '06:30', '06:40', 390, 400, 10],\n",
205 " [24, '06:31', '06:43', 391, 403, 12],\n",
206 " [25, '06:33', '07:53', 393, 473, 80],\n",
207 " [26, '06:34', '07:09', 394, 429, 35],\n",
208 " [27, '06:40', '06:56', 400, 416, 16],\n",
209 " [28, '06:44', '07:17', 404, 437, 33],\n",
210 " [29, '06:46', '06:58', 406, 418, 12],\n",
211 " [30, '06:49', '07:43', 409, 463, 54],\n",
212 " [31, '06:50', '07:05', 410, 425, 15],\n",
213 " [32, '06:52', '07:36', 412, 456, 44],\n",
214 " [33, '06:54', '07:27', 414, 447, 33],\n",
215 " [34, '06:56', '08:23', 416, 503, 87],\n",
216 " [35, '07:04', '07:44', 424, 464, 40],\n",
217 " [36, '07:11', '08:36', 431, 516, 85],\n",
218 " [37, '07:17', '07:35', 437, 455, 18],\n",
219 " [38, '07:22', '08:06', 442, 486, 44],\n",
220 " [39, '07:27', '08:15', 447, 495, 48],\n",
221 " [40, '07:35', '07:45', 455, 465, 10],\n",
222 " [41, '07:43', '08:08', 463, 488, 25],\n",
223 " [42, '07:50', '08:37', 470, 517, 47],\n",
224 " [43, '07:58', '08:45', 478, 525, 47],\n",
225 " [44, '08:00', '08:35', 480, 515, 35],\n",
226 " [45, '08:06', '08:51', 486, 531, 45],\n",
227 " [46, '08:10', '08:45', 490, 525, 35],\n",
228 " [47, '08:15', '08:30', 495, 510, 15],\n",
229 " [48, '08:16', '09:00', 496, 540, 44],\n",
230 " [49, '08:18', '09:16', 498, 556, 58],\n",
231 " [50, '08:20', '08:36', 500, 516, 16],\n",
232 " [51, '08:27', '09:07', 507, 547, 40],\n",
233 " [52, '08:30', '08:45', 510, 525, 15],\n",
234 " [53, '08:35', '09:15', 515, 555, 40],\n",
235 " [54, '08:46', '09:30', 526, 570, 44],\n",
236 " [55, '08:51', '09:17', 531, 557, 26],\n",
237 " [56, '08:55', '09:15', 535, 555, 20],\n",
238 " [57, '08:58', '09:38', 538, 578, 40],\n",
239 " [58, '09:00', '09:35', 540, 575, 35],\n",
240 " [59, '09:00', '09:16', 540, 556, 16],\n",
241 " [60, '09:20', '09:36', 560, 576, 16],\n",
242 " [61, '09:31', '09:43', 571, 583, 12],\n",
243 " [62, '09:33', '10:15', 573, 615, 42],\n",
244 " [63, '09:54', '10:05', 594, 605, 11],\n",
245 " [64, '10:11', '10:38', 611, 638, 27],\n",
246 " [65, '10:18', '11:00', 618, 660, 42],\n",
247 " [66, '10:21', '10:47', 621, 647, 26],\n",
248 " [67, '10:25', '11:04', 625, 664, 39],\n",
249 " [68, '10:26', '11:08', 626, 668, 42],\n",
250 " [69, '10:44', '12:11', 644, 731, 87],\n",
251 " [70, '11:00', '11:16', 660, 676, 16],\n",
252 " [71, '11:15', '11:54', 675, 714, 39],\n",
253 " [72, '11:16', '11:28', 676, 688, 12],\n",
254 " [73, '11:20', '11:30', 680, 690, 10],\n",
255 " [74, '11:21', '11:47', 681, 707, 26],\n",
256 " [75, '11:25', '12:04', 685, 724, 39],\n",
257 " [76, '11:34', '11:45', 694, 705, 11],\n",
258 " [77, '11:35', '12:14', 695, 734, 39],\n",
259 " [78, '11:41', '12:23', 701, 743, 42],\n",
260 " [79, '11:44', '12:35', 704, 755, 51],\n",
261 " [80, '11:46', '11:58', 706, 718, 12],\n",
262 " [81, '12:00', '12:10', 720, 730, 10],\n",
263 " [82, '12:04', '12:15', 724, 735, 11],\n",
264 " [83, '12:04', '13:04', 724, 784, 60],\n",
265 " [84, '12:11', '12:38', 731, 758, 27],\n",
266 " [85, '12:15', '12:54', 735, 774, 39],\n",
267 " [86, '12:25', '13:10', 745, 790, 45],\n",
268 " [87, '12:30', '12:40', 750, 760, 10],\n",
269 " [88, '12:34', '13:58', 754, 838, 84],\n",
270 " [89, '12:38', '13:25', 758, 805, 47],\n",
271 " [90, '12:48', '13:35', 768, 815, 47],\n",
272 " [91, '13:00', '13:16', 780, 796, 16],\n",
273 " [92, '13:05', '13:44', 785, 824, 39],\n",
274 " [93, '13:08', '13:55', 788, 835, 47],\n",
275 " [94, '13:14', '14:38', 794, 878, 84],\n",
276 " [95, '13:23', '13:49', 803, 829, 26],\n",
277 " [96, '13:25', '14:04', 805, 844, 39],\n",
278 " [97, '13:28', '14:54', 808, 894, 86],\n",
279 " [98, '13:31', '13:43', 811, 823, 12],\n",
280 " [99, '13:34', '14:58', 814, 898, 84],\n",
281 " [100, '13:38', '14:25', 818, 865, 47],\n",
282 " [101, '13:38', '15:04', 818, 904, 86],\n",
283 " [102, '13:39', '14:33', 819, 873, 54],\n",
284 " [103, '13:40', '13:50', 820, 830, 10],\n",
285 " [104, '13:43', '14:10', 823, 850, 27],\n",
286 " [105, '13:48', '14:35', 828, 875, 47],\n",
287 " [106, '13:48', '14:35', 828, 875, 47],\n",
288 " [107, '13:53', '14:40', 833, 880, 47],\n",
289 " [108, '13:58', '15:24', 838, 924, 86],\n",
290 " [109, '13:58', '14:25', 838, 865, 27],\n",
291 " [110, '14:00', '14:16', 840, 856, 16],\n",
292 " [111, '14:13', '15:00', 853, 900, 47],\n",
293 " [112, '14:20', '15:31', 860, 931, 71],\n",
294 " [113, '14:25', '15:02', 865, 902, 37],\n",
295 " [114, '14:34', '14:45', 874, 885, 11],\n",
296 " [115, '14:40', '15:51', 880, 951, 71],\n",
297 " [116, '14:40', '14:56', 880, 896, 16],\n",
298 " [117, '14:46', '14:58', 886, 898, 12],\n",
299 " [118, '14:49', '15:43', 889, 943, 54],\n",
300 " [119, '14:52', '15:21', 892, 921, 29],\n",
301 " [120, '14:58', '16:24', 898, 984, 86],\n",
302 " [121, '14:59', '15:53', 899, 953, 54],\n",
303 " [122, '15:00', '15:10', 900, 910, 10],\n",
304 " [123, '15:00', '15:35', 900, 935, 35],\n",
305 " [124, '15:08', '15:45', 908, 945, 37],\n",
306 " [125, '15:12', '15:36', 912, 936, 24],\n",
307 " [126, '15:18', '16:05', 918, 965, 47],\n",
308 " [127, '15:24', '16:05', 924, 965, 41],\n",
309 " [128, '15:31', '15:43', 931, 943, 12],\n",
310 " [129, '15:35', '15:54', 935, 954, 19],\n",
311 " [130, '15:36', '16:21', 936, 981, 45],\n",
312 " [131, '15:39', '16:33', 939, 993, 54],\n",
313 " [132, '15:48', '16:35', 948, 995, 47],\n",
314 " [133, '15:50', '17:01', 950, 1021, 71],\n",
315 " [134, '16:03', '16:50', 963, 1010, 47],\n",
316 " [135, '16:18', '17:44', 978, 1064, 86],\n",
317 " [136, '16:24', '17:05', 984, 1025, 41],\n",
318 " [137, '16:28', '17:15', 988, 1035, 47],\n",
319 " [138, '16:34', '17:15', 994, 1035, 41],\n",
320 " [139, '16:38', '17:25', 998, 1045, 47],\n",
321 " [140, '16:40', '16:56', 1000, 1016, 16],\n",
322 " [141, '16:45', '17:04', 1005, 1024, 19],\n",
323 " [142, '16:52', '17:36', 1012, 1056, 44],\n",
324 " [143, '16:58', '17:45', 1018, 1065, 47],\n",
325 " [144, '17:04', '18:30', 1024, 1110, 86],\n",
326 " [145, '17:04', '17:45', 1024, 1065, 41],\n",
327 " [146, '17:09', '18:03', 1029, 1083, 54],\n",
328 " [147, '17:18', '18:44', 1038, 1124, 86],\n",
329 " [148, '17:28', '18:15', 1048, 1095, 47],\n",
330 " [149, '17:29', '18:41', 1049, 1121, 72],\n",
331 " [150, '17:36', '18:21', 1056, 1101, 45],\n",
332 " [151, '17:38', '18:25', 1058, 1105, 47],\n",
333 " [152, '17:40', '17:56', 1060, 1076, 16],\n",
334 " [153, '17:45', '18:04', 1065, 1084, 19],\n",
335 " [154, '17:46', '17:58', 1066, 1078, 12],\n",
336 " [155, '17:48', '18:35', 1068, 1115, 47],\n",
337 " [156, '17:49', '18:43', 1069, 1123, 54],\n",
338 " [157, '17:55', '18:14', 1075, 1094, 19],\n",
339 " [158, '17:58', '18:45', 1078, 1125, 47],\n",
340 " [159, '18:00', '19:11', 1080, 1151, 71],\n",
341 " [160, '18:04', '18:45', 1084, 1125, 41],\n",
342 " [161, '18:09', '19:03', 1089, 1143, 54],\n",
343 " [162, '18:13', '19:00', 1093, 1140, 47],\n",
344 " [163, '18:13', '18:40', 1093, 1120, 27],\n",
345 " [164, '18:19', '19:13', 1099, 1153, 54],\n",
346 " [165, '18:28', '19:25', 1108, 1165, 57],\n",
347 " [166, '18:48', '19:28', 1128, 1168, 40],\n",
348 " [167, '19:03', '19:45', 1143, 1185, 42],\n",
349 " [168, '19:20', '19:36', 1160, 1176, 16],\n",
350 " [169, '19:21', '19:31', 1161, 1171, 10],\n",
351 " [170, '19:25', '20:04', 1165, 1204, 39],\n",
352 " [171, '19:26', '20:08', 1166, 1208, 42],\n",
353 " [172, '19:30', '19:40', 1170, 1180, 10],\n",
354 " [173, '19:44', '20:33', 1184, 1233, 49],\n",
355 " [174, '19:48', '21:09', 1188, 1269, 81],\n",
356 " [175, '19:53', '21:02', 1193, 1262, 69],\n",
357 " [176, '20:04', '20:29', 1204, 1229, 25],\n",
358 " [177, '20:17', '21:03', 1217, 1263, 46],\n",
359 " [178, '20:20', '20:57', 1220, 1257, 37],\n",
360 " [179, '20:29', '21:18', 1229, 1278, 49],\n",
361 " [180, '20:35', '21:54', 1235, 1314, 79],\n",
362 " [181, '20:40', '20:50', 1240, 1250, 10],\n",
363 " [182, '20:47', '21:42', 1247, 1302, 55],\n",
364 " [183, '21:00', '21:10', 1260, 1270, 10],\n",
365 " [184, '21:07', '21:44', 1267, 1304, 37],\n",
366 " [185, '21:14', '22:03', 1274, 1323, 49],\n",
367 " [186, '21:39', '21:55', 1299, 1315, 16],\n",
368 " [187, '21:40', '22:17', 1300, 1337, 37],\n",
369 " [188, '21:40', '21:50', 1300, 1310, 10],\n",
370 " [189, '21:48', '22:03', 1308, 1323, 15],\n",
371 " [190, '22:17', '23:03', 1337, 1383, 46],\n",
372 " [191, '22:43', '23:08', 1363, 1388, 25],\n",
373 " [192, '23:35', '01:05', 1415, 1505, 90],\n",
374 " [193, '23:46', '00:01', 1426, 1441, 15],\n",
375 " [194, '23:47', '00:33', 1427, 1473, 46],\n",
376 " [195, '23:52', '00:24', 1432, 1464, 32],\n",
377 " [196, '23:58', '00:38', 1438, 1478, 40],\n",
378 " [197, '00:02', '00:12', 1442, 1452, 10],\n",
379 " [198, '00:07', '00:39', 1447, 1479, 32],\n",
380 " [199, '00:25', '01:12', 1465, 1512, 47]\n",
381 "] # yapf:disable\n",
382 "\n",
383 "SAMPLE_SHIFTS_LARGE = [\n",
384 " [0, '04:18', '05:00', 258, 300, 42],\n",
385 " [1, '04:27', '05:08', 267, 308, 41],\n",
386 " [2, '04:29', '05:26', 269, 326, 57],\n",
387 " [3, '04:29', '04:55', 269, 295, 26],\n",
388 " [4, '04:30', '04:53', 270, 293, 23],\n",
389 " [5, '04:30', '04:51', 270, 291, 21],\n",
390 " [6, '04:31', '04:53', 271, 293, 22],\n",
391 " [7, '04:33', '05:15', 273, 315, 42],\n",
392 " [8, '04:34', '04:44', 274, 284, 10],\n",
393 " [9, '04:34', '05:03', 274, 303, 29],\n",
394 " [10, '04:35', '04:50', 275, 290, 15],\n",
395 " [11, '04:36', '04:46', 276, 286, 10],\n",
396 " [12, '04:37', '05:18', 277, 318, 41],\n",
397 " [13, '04:41', '05:13', 281, 313, 32],\n",
398 " [14, '04:42', '05:23', 282, 323, 41],\n",
399 " [15, '04:43', '04:53', 283, 293, 10],\n",
400 " [16, '04:44', '05:45', 284, 345, 61],\n",
401 " [17, '04:45', '05:11', 285, 311, 26],\n",
402 " [18, '04:46', '05:01', 286, 301, 15],\n",
403 " [19, '04:46', '04:56', 286, 296, 10],\n",
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1605 " [1221, '20:35', '21:54', 1235, 1314, 79],\n",
1606 " [1222, '20:37', '21:14', 1237, 1274, 37],\n",
1607 " [1223, '20:38', '21:08', 1238, 1268, 30],\n",
1608 " [1224, '20:40', '20:50', 1240, 1250, 10],\n",
1609 " [1225, '20:40', '21:17', 1240, 1277, 37],\n",
1610 " [1226, '20:40', '20:56', 1240, 1256, 16],\n",
1611 " [1227, '20:44', '21:33', 1244, 1293, 49],\n",
1612 " [1228, '20:47', '21:33', 1247, 1293, 46],\n",
1613 " [1229, '20:47', '21:42', 1247, 1302, 55],\n",
1614 " [1230, '20:50', '21:00', 1250, 1260, 10],\n",
1615 " [1231, '20:50', '22:00', 1250, 1320, 70],\n",
1616 " [1232, '20:50', '22:09', 1250, 1329, 79],\n",
1617 " [1233, '20:50', '21:27', 1250, 1287, 37],\n",
1618 " [1234, '20:52', '21:29', 1252, 1289, 37],\n",
1619 " [1235, '20:53', '21:20', 1253, 1280, 27],\n",
1620 " [1236, '20:56', '21:11', 1256, 1271, 15],\n",
1621 " [1237, '20:59', '21:48', 1259, 1308, 49],\n",
1622 " [1238, '21:00', '21:10', 1260, 1270, 10],\n",
1623 " [1239, '21:00', '21:37', 1260, 1297, 37],\n",
1624 " [1240, '21:02', '21:48', 1262, 1308, 46],\n",
1625 " [1241, '21:05', '22:24', 1265, 1344, 79],\n",
1626 " [1242, '21:07', '21:44', 1267, 1304, 37],\n",
1627 " [1243, '21:07', '22:02', 1267, 1322, 55],\n",
1628 " [1244, '21:08', '21:38', 1268, 1298, 30],\n",
1629 " [1245, '21:10', '22:25', 1270, 1345, 75],\n",
1630 " [1246, '21:10', '21:20', 1270, 1280, 10],\n",
1631 " [1247, '21:10', '21:47', 1270, 1307, 37],\n",
1632 " [1248, '21:14', '22:03', 1274, 1323, 49],\n",
1633 " [1249, '21:17', '22:03', 1277, 1323, 46],\n",
1634 " [1250, '21:20', '22:18', 1280, 1338, 58],\n",
1635 " [1251, '21:20', '21:57', 1280, 1317, 37],\n",
1636 " [1252, '21:20', '21:30', 1280, 1290, 10],\n",
1637 " [1253, '21:22', '21:59', 1282, 1319, 37],\n",
1638 " [1254, '21:24', '21:49', 1284, 1309, 25],\n",
1639 " [1255, '21:27', '22:21', 1287, 1341, 54],\n",
1640 " [1256, '21:30', '22:07', 1290, 1327, 37],\n",
1641 " [1257, '21:30', '22:20', 1290, 1340, 50],\n",
1642 " [1258, '21:30', '21:40', 1290, 1300, 10],\n",
1643 " [1259, '21:32', '22:18', 1292, 1338, 46],\n",
1644 " [1260, '21:32', '22:01', 1292, 1321, 29],\n",
1645 " [1261, '21:35', '22:54', 1295, 1374, 79],\n",
1646 " [1262, '21:37', '22:14', 1297, 1334, 37],\n",
1647 " [1263, '21:39', '21:55', 1299, 1315, 16],\n",
1648 " [1264, '21:40', '22:17', 1300, 1337, 37],\n",
1649 " [1265, '21:40', '21:50', 1300, 1310, 10],\n",
1650 " [1266, '21:41', '22:08', 1301, 1328, 27],\n",
1651 " [1267, '21:47', '22:16', 1307, 1336, 29],\n",
1652 " [1268, '21:47', '22:51', 1307, 1371, 64],\n",
1653 " [1269, '21:47', '22:33', 1307, 1353, 46],\n",
1654 " [1270, '21:48', '22:03', 1308, 1323, 15],\n",
1655 " [1271, '21:50', '22:55', 1310, 1375, 65],\n",
1656 " [1272, '21:50', '22:27', 1310, 1347, 37],\n",
1657 " [1273, '21:50', '22:00', 1310, 1320, 10],\n",
1658 " [1274, '21:52', '22:29', 1312, 1349, 37],\n",
1659 " [1275, '21:53', '22:19', 1313, 1339, 26],\n",
1660 " [1276, '22:00', '22:38', 1320, 1358, 38],\n",
1661 " [1277, '22:00', '22:10', 1320, 1330, 10],\n",
1662 " [1278, '22:02', '22:12', 1322, 1332, 10],\n",
1663 " [1279, '22:02', '22:48', 1322, 1368, 46],\n",
1664 " [1280, '22:04', '22:31', 1324, 1351, 27],\n",
1665 " [1281, '22:05', '23:24', 1325, 1404, 79],\n",
1666 " [1282, '22:07', '22:44', 1327, 1364, 37],\n",
1667 " [1283, '22:07', '22:39', 1327, 1359, 32],\n",
1668 " [1284, '22:09', '22:25', 1329, 1345, 16],\n",
1669 " [1285, '22:10', '23:25', 1330, 1405, 75],\n",
1670 " [1286, '22:13', '22:38', 1333, 1358, 25],\n",
1671 " [1287, '22:13', '22:53', 1333, 1373, 40],\n",
1672 " [1288, '22:17', '22:27', 1337, 1347, 10],\n",
1673 " [1289, '22:17', '23:03', 1337, 1383, 46],\n",
1674 " [1290, '22:19', '22:46', 1339, 1366, 27],\n",
1675 " [1291, '22:22', '22:59', 1342, 1379, 37],\n",
1676 " [1292, '22:24', '22:48', 1344, 1368, 24],\n",
1677 " [1293, '22:27', '22:52', 1347, 1372, 25],\n",
1678 " [1294, '22:27', '23:21', 1347, 1401, 54],\n",
1679 " [1295, '22:28', '23:08', 1348, 1388, 40],\n",
1680 " [1296, '22:30', '23:17', 1350, 1397, 47],\n",
1681 " [1297, '22:32', '22:42', 1352, 1362, 10],\n",
1682 " [1298, '22:32', '23:11', 1352, 1391, 39],\n",
1683 " [1299, '22:34', '23:01', 1354, 1381, 27],\n",
1684 " [1300, '22:35', '23:54', 1355, 1434, 79],\n",
1685 " [1301, '22:37', '23:14', 1357, 1394, 37],\n",
1686 " [1302, '22:43', '23:23', 1363, 1403, 40],\n",
1687 " [1303, '22:43', '23:08', 1363, 1388, 25],\n",
1688 " [1304, '22:47', '23:33', 1367, 1413, 46],\n",
1689 " [1305, '22:47', '22:57', 1367, 1377, 10],\n",
1690 " [1306, '22:49', '23:16', 1369, 1396, 27],\n",
1691 " [1307, '22:52', '23:29', 1372, 1409, 37],\n",
1692 " [1308, '22:53', '23:15', 1373, 1395, 22],\n",
1693 " [1309, '22:55', '23:55', 1375, 1435, 60],\n",
1694 " [1310, '22:57', '23:51', 1377, 1431, 54],\n",
1695 " [1311, '22:58', '23:38', 1378, 1418, 40],\n",
1696 " [1312, '23:02', '23:41', 1382, 1421, 39],\n",
1697 " [1313, '23:02', '23:12', 1382, 1392, 10],\n",
1698 " [1314, '23:04', '23:31', 1384, 1411, 27],\n",
1699 " [1315, '23:05', '00:24', 1385, 1464, 79],\n",
1700 " [1316, '23:07', '23:44', 1387, 1424, 37],\n",
1701 " [1317, '23:13', '23:53', 1393, 1433, 40],\n",
1702 " [1318, '23:13', '23:38', 1393, 1418, 25],\n",
1703 " [1319, '23:17', '00:03', 1397, 1443, 46],\n",
1704 " [1320, '23:17', '23:27', 1397, 1407, 10],\n",
1705 " [1321, '23:19', '23:46', 1399, 1426, 27],\n",
1706 " [1322, '23:22', '23:59', 1402, 1439, 37],\n",
1707 " [1323, '23:25', '00:25', 1405, 1465, 60],\n",
1708 " [1324, '23:27', '00:21', 1407, 1461, 54],\n",
1709 " [1325, '23:28', '00:08', 1408, 1448, 40],\n",
1710 " [1326, '23:32', '23:42', 1412, 1422, 10],\n",
1711 " [1327, '23:34', '00:01', 1414, 1441, 27],\n",
1712 " [1328, '23:35', '01:05', 1415, 1505, 90],\n",
1713 " [1329, '23:37', '00:09', 1417, 1449, 32],\n",
1714 " [1330, '23:43', '00:23', 1423, 1463, 40],\n",
1715 " [1331, '23:43', '00:08', 1423, 1448, 25],\n",
1716 " [1332, '23:46', '00:01', 1426, 1441, 15],\n",
1717 " [1333, '23:47', '23:57', 1427, 1437, 10],\n",
1718 " [1334, '23:47', '00:33', 1427, 1473, 46],\n",
1719 " [1335, '23:52', '00:24', 1432, 1464, 32],\n",
1720 " [1336, '23:55', '00:49', 1435, 1489, 54],\n",
1721 " [1337, '23:57', '00:57', 1437, 1497, 60],\n",
1722 " [1338, '23:58', '00:38', 1438, 1478, 40],\n",
1723 " [1339, '00:02', '00:12', 1442, 1452, 10],\n",
1724 " [1340, '00:07', '00:39', 1447, 1479, 32],\n",
1725 " [1341, '00:13', '00:38', 1453, 1478, 25],\n",
1726 " [1342, '00:13', '00:51', 1453, 1491, 38],\n",
1727 " [1343, '00:15', '01:14', 1455, 1514, 59],\n",
1728 " [1344, '00:17', '01:23', 1457, 1523, 66],\n",
1729 " [1345, '00:23', '00:33', 1463, 1473, 10],\n",
1730 " [1346, '00:24', '00:40', 1464, 1480, 16],\n",
1731 " [1347, '00:25', '01:12', 1465, 1512, 47],\n",
1732 " [1348, '00:28', '01:07', 1468, 1507, 39],\n",
1733 " [1349, '00:33', '01:05', 1473, 1505, 32],\n",
1734 " [1350, '00:43', '01:21', 1483, 1521, 38],\n",
1735 " [1351, '00:44', '00:54', 1484, 1494, 10],\n",
1736 " [1352, '00:47', '01:09', 1487, 1509, 22],\n",
1737 " [1353, '00:47', '01:26', 1487, 1526, 39],\n",
1738 " [1354, '00:54', '01:04', 1494, 1504, 10],\n",
1739 " [1355, '00:57', '01:07', 1497, 1507, 10]\n",
1740 "] # yapf:disable\n",
1741 "\n",
1742 "# pytype: disable=wrong-arg-types\n",
1743 "\n",
1744 "\n",
1745 "def bus_driver_scheduling(minimize_drivers, max_num_drivers):\n",
1746 " \"\"\"Optimize the bus driver scheduling problem.\n",
1747 "\n",
1748 " This model has two modes.\n",
1749 "\n",
1750 " If minimize_drivers == True, the objective will be to find the minimal\n",
1751 " number of drivers, independently of the working times of each drivers.\n",
1752 "\n",
1753 " Otherwise, will will create max_num_drivers non optional drivers, and\n",
1754 " minimize the sum of working times of these drivers.\n",
1755 "\n",
1756 " Args:\n",
1757 " minimize_drivers: A Boolean parameter specifying the objective of the\n",
1758 " problem. If True, it tries to minimize the number of used drivers. If\n",
1759 " false, it minimizes the sum of working times per workers.\n",
1760 " max_num_drivers: This number specifies the exact number of non optional\n",
1761 " drivers to use. This is only used if 'minimize_drivers' is False.\n",
1762 "\n",
1763 " Returns:\n",
1764 " The objective value of the model.\n",
1765 " \"\"\"\n",
1766 " shifts = None\n",
1767 " if FLAGS.instance == 1:\n",
1768 " shifts = SAMPLE_SHIFTS_SMALL\n",
1769 " elif FLAGS.instance == 2:\n",
1770 " shifts = SAMPLE_SHIFTS_MEDIUM\n",
1771 " elif FLAGS.instance == 3:\n",
1772 " shifts = SAMPLE_SHIFTS_LARGE\n",
1773 "\n",
1774 " num_shifts = len(shifts)\n",
1775 "\n",
1776 " # All durations are in minutes.\n",
1777 " max_driving_time = 540 # 8 hours.\n",
1778 " max_driving_time_without_pauses = 240 # 4 hours\n",
1779 " min_pause_after_4h = 30\n",
1780 " min_delay_between_shifts = 2\n",
1781 " max_working_time = 720\n",
1782 " min_working_time = 390 # 6.5 hours\n",
1783 " setup_time = 10\n",
1784 " cleanup_time = 15\n",
1785 "\n",
1786 " # Computed data.\n",
1787 " total_driving_time = sum(shift[5] for shift in shifts)\n",
1788 " min_num_drivers = int(math.ceil(total_driving_time * 1.0 /\n",
1789 " max_driving_time))\n",
1790 " num_drivers = 2 * min_num_drivers if minimize_drivers else max_num_drivers\n",
1791 " min_start_time = min(shift[3] for shift in shifts)\n",
1792 " max_end_time = max(shift[4] for shift in shifts)\n",
1793 "\n",
1794 " print('Bus driver scheduling')\n",
1795 " print(' num shifts =', num_shifts)\n",
1796 " print(' total driving time =', total_driving_time, 'minutes')\n",
1797 " print(' min num drivers =', min_num_drivers)\n",
1798 " print(' num drivers =', num_drivers)\n",
1799 " print(' min start time =', min_start_time)\n",
1800 " print(' max end time =', max_end_time)\n",
1801 "\n",
1802 " model = cp_model.CpModel()\n",
1803 "\n",
1804 " # For each driver and each shift, we store:\n",
1805 " # - the total driving time including this shift\n",
1806 " # - the acrued driving time since the last 30 minute break\n",
1807 " # Special arcs have the following effect:\n",
1808 " # - 'from source to shift' sets the starting time and accumulate the first\n",
1809 " # shift\n",
1810 " # - 'from shift to end' sets the ending time, and fill the driving_times\n",
1811 " # variable\n",
1812 " # Arcs between two shifts have the following impact\n",
1813 " # - add the duration of the shift to the total driving time\n",
1814 " # - reset the accumulated driving time if the distance between the two\n",
1815 " # shifts is more than 30 minutes, add the duration of the shift to the\n",
1816 " # accumulated driving time since the last break otherwise\n",
1817 "\n",
1818 " # Per (driver, node) info (driving time, performed,\n",
1819 " # driving time since break)\n",
1820 " total_driving = {}\n",
1821 " no_break_driving = {}\n",
1822 " performed = {}\n",
1823 " starting_shifts = {}\n",
1824 "\n",
1825 " # Per driver info (start, end, driving times, is working)\n",
1826 " start_times = []\n",
1827 " end_times = []\n",
1828 " driving_times = []\n",
1829 " working_drivers = []\n",
1830 " working_times = []\n",
1831 "\n",
1832 " # Weighted objective\n",
1833 " delay_literals = []\n",
1834 " delay_weights = []\n",
1835 "\n",
1836 " # Used to propagate more between drivers\n",
1837 " shared_incoming_literals = collections.defaultdict(list)\n",
1838 " shared_outgoing_literals = collections.defaultdict(list)\n",
1839 "\n",
1840 " for d in range(num_drivers):\n",
1841 " start_times.append(\n",
1842 " model.NewIntVar(min_start_time - setup_time, max_end_time,\n",
1843 " 'start_%i' % d))\n",
1844 " end_times.append(\n",
1845 " model.NewIntVar(min_start_time, max_end_time + cleanup_time,\n",
1846 " 'end_%i' % d))\n",
1847 " driving_times.append(\n",
1848 " model.NewIntVar(0, max_driving_time, 'driving_%i' % d))\n",
1849 " working_times.append(\n",
1850 " model.NewIntVar(0, max_working_time, 'working_times_%i' % d))\n",
1851 "\n",
1852 " incoming_literals = collections.defaultdict(list)\n",
1853 " outgoing_literals = collections.defaultdict(list)\n",
1854 " outgoing_source_literals = []\n",
1855 " incoming_sink_literals = []\n",
1856 "\n",
1857 " # Create all the shift variables before iterating on the transitions\n",
1858 " # between these shifts.\n",
1859 " for s in range(num_shifts):\n",
1860 " total_driving[d, s] = model.NewIntVar(0, max_driving_time,\n",
1861 " 'dr_%i_%i' % (d, s))\n",
1862 " no_break_driving[d, s] = model.NewIntVar(\n",
1863 " 0, max_driving_time_without_pauses, 'mdr_%i_%i' % (d, s))\n",
1864 " performed[d, s] = model.NewBoolVar('performed_%i_%i' % (d, s))\n",
1865 "\n",
1866 " for s in range(num_shifts):\n",
1867 " shift = shifts[s]\n",
1868 " duration = shift[5]\n",
1869 "\n",
1870 " # Arc from source to shift.\n",
1871 " # - set the start time of the driver\n",
1872 " # - increase driving time and driving time since break\n",
1873 " source_lit = model.NewBoolVar('%i from source to %i' % (d, s))\n",
1874 " outgoing_source_literals.append(source_lit)\n",
1875 " incoming_literals[s].append(source_lit)\n",
1876 " shared_incoming_literals[s].append(source_lit)\n",
1877 " model.Add(start_times[d] == shift[3] -\n",
1878 " setup_time).OnlyEnforceIf(source_lit)\n",
1879 " model.Add(total_driving[d, s] == duration).OnlyEnforceIf(source_lit)\n",
1880 " model.Add(no_break_driving[d,\n",
1881 " s] == duration).OnlyEnforceIf(source_lit)\n",
1882 " starting_shifts[d, s] = source_lit\n",
1883 "\n",
1884 " # Arc from shift to sink\n",
1885 " # - set the end time of the driver\n",
1886 " # - set the driving times of the driver\n",
1887 " sink_lit = model.NewBoolVar('%i from %i to sink' % (d, s))\n",
1888 " outgoing_literals[s].append(sink_lit)\n",
1889 " shared_outgoing_literals[s].append(sink_lit)\n",
1890 " incoming_sink_literals.append(sink_lit)\n",
1891 " model.Add(end_times[d] == shift[4] +\n",
1892 " cleanup_time).OnlyEnforceIf(sink_lit)\n",
1893 " model.Add(\n",
1894 " driving_times[d] == total_driving[d, s]).OnlyEnforceIf(sink_lit)\n",
1895 "\n",
1896 " # Node not performed\n",
1897 " # - set both driving times to 0\n",
1898 " # - add a looping arc on the node\n",
1899 " model.Add(total_driving[d,\n",
1900 " s] == 0).OnlyEnforceIf(performed[d,\n",
1901 " s].Not())\n",
1902 " model.Add(no_break_driving[d, s] == 0).OnlyEnforceIf(\n",
1903 " performed[d, s].Not())\n",
1904 " incoming_literals[s].append(performed[d, s].Not())\n",
1905 " outgoing_literals[s].append(performed[d, s].Not())\n",
1906 " # Not adding to the shared lists, because, globally, each node will have\n",
1907 " # one incoming literal, and one outgoing literal.\n",
1908 "\n",
1909 " # Node performed:\n",
1910 " # - add upper bound on start_time\n",
1911 " # - add lower bound on end_times\n",
1912 " model.Add(start_times[d] <= shift[3] - setup_time).OnlyEnforceIf(\n",
1913 " performed[d, s])\n",
1914 " model.Add(end_times[d] >= shift[4] + cleanup_time).OnlyEnforceIf(\n",
1915 " performed[d, s])\n",
1916 "\n",
1917 " for o in range(num_shifts):\n",
1918 " other = shifts[o]\n",
1919 " delay = other[3] - shift[4]\n",
1920 " if delay < min_delay_between_shifts:\n",
1921 " continue\n",
1922 " lit = model.NewBoolVar('%i from %i to %i' % (d, s, o))\n",
1923 "\n",
1924 " # Increase driving time\n",
1925 " model.Add(total_driving[d, o] == total_driving[d, s] +\n",
1926 " other[5]).OnlyEnforceIf(lit)\n",
1927 "\n",
1928 " # Increase no_break_driving or reset it to 0 depending on the delay\n",
1929 " if delay >= min_pause_after_4h:\n",
1930 " model.Add(\n",
1931 " no_break_driving[d, o] == other[5]).OnlyEnforceIf(lit)\n",
1932 " else:\n",
1933 " model.Add(no_break_driving[d, o] == no_break_driving[d, s] +\n",
1934 " other[5]).OnlyEnforceIf(lit)\n",
1935 "\n",
1936 " # Add arc\n",
1937 " outgoing_literals[s].append(lit)\n",
1938 " shared_outgoing_literals[s].append(lit)\n",
1939 " incoming_literals[o].append(lit)\n",
1940 " shared_incoming_literals[o].append(lit)\n",
1941 "\n",
1942 " # Cost part\n",
1943 " delay_literals.append(lit)\n",
1944 " delay_weights.append(delay)\n",
1945 "\n",
1946 " model.Add(working_times[d] == end_times[d] - start_times[d])\n",
1947 "\n",
1948 " if minimize_drivers:\n",
1949 " # Driver is not working.\n",
1950 " working = model.NewBoolVar('working_%i' % d)\n",
1951 " model.Add(start_times[d] == min_start_time).OnlyEnforceIf(\n",
1952 " working.Not())\n",
1953 " model.Add(end_times[d] == min_start_time).OnlyEnforceIf(\n",
1954 " working.Not())\n",
1955 " model.Add(driving_times[d] == 0).OnlyEnforceIf(working.Not())\n",
1956 " working_drivers.append(working)\n",
1957 " outgoing_source_literals.append(working.Not())\n",
1958 " incoming_sink_literals.append(working.Not())\n",
1959 " # Conditional working time constraints\n",
1960 " model.Add(\n",
1961 " working_times[d] >= min_working_time).OnlyEnforceIf(working)\n",
1962 " model.Add(working_times[d] == 0).OnlyEnforceIf(working.Not())\n",
1963 " else:\n",
1964 " # Working time constraints\n",
1965 " model.Add(working_times[d] >= min_working_time)\n",
1966 "\n",
1967 " # Create circuit constraint.\n",
1968 " model.Add(sum(outgoing_source_literals) == 1)\n",
1969 " for s in range(num_shifts):\n",
1970 " model.Add(sum(outgoing_literals[s]) == 1)\n",
1971 " model.Add(sum(incoming_literals[s]) == 1)\n",
1972 " model.Add(sum(incoming_sink_literals) == 1)\n",
1973 "\n",
1974 " # Each shift is covered.\n",
1975 " for s in range(num_shifts):\n",
1976 " model.Add(sum(performed[d, s] for d in range(num_drivers)) == 1)\n",
1977 " # Globally, each node has one incoming and one outgoing literal\n",
1978 " model.Add(sum(shared_incoming_literals[s]) == 1)\n",
1979 " model.Add(sum(shared_outgoing_literals[s]) == 1)\n",
1980 "\n",
1981 " # Symmetry breaking\n",
1982 "\n",
1983 " # The first 3 shifts must be performed by 3 different drivers.\n",
1984 " # Let's assign them to the first 3 drivers in sequence\n",
1985 " model.Add(starting_shifts[0, 0] == 1)\n",
1986 " model.Add(starting_shifts[1, 1] == 1)\n",
1987 " model.Add(starting_shifts[2, 2] == 1)\n",
1988 "\n",
1989 " if minimize_drivers:\n",
1990 " # Push non working drivers to the end\n",
1991 " for d in range(num_drivers - 1):\n",
1992 " model.AddImplication(working_drivers[d].Not(),\n",
1993 " working_drivers[d + 1].Not())\n",
1994 "\n",
1995 " # Redundant constraints: sum of driving times = sum of shift driving times\n",
1996 " model.Add(cp_model.LinearExpr.Sum(driving_times) == total_driving_time)\n",
1997 " if not minimize_drivers:\n",
1998 " model.Add(\n",
1999 " cp_model.LinearExpr.Sum(working_times) == total_driving_time +\n",
2000 " num_drivers * (setup_time + cleanup_time) +\n",
2001 " cp_model.LinearExpr.ScalProd(delay_literals, delay_weights))\n",
2002 "\n",
2003 " if minimize_drivers:\n",
2004 " # Minimize the number of working drivers\n",
2005 " model.Minimize(cp_model.LinearExpr.Sum(working_drivers))\n",
2006 " else:\n",
2007 " # Minimize the sum of delays between tasks, which in turns minimize the\n",
2008 " # sum of working times as the total driving time is fixed\n",
2009 " model.Minimize(\n",
2010 " cp_model.LinearExpr.ScalProd(delay_literals, delay_weights))\n",
2011 "\n",
2012 " if not minimize_drivers and FLAGS.output_proto:\n",
2013 " print('Writing proto to %s' % FLAGS.output_proto)\n",
2014 " with open(FLAGS.output_proto, 'w') as text_file:\n",
2015 " text_file.write(str(model))\n",
2016 "\n",
2017 " # Solve model.\n",
2018 " solver = cp_model.CpSolver()\n",
2019 " if FLAGS.params:\n",
2020 " text_format.Parse(FLAGS.params, solver.parameters)\n",
2021 "\n",
2022 " status = solver.Solve(model)\n",
2023 "\n",
2024 " if status != cp_model.OPTIMAL and status != cp_model.FEASIBLE:\n",
2025 " return -1\n",
2026 "\n",
2027 " # Display solution\n",
2028 " if minimize_drivers:\n",
2029 " max_num_drivers = int(solver.ObjectiveValue())\n",
2030 " print('minimal number of drivers =', max_num_drivers)\n",
2031 " return max_num_drivers\n",
2032 "\n",
2033 " for d in range(num_drivers):\n",
2034 " print('Driver %i: ' % (d + 1))\n",
2035 " print(' total driving time =', solver.Value(driving_times[d]))\n",
2036 " print(' working time =',\n",
2037 " solver.Value(working_times[d]) + setup_time + cleanup_time)\n",
2038 "\n",
2039 " first = True\n",
2040 " for s in range(num_shifts):\n",
2041 " shift = shifts[s]\n",
2042 "\n",
2043 " if not solver.BooleanValue(performed[d, s]):\n",
2044 " continue\n",
2045 "\n",
2046 " # Hack to detect if the waiting time between the last shift and\n",
2047 " # this one exceeds 30 minutes. For this, we look at the\n",
2048 " # no_break_driving which was reinitialized in that case.\n",
2049 " if solver.Value(no_break_driving[d, s]) == shift[5] and not first:\n",
2050 " print(' **break**')\n",
2051 " print(' shift ', shift[0], ':', shift[1], '-', shift[2])\n",
2052 " first = False\n",
2053 "\n",
2054 " return int(solver.ObjectiveValue())\n",
2055 "\n",
2056 "\n",
2057 "\"\"\"Optimize the bus driver allocation in two passes.\"\"\"\n",
2058 "print('----------- first pass: minimize the number of drivers')\n",
2059 "num_drivers = bus_driver_scheduling(True, -1)\n",
2060 "if num_drivers == -1:\n",
2061 " print('no solution found, skipping the final step')\n",
2062 "else:\n",
2063 " print('----------- second pass: minimize the sum of working times')\n",
2064 " bus_driver_scheduling(False, num_drivers)\n",
2065 "\n"