431 lines
16 KiB
Python
431 lines
16 KiB
Python
# Copyright 2010-2018 Google LLC
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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"""Creates a shift scheduling problem and solves it."""
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from __future__ import print_function
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import argparse
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from ortools.sat.python import cp_model
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from google.protobuf import text_format
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PARSER = argparse.ArgumentParser()
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PARSER.add_argument(
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'--output_proto',
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default="",
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help='Output file to write the cp_model'
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'proto to.')
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PARSER.add_argument('--params', default="", help='Sat solver parameters.')
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def negated_bounded_span(works, start, length):
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"""Filters an isolated sub-sequence of variables assined to True.
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Extract the span of Boolean variables [start, start + length), negate them,
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and if there is variables to the left/right of this span, surround the span by
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them in non negated form.
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Args:
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works: a list of variables to extract the span from.
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start: the start to the span.
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length: the length of the span.
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Returns:
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a list of variables which conjunction will be false if the sub-list is
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assigned to True, and correctly bounded by variables assigned to False,
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or by the start or end of works.
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"""
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sequence = []
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# Left border (start of works, or works[start - 1])
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if start > 0:
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sequence.append(works[start - 1])
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for i in range(length):
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sequence.append(works[start + i].Not())
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# Right border (end of works or works[start + length])
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if start + length < len(works):
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sequence.append(works[start + length])
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return sequence
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def add_soft_sequence_constraint(model, works, hard_min, soft_min, min_cost,
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soft_max, hard_max, max_cost, prefix):
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"""Sequence constraint on true variables with soft and hard bounds.
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This constraint look at every maximal contiguous sequence of variables
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assigned to true. If forbids sequence of length < hard_min or > hard_max.
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Then it creates penalty terms if the length is < soft_min or > soft_max.
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Args:
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model: the sequence constraint is built on this model.
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works: a list of Boolean variables.
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hard_min: any sequence of true variables must have a length of at least
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hard_min.
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soft_min: any sequence should have a length of at least soft_min, or a
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linear penalty on the delta will be added to the objective.
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min_cost: the coefficient of the linear penalty if the length is less than
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soft_min.
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soft_max: any sequence should have a length of at most soft_max, or a linear
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penalty on the delta will be added to the objective.
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hard_max: any sequence of true variables must have a length of at most
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hard_max.
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max_cost: the coefficient of the linear penalty if the length is more than
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soft_max.
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prefix: a base name for penalty literals.
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Returns:
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a tuple (variables_list, coefficient_list) containing the different
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penalties created by the sequence constraint.
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"""
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cost_literals = []
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cost_coefficients = []
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# Forbid sequences that are too short.
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for length in range(1, hard_min):
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for start in range(len(works) - length - 1):
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model.AddBoolOr(negated_bounded_span(works, start, length))
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# Penalize sequences that are below the soft limit.
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if min_cost > 0:
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for length in range(hard_min, soft_min):
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for start in range(len(works) - length - 1):
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span = negated_bounded_span(works, start, length)
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name = ': under_span(start=%i, length=%i)' % (start, length)
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lit = model.NewBoolVar(prefix + name)
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span.append(lit)
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model.AddBoolOr(span)
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cost_literals.append(lit)
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# We filter exactly the sequence with a short length.
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# The penalty is proportional to the delta with soft_min.
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cost_coefficients.append(min_cost * (soft_min - length))
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# Penalize sequences that are above the soft limit.
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if max_cost > 0:
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for length in range(soft_max + 1, hard_max + 1):
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for start in range(len(works) - length - 1):
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span = negated_bounded_span(works, start, length)
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name = ': over_span(start=%i, length=%i)' % (start, length)
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lit = model.NewBoolVar(prefix + name)
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span.append(lit)
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model.AddBoolOr(span)
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cost_literals.append(lit)
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# Cost paid is max_cost * excess length.
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cost_coefficients.append(max_cost * (length - soft_max))
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# Just forbid any sequence of true variables with length hard_max + 1
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for start in range(len(works) - hard_max - 1):
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model.AddBoolOr(
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[works[i].Not() for i in range(start, start + hard_max + 1)])
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return cost_literals, cost_coefficients
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def add_soft_sum_constraint(model, works, hard_min, soft_min, min_cost,
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soft_max, hard_max, max_cost, prefix):
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"""Sum constraint with soft and hard bounds.
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This constraint counts the variables assigned to true from works.
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If forbids sum < hard_min or > hard_max.
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Then it creates penalty terms if the sum is < soft_min or > soft_max.
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Args:
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model: the sequence constraint is built on this model.
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works: a list of Boolean variables.
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hard_min: any sequence of true variables must have a sum of at least
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hard_min.
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soft_min: any sequence should have a sum of at least soft_min, or a linear
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penalty on the delta will be added to the objective.
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min_cost: the coefficient of the linear penalty if the sum is less than
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soft_min.
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soft_max: any sequence should have a sum of at most soft_max, or a linear
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penalty on the delta will be added to the objective.
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hard_max: any sequence of true variables must have a sum of at most
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hard_max.
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max_cost: the coefficient of the linear penalty if the sum is more than
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soft_max.
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prefix: a base name for penalty variables.
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Returns:
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a tuple (variables_list, coefficient_list) containing the different
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penalties created by the sequence constraint.
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"""
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cost_variables = []
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cost_coefficients = []
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sum_var = model.NewIntVar(hard_min, hard_max, '')
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# This adds the hard constraints on the sum.
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model.Add(sum_var == sum(works))
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# Penalize sums below the soft_min target.
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if soft_min > hard_min and min_cost > 0:
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delta = model.NewIntVar(-len(works), len(works), '')
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model.Add(delta == soft_min - sum_var)
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# TODO(user): Compare efficiency with only excess >= soft_min - sum_var.
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excess = model.NewIntVar(0, 7, prefix + ': under_sum')
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model.AddMaxEquality(excess, [delta, 0])
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cost_variables.append(excess)
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cost_coefficients.append(min_cost)
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# Penalize sums above the soft_max target.
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if soft_max < hard_max and max_cost > 0:
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delta = model.NewIntVar(-7, 7, '')
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model.Add(delta == sum_var - soft_max)
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excess = model.NewIntVar(0, 7, prefix + ': over_sum')
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model.AddMaxEquality(excess, [delta, 0])
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cost_variables.append(excess)
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cost_coefficients.append(max_cost)
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return cost_variables, cost_coefficients
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def solve_shift_scheduling(params, output_proto):
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"""Solves the shift scheduling problem."""
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# Data
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num_employees = 8
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num_weeks = 3
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shifts = ['O', 'M', 'A', 'N']
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# Fixed assignment: (employee, shift, day).
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# This fixes the first 2 days of the schedule.
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fixed_assignments = [
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(0, 0, 0),
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(1, 0, 0),
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(2, 1, 0),
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(3, 1, 0),
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(4, 2, 0),
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(5, 2, 0),
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(6, 2, 3),
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(7, 3, 0),
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(0, 1, 1),
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(1, 1, 1),
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(2, 2, 1),
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(3, 2, 1),
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(4, 2, 1),
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(5, 0, 1),
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(6, 0, 1),
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(7, 3, 1),
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]
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# Request: (employee, shift, day, weight)
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# A negative weight indicates that the employee desire this assignment.
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requests = [
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# Employee 3 wants the first Saturday off.
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(3, 0, 5, -2),
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# Employee 5 wants a night shift on the second Thursday.
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(5, 3, 10, -2),
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# Employee 2 does not want a night shift on the third Friday.
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(2, 3, 4, 4)
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]
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# Shift constraints on continuous sequence :
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# (shift, hard_min, soft_min, min_penalty,
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# soft_max, hard_max, max_penalty)
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shift_constraints = [
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# One or two consecutive days of rest, this is a hard constraint.
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(0, 1, 1, 0, 2, 2, 0),
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# betweem 2 and 3 consecutive days of night shifts, 1 and 4 are
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# possible but penalized.
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(3, 1, 2, 20, 3, 4, 5),
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]
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# Weekly sum constraints on shifts days:
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# (shift, hard_min, soft_min, min_penalty,
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# soft_max, hard_max, max_penalty)
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weekly_sum_constraints = [
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# Constraints on rests per week.
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(0, 1, 2, 7, 2, 3, 4),
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# At least 1 night shift per week (penalized). At most 4 (hard).
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(3, 0, 1, 3, 4, 4, 0),
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]
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# Penalized transitions:
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# (previous_shift, next_shift, penalty (0 means forbidden))
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penalized_transitions = [
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# Afternoon to night has a penalty of 4.
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(2, 3, 4),
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# Night to morning is forbidden.
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(3, 1, 0),
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]
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# daily demands for work shifts (morning, afternon, night) for each day
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# of the week starting on Monday.
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weekly_cover_demands = [
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(2, 3, 1), # Monday
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(2, 3, 1), # Tuesday
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(2, 2, 2), # Wednesday
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(2, 3, 1), # Thursday
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(2, 2, 2), # Friday
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(1, 2, 3), # Saturday
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(1, 3, 1), # Sunday
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]
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# Penalty for exceeding the cover constraint per shift type.
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excess_cover_penalties = (2, 2, 5)
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num_days = num_weeks * 7
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num_shifts = len(shifts)
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model = cp_model.CpModel()
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work = {}
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for e in range(num_employees):
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for s in range(num_shifts):
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for d in range(num_days):
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work[e, s, d] = model.NewBoolVar('work%i_%i_%i' % (e, s, d))
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# Linear terms of the objective in a minimization context.
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obj_int_vars = []
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obj_int_coeffs = []
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obj_bool_vars = []
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obj_bool_coeffs = []
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# Exactly one shift per day.
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for e in range(num_employees):
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for d in range(num_days):
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model.Add(sum(work[e, s, d] for s in range(num_shifts)) == 1)
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# Fixed assignments.
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for e, s, d in fixed_assignments:
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model.Add(work[e, s, d] == 1)
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# Employee requests
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for e, s, d, w in requests:
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obj_bool_vars.append(work[e, s, d])
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obj_bool_coeffs.append(w)
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# Shift constraints
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for ct in shift_constraints:
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shift, hard_min, soft_min, min_cost, soft_max, hard_max, max_cost = ct
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for e in range(num_employees):
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works = [work[e, shift, d] for d in range(num_days)]
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variables, coeffs = add_soft_sequence_constraint(
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model, works, hard_min, soft_min, min_cost, soft_max, hard_max,
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max_cost, 'shift_constraint(employee %i, shift %i)' % (e,
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shift))
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obj_bool_vars.extend(variables)
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obj_bool_coeffs.extend(coeffs)
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# Weekly sum constraints
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for ct in weekly_sum_constraints:
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shift, hard_min, soft_min, min_cost, soft_max, hard_max, max_cost = ct
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for e in range(num_employees):
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for w in range(num_weeks):
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works = [work[e, shift, d + w * 7] for d in range(7)]
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variables, coeffs = add_soft_sum_constraint(
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model, works, hard_min, soft_min, min_cost, soft_max,
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hard_max, max_cost,
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'weekly_sum_constraint(employee %i, shift %i, week %i)' %
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(e, shift, w))
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obj_int_vars.extend(variables)
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obj_int_coeffs.extend(coeffs)
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# Penalized transitions
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for previous_shift, next_shift, cost in penalized_transitions:
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for e in range(num_employees):
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for d in range(num_days - 1):
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transition = [
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work[e, previous_shift, d].Not(),
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work[e, next_shift, d + 1].Not()
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]
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if cost == 0:
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model.AddBoolOr(transition)
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else:
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trans_var = model.NewBoolVar(
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'transition (employee=%i, day=%i)' % (e, d))
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transition.append(trans_var)
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model.AddBoolOr(transition)
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obj_bool_vars.append(trans_var)
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obj_bool_coeffs.append(cost)
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# Cover constraints
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for s in range(1, num_shifts):
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for w in range(num_weeks):
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for d in range(7):
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works = [work[e, s, w * 7 + d] for e in range(num_employees)]
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# Ignore Off shift.
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min_demand = weekly_cover_demands[d][s - 1]
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worked = model.NewIntVar(min_demand, num_employees, '')
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model.Add(worked == sum(works))
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over_penalty = excess_cover_penalties[s - 1]
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if over_penalty > 0:
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name = 'excess_demand(shift=%i, week=%i, day=%i)' % (s, w,
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d)
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excess = model.NewIntVar(0, num_employees - min_demand,
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name)
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model.Add(excess == worked - min_demand)
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obj_int_vars.append(excess)
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obj_int_coeffs.append(over_penalty)
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# Objective
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model.Minimize(
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sum(obj_bool_vars[i] * obj_bool_coeffs[i]
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for i in range(len(obj_bool_vars)))
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+ sum(obj_int_vars[i] * obj_int_coeffs[i]
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for i in range(len(obj_int_vars))))
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if output_proto:
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print('Writing proto to %s' % output_proto)
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with open(output_proto, 'w') as text_file:
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text_file.write(str(model))
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# Solve the model.
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solver = cp_model.CpSolver()
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solver.parameters.num_search_workers = 8
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if params:
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text_format.Merge(params, solver.parameters)
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solution_printer = cp_model.ObjectiveSolutionPrinter()
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status = solver.SolveWithSolutionCallback(model, solution_printer)
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# Print solution.
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if status == cp_model.OPTIMAL or status == cp_model.FEASIBLE:
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print()
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header = ' '
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for w in range(num_weeks):
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header += 'M T W T F S S '
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print(header)
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for e in range(num_employees):
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schedule = ''
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for d in range(num_days):
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for s in range(num_shifts):
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if solver.BooleanValue(work[e, s, d]):
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schedule += shifts[s] + ' '
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print('worker %i: %s' % (e, schedule))
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print()
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print('Penalties:')
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for i, var in enumerate(obj_bool_vars):
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if solver.BooleanValue(var):
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penalty = obj_bool_coeffs[i]
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if penalty > 0:
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print(' %s violated, penalty=%i' % (var.Name(), penalty))
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else:
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print(' %s fulfilled, gain=%i' % (var.Name(), -penalty))
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for i, var in enumerate(obj_int_vars):
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if solver.Value(var) > 0:
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print(' %s violated by %i, linear penalty=%i' %
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(var.Name(), solver.Value(var), obj_int_coeffs[i]))
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print()
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print('Statistics')
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print(' - status : %s' % solver.StatusName(status))
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print(' - conflicts : %i' % solver.NumConflicts())
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print(' - branches : %i' % solver.NumBranches())
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print(' - wall time : %f s' % solver.WallTime())
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def main(args):
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"""Main."""
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solve_shift_scheduling(args.params, args.output_proto)
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if __name__ == '__main__':
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main(PARSER.parse_args())
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