nurses.py

This example solves the problem of finding an optimal assignment of nurses to shifts.

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
# --------------------------------------------------------------------------
# Source file provided under Apache License, Version 2.0, January 2004,
# http://www.apache.org/licenses/
# (c) Copyright IBM Corp. 2015, 2018
# --------------------------------------------------------------------------

from collections import namedtuple

from docplex.mp.model import Model
from docplex.util.environment import get_environment

# ----------------------------------------------------------------------------
# Initialize the problem data
# ----------------------------------------------------------------------------

# utility to convert a weekday string to an index in 0..6
_all_days = ["monday",
             "tuesday",
             "wednesday",
             "thursday",
             "friday",
             "saturday",
             "sunday"]


def day_to_day_week(day):
    day_map = {day: d for d, day in enumerate(_all_days)}
    return day_map[day.lower()]


TWorkRules = namedtuple("TWorkRules", ["work_time_max"])
TVacation = namedtuple("TVacation", ["nurse", "day"])
TNursePair = namedtuple("TNursePair", ["firstNurse", "secondNurse"])
TSkillRequirement = namedtuple("TSkillRequirement", ["department", "skill", "required"])


NURSES = [("Anne", 11, 1, 25),
          ("Bethanie", 4, 5, 28),
          ("Betsy", 2, 2, 17),
          ("Cathy", 2, 2, 17),
          ("Cecilia", 9, 5, 38),
          ("Chris", 11, 4, 38),
          ("Cindy", 5, 2, 21),
          ("David", 1, 2, 15),
          ("Debbie", 7, 2, 24),
          ("Dee", 3, 3, 21),
          ("Gloria", 8, 2, 25),
          ("Isabelle", 3, 1, 16),
          ("Jane", 3, 4, 23),
          ("Janelle", 4, 3, 22),
          ("Janice", 2, 2, 17),
          ("Jemma", 2, 4, 22),
          ("Joan", 5, 3, 24),
          ("Joyce", 8, 3, 29),
          ("Jude", 4, 3, 22),
          ("Julie", 6, 2, 22),
          ("Juliet", 7, 4, 31),
          ("Kate", 5, 3, 24),
          ("Nancy", 8, 4, 32),
          ("Nathalie", 9, 5, 38),
          ("Nicole", 0, 2, 14),
          ("Patricia", 1, 1, 13),
          ("Patrick", 6, 1, 19),
          ("Roberta", 3, 5, 26),
          ("Suzanne", 5, 1, 18),
          ("Vickie", 7, 1, 20),
          ("Wendie", 5, 2, 21),
          ("Zoe", 8, 3, 29)
          ]

SHIFTS = [("Emergency", "monday", 2, 8, 3, 5),
          ("Emergency", "monday", 8, 12, 4, 7),
          ("Emergency", "monday", 12, 18, 2, 5),
          ("Emergency", "monday", 18, 2, 3, 7),
          ("Consultation", "monday", 8, 12, 10, 13),
          ("Consultation", "monday", 12, 18, 8, 12),
          ("Cardiac_Care", "monday", 8, 12, 10, 13),
          ("Cardiac_Care", "monday", 12, 18, 8, 12),
          ("Emergency", "tuesday", 8, 12, 4, 7),
          ("Emergency", "tuesday", 12, 18, 2, 5),
          ("Emergency", "tuesday", 18, 2, 3, 7),
          ("Consultation", "tuesday", 8, 12, 10, 13),
          ("Consultation", "tuesday", 12, 18, 8, 12),
          ("Cardiac_Care", "tuesday", 8, 12, 4, 7),
          ("Cardiac_Care", "tuesday", 12, 18, 2, 5),
          ("Cardiac_Care", "tuesday", 18, 2, 3, 7),
          ("Emergency", "wednesday", 2, 8, 3, 5),
          ("Emergency", "wednesday", 8, 12, 4, 7),
          ("Emergency", "wednesday", 12, 18, 2, 5),
          ("Emergency", "wednesday", 18, 2, 3, 7),
          ("Consultation", "wednesday", 8, 12, 10, 13),
          ("Consultation", "wednesday", 12, 18, 8, 12),
          ("Emergency", "thursday", 2, 8, 3, 5),
          ("Emergency", "thursday", 8, 12, 4, 7),
          ("Emergency", "thursday", 12, 18, 2, 5),
          ("Emergency", "thursday", 18, 2, 3, 7),
          ("Consultation", "thursday", 8, 12, 10, 13),
          ("Consultation", "thursday", 12, 18, 8, 12),
          ("Emergency", "friday", 2, 8, 3, 5),
          ("Emergency", "friday", 8, 12, 4, 7),
          ("Emergency", "friday", 12, 18, 2, 5),
          ("Emergency", "friday", 18, 2, 3, 7),
          ("Consultation", "friday", 8, 12, 10, 13),
          ("Consultation", "friday", 12, 18, 8, 12),
          ("Emergency", "saturday", 2, 12, 5, 7),
          ("Emergency", "saturday", 12, 20, 7, 9),
          ("Emergency", "saturday", 20, 2, 12, 12),
          ("Emergency", "sunday", 2, 12, 5, 7),
          ("Emergency", "sunday", 12, 20, 7, 9),
          ("Emergency", "sunday", 20, 2, 12, 12),
          ("Geriatrics", "sunday", 8, 10, 2, 5)]

NURSE_SKILLS = {"Anne": ["Anaesthesiology", "Oncology", "Pediatrics"],
                "Betsy": ["Cardiac_Care"],
                "Cathy": ["Anaesthesiology"],
                "Cecilia": ["Anaesthesiology", "Oncology", "Pediatrics"],
                "Chris": ["Cardiac_Care", "Oncology", "Geriatrics"],
                "Gloria": ["Pediatrics"], "Jemma": ["Cardiac_Care"],
                "Joyce": ["Anaesthesiology", "Pediatrics"],
                "Julie": ["Geriatrics"], "Juliet": ["Pediatrics"],
                "Kate": ["Pediatrics"], "Nancy": ["Cardiac_Care"],
                "Nathalie": ["Anaesthesiology", "Geriatrics"],
                "Patrick": ["Oncology"], "Suzanne": ["Pediatrics"],
                "Wendie": ["Geriatrics"],
                "Zoe": ["Cardiac_Care"]
                }

VACATIONS = [("Anne", "friday"),
             ("Anne", "sunday"),
             ("Cathy", "thursday"),
             ("Cathy", "tuesday"),
             ("Joan", "thursday"),
             ("Joan", "saturday"),
             ("Juliet", "monday"),
             ("Juliet", "tuesday"),
             ("Juliet", "thursday"),
             ("Nathalie", "sunday"),
             ("Nathalie", "thursday"),
             ("Isabelle", "monday"),
             ("Isabelle", "thursday"),
             ("Patricia", "saturday"),
             ("Patricia", "wednesday"),
             ("Nicole", "friday"),
             ("Nicole", "wednesday"),
             ("Jude", "tuesday"),
             ("Jude", "friday"),
             ("Debbie", "saturday"),
             ("Debbie", "wednesday"),
             ("Joyce", "sunday"),
             ("Joyce", "thursday"),
             ("Chris", "thursday"),
             ("Chris", "tuesday"),
             ("Cecilia", "friday"),
             ("Cecilia", "wednesday"),
             ("Patrick", "saturday"),
             ("Patrick", "sunday"),
             ("Cindy", "sunday"),
             ("Dee", "tuesday"),
             ("Dee", "friday"),
             ("Jemma", "friday"),
             ("Jemma", "wednesday"),
             ("Bethanie", "wednesday"),
             ("Bethanie", "tuesday"),
             ("Betsy", "monday"),
             ("Betsy", "thursday"),
             ("David", "monday"),
             ("Gloria", "monday"),
             ("Jane", "saturday"),
             ("Jane", "sunday"),
             ("Janelle", "wednesday"),
             ("Janelle", "friday"),
             ("Julie", "sunday"),
             ("Kate", "tuesday"),
             ("Kate", "monday"),
             ("Nancy", "sunday"),
             ("Roberta", "friday"),
             ("Roberta", "saturday"),
             ("Janice", "tuesday"),
             ("Janice", "friday"),
             ("Suzanne", "monday"),
             ("Vickie", "wednesday"),
             ("Vickie", "friday"),
             ("Wendie", "thursday"),
             ("Wendie", "saturday"),
             ("Zoe", "saturday"),
             ("Zoe", "sunday")]

NURSE_ASSOCIATIONS = [("Isabelle", "Dee"),
                      ("Anne", "Patrick")]

NURSE_INCOMPATIBILITIES = [("Patricia", "Patrick"),
                           ("Janice", "Wendie"),
                           ("Suzanne", "Betsy"),
                           ("Janelle", "Jane"),
                           ("Gloria", "David"),
                           ("Dee", "Jemma"),
                           ("Bethanie", "Dee"),
                           ("Roberta", "Zoe"),
                           ("Nicole", "Patricia"),
                           ("Vickie", "Dee"),
                           ("Joan", "Anne")
                           ]

SKILL_REQUIREMENTS = [("Emergency", "Cardiac_Care", 1)]

DEFAULT_WORK_RULES = TWorkRules(40)


# ----------------------------------------------------------------------------
# Prepare the data for modeling
# ----------------------------------------------------------------------------
# subclass the namedtuple to refine the str() method as the nurse's name
class TNurse(namedtuple("TNurse1", ["name", "seniority", "qualification", "pay_rate"])):
    def __str__(self):
        return self.name


# specialized namedtuple to redefine its str() method
class TShift(namedtuple("TShift",
                        ["department", "day", "start_time", "end_time", "min_requirement", "max_requirement"])):

    def __str__(self):
        # keep first two characters in department, uppercase
        dept2 = self.department[0:4].upper()
        # keep 3 days of weekday
        dayname = self.day[0:3]
        return '{}_{}_{:02d}'.format(dept2, dayname, self.start_time).replace(" ", "_")


class ShiftActivity(object):
    @staticmethod
    def to_abstime(day_index, time_of_day):
        """ Convert a pair (day_index, time) into a number of hours since Monday 00:00

        :param day_index: The index of the day from 1 to 7 (Monday is 1).
        :param time_of_day: An integer number of hours.

        :return:
        """
        time = 24 * (day_index - 1)
        time += time_of_day
        return time

    def __init__(self, weekday, start_time_of_day, end_time_of_day):
        assert (start_time_of_day >= 0)
        assert (start_time_of_day <= 24)
        assert (end_time_of_day >= 0)
        assert (end_time_of_day <= 24)

        self._weekday = weekday
        self._start_time_of_day = start_time_of_day
        self._end_time_of_day = end_time_of_day
        # conversion to absolute time.
        start_day_index = day_to_day_week(self._weekday)
        self.start_time = self.to_abstime(start_day_index, start_time_of_day)
        end_day_index = start_day_index if end_time_of_day > start_time_of_day else start_day_index + 1
        self.end_time = self.to_abstime(end_day_index, end_time_of_day)
        assert self.end_time > self.start_time

    @property
    def duration(self):
        return self.end_time - self.start_time

    def overlaps(self, other_shift):
        if not isinstance(other_shift, ShiftActivity):
            return False
        else:
            return other_shift.end_time > self.start_time and other_shift.start_time < self.end_time


def solve(model, **kwargs):
    # Here, we set the number of threads for CPLEX to 2 and set the time limit to 2mins.
    model.parameters.threads = 2
    model.parameters.timelimit = 120  # nurse should not take more than that !
    sol = model.solve(log_output=True, **kwargs)
    if sol is not None:
        print("solution for a cost of {}".format(model.objective_value))
        print_information(model)
        print_solution(model)
        return model.objective_value
    else:
        print("* model is infeasible")
        return None


def load_data(model, shifts_, nurses_, nurse_skills, vacations_=None,
              nurse_associations_=None, nurse_imcompatibilities_=None, verbose=True):
    """ Usage: load_data(shifts, nurses, nurse_skills, vacations) """
    model.number_of_overlaps = 0
    model.work_rules = DEFAULT_WORK_RULES
    model.shifts = [TShift(*shift_row) for shift_row in shifts_]
    model.nurses = [TNurse(*nurse_row) for nurse_row in nurses_]
    model.skill_requirements = SKILL_REQUIREMENTS
    model.nurse_skills = nurse_skills
    # transactional data
    model.vacations = [TVacation(*vacation_row) for vacation_row in vacations_] if vacations_ else []
    model.nurse_associations = [TNursePair(*npr) for npr in nurse_associations_]\
    if nurse_associations_ else []
    model.nurse_incompatibilities = [TNursePair(*npr) for npr in nurse_imcompatibilities_]\
    if nurse_imcompatibilities_ else []

    # computed
    model.departments = set(sh.department for sh in model.shifts)

    if verbose:
        print('#nurses: {0}'.format(len(model.nurses)))
        print('#shifts: {0}'.format(len(model.shifts)))
        print('#vacations: {0}'.format(len(model.vacations)))
        print("#associations=%d" % len(model.nurse_associations))
        print("#incompatibilities=%d" % len(model.nurse_incompatibilities))


def setup_data(model):
    """ compute internal data """
    # compute shift activities (start, end duration) and stor ethem in a dict indexed by shifts
    model.shift_activities = {s: ShiftActivity(s.day, s.start_time, s.end_time) for s in model.shifts}
    # map from nurse names to nurse tuples.
    model.nurses_by_id = {n.name: n for n in model.nurses}


def setup_variables(model):
    all_nurses, all_shifts = model.nurses, model.shifts
    # one binary variable for each pair (nurse, shift) equal to 1 iff nurse n is assigned to shift s
    model.nurse_assignment_vars = model.binary_var_matrix(all_nurses, all_shifts, 'NurseAssigned')
    # for each nurse, allocate one variable for work time
    model.nurse_work_time_vars = model.continuous_var_dict(all_nurses, lb=0, name='NurseWorkTime')
    # and two variables for over_average and under-average work time
    model.nurse_over_average_time_vars = model.continuous_var_dict(all_nurses, lb=0,
                                                                   name='NurseOverAverageWorkTime')
    model.nurse_under_average_time_vars = model.continuous_var_dict(all_nurses, lb=0,
                                                                    name='NurseUnderAverageWorkTime')
    # finally the global average work time
    model.average_nurse_work_time = model.continuous_var(lb=0, name='AverageWorkTime')


def setup_constraints(model):
    all_nurses = model.nurses
    all_shifts = model.shifts
    nurse_assigned = model.nurse_assignment_vars
    nurse_work_time = model.nurse_work_time_vars
    shift_activities = model.shift_activities
    nurses_by_id = model.nurses_by_id
    max_work_time = model.work_rules.work_time_max

    # define average
    model.add_constraint(
        len(all_nurses) * model.average_nurse_work_time == model.sum(nurse_work_time[n] for n in all_nurses), "average")

    # compute nurse work time , average and under, over
    for n in all_nurses:
        work_time_var = nurse_work_time[n]
        model.add_constraint(
            work_time_var == model.sum(nurse_assigned[n, s] * shift_activities[s].duration for s in all_shifts),
            "work_time_{0!s}".format(n))

        # relate over/under average worktime variables to the worktime variables
        # the trick here is that variables have zero lower bound
        # however, thse variables are not completely defined by this constraint,
        # only their difference is.
        # if these variables are part of the objective, CPLEX wil naturally minimize their value,
        # as expected
        model.add_constraint(
            work_time_var == model.average_nurse_work_time
            + model.nurse_over_average_time_vars[n]
            - model.nurse_under_average_time_vars[n],
            "average_work_time_{0!s}".format(n))

        # state the maximum work time as a constraint, so that is can be relaxed,
        # should the problem become infeasible.
        model.add_constraint(work_time_var <= max_work_time, "max_time_{0!s}".format(n))

    # vacations
    v = 0
    for vac_nurse_id, vac_day in model.vacations:
        vac_n = nurses_by_id[vac_nurse_id]
        for shift in (s for s in all_shifts if s.day == vac_day):
            v += 1
            model.add_constraint(nurse_assigned[vac_n, shift] == 0,
                                 "medium_vacations_{0!s}_{1!s}_{2!s}".format(vac_n, vac_day, shift))
    #print('#vacation cts: {0}'.format(v))

    # a nurse cannot be assigned overlapping shifts
    # post only one constraint per couple(s1, s2)
    number_of_overlaps = 0
    nb_shifts = len(all_shifts)
    for i1 in range(nb_shifts):
        for i2 in range(i1 + 1, nb_shifts):
            s1 = all_shifts[i1]
            s2 = all_shifts[i2]
            if shift_activities[s1].overlaps(shift_activities[s2]):
                number_of_overlaps += 1
                for n in all_nurses:
                    model.add_constraint(nurse_assigned[n, s1] + nurse_assigned[n, s2] <= 1,
                                         "high_overlapping_{0!s}_{1!s}_{2!s}".format(s1, s2, n))
    #print('# overlapping cts: {0}'.format(number_of_overlaps))

    for s in all_shifts:
        demand_min = s.min_requirement
        demand_max = s.max_requirement
        total_assigned = model.sum(nurse_assigned[n, s] for n in model.nurses)
        model.add_constraint(total_assigned >= demand_min,
                             "high_req_min_{0!s}_{1}".format(s, demand_min))
        model.add_constraint(total_assigned <= demand_max,
                             "medium_req_max_{0!s}_{1}".format(s, demand_max))
        model.add_constraint(total_assigned >= 1, "mandatory_presence_{0!s}".format(s))

    for (dept, skill, required) in model.skill_requirements:
        if required > 0:
            for dsh in (s for s in all_shifts if dept == s.department):
                model.add_constraint(model.sum(nurse_assigned[skilled_nurse, dsh] for skilled_nurse in
                                               (n for n in all_nurses if
                                                n.name in model.nurse_skills.keys() and skill in model.nurse_skills[
                                                    n.name])) >= required,
                                     "high_required_{0!s}_{1!s}_{2!s}_{3!s}".format(dept, skill, required, dsh))

    # nurse-nurse associations
    # for each pair of associated nurses, their assignment variables are equal
    # over all shifts.
    c = 0
    for (nurse_id1, nurse_id2) in model.nurse_associations:
        if nurse_id1 in nurses_by_id and nurse_id2 in nurses_by_id:
            nurse1 = nurses_by_id[nurse_id1]
            nurse2 = nurses_by_id[nurse_id2]
            for s in all_shifts:
                c += 1
                ctname = 'medium_ct_nurse_assoc_{0!s}_{1!s}_{2:d}'.format(nurse_id1, nurse_id2, c)
                model.add_constraint(nurse_assigned[nurse1, s] == nurse_assigned[nurse2, s], ctname)

    # nurse-nurse incompatibilities
    # for each pair of incompatible nurses, the sum of assigned variables is less than one
    # in other terms, both nurses can never be assigned to the same shift
    c = 0
    for (nurse_id1, nurse_id2) in model.nurse_incompatibilities:
        if nurse_id1 in nurses_by_id and nurse_id2 in nurses_by_id:
            nurse1 = nurses_by_id[nurse_id1]
            nurse2 = nurses_by_id[nurse_id2]
            for s in all_shifts:
                c += 1
                ctname = 'medium_ct_nurse_incompat_{0!s}_{1!s}_{2:d}'.format(nurse_id1, nurse_id2, c)
                model.add_constraint(nurse_assigned[nurse1, s] + nurse_assigned[nurse2, s] <= 1, ctname)

    model.total_number_of_assignments = model.sum(nurse_assigned[n, s] for n in all_nurses for s in all_shifts)
    # model.nurse_costs = [model.nurse_assignment_vars[n, s] * n.pay_rate * model.shift_activities[s].duration
    #                      for n in model.nurses for s in model.shifts]

    def assignment_cost_f(ns):
        n, s = ns
        return n.pay_rate * model.shift_activities[s].duration

    model.nurse_costs = model.scal_prod_f(nurse_assigned, assignment_cost_f)
    model.total_salary_cost = model.sum(model.nurse_costs)


def setup_objective(model):
    model.add_kpi(model.total_salary_cost, "Total salary cost")
    model.add_kpi(model.total_number_of_assignments, "Total number of assignments")
    model.add_kpi(model.average_nurse_work_time, "average work time")

    total_over_average_worktime = model.sum(model.nurse_over_average_time_vars[n] for n in model.nurses)
    total_under_average_worktime = model.sum(model.nurse_under_average_time_vars[n] for n in model.nurses)
    model.add_kpi(total_over_average_worktime, "Total over-average worktime")
    model.add_kpi(total_under_average_worktime, "Total under-average worktime")
    total_fairness = total_over_average_worktime + total_under_average_worktime
    model.add_kpi(total_fairness, "Total fairness")

    model.minimize(model.total_salary_cost + total_fairness + model.total_number_of_assignments)


def print_information(model):
    print("#shifts=%d" % len(model.shifts))
    print("#nurses=%d" % len(model.nurses))
    print("#vacations=%d" % len(model.vacations))
    print("#nurse skills=%d" % len(model.nurse_skills))
    print("#nurse associations=%d" % len(model.nurse_associations))
    print("#incompatibilities=%d" % len(model.nurse_incompatibilities))
    model.print_information()
    model.report_kpis()


def print_solution(model):
    print("*************************** Solution ***************************")
    print("Allocation By Department:")
    for d in model.departments:
        print("\t{}: {}".format(d, sum(
            model.nurse_assignment_vars[n, s].solution_value for n in model.nurses for s in model.shifts if
            s.department == d)))
    print("Cost By Department:")
    for d in model.departments:
        cost = sum(
            model.nurse_assignment_vars[n, s].solution_value * n.pay_rate * model.shift_activities[s].duration for n in
            model.nurses for s in model.shifts if s.department == d)
        print("\t{}: {}".format(d, cost))
    print("Nurses Assignments")
    for n in sorted(model.nurses):
        total_hours = sum(
            model.nurse_assignment_vars[n, s].solution_value * model.shift_activities[s].duration for s in model.shifts)
        print("\t{}: total hours:{}".format(n.name, total_hours))
        for s in model.shifts:
            if model.nurse_assignment_vars[n, s].solution_value == 1:
                print("\t\t{}: {} {}-{}".format(s.day, s.department, s.start_time, s.end_time))


# ----------------------------------------------------------------------------
# Build the model
# ----------------------------------------------------------------------------

def build(context=None, verbose=False, **kwargs):
    mdl = Model("Nurses", context=context, **kwargs)
    load_data(mdl, SHIFTS, NURSES, NURSE_SKILLS, VACATIONS, NURSE_ASSOCIATIONS,
              NURSE_INCOMPATIBILITIES, verbose=verbose)
    setup_data(mdl)
    setup_variables(mdl)
    setup_constraints(mdl)
    setup_objective(mdl)
    return mdl


# ----------------------------------------------------------------------------
# Solve the model and display the result
# ----------------------------------------------------------------------------

if __name__ == '__main__':
    # Build model
    model = build()

    # Solve the model and print solution
    solve(model)

    # Save the CPLEX solution as "solution.json" program output
    with get_environment().get_output_stream("solution.json") as fp:
        model.solution.export(fp, "json")
    model.end()