# Copyright 2010 Hakan Kjellerstrand hakank@bonetmail.com
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""
Nurse rostering in Google CP Solver.
This is a simple nurse rostering model using a DFA and
my decomposition of regular constraint.
The DFA is from MiniZinc Tutorial, Nurse Rostering example:
- one day off every 4 days
- no 3 nights in a row.
This model was created by Hakan Kjellerstrand (hakank@bonetmail.com)
Also see my other Google CP Solver models:
http://www.hakank.org/google_or_tools/
"""
from ortools.constraint_solver import pywrapcp
from collections import defaultdict
#
# Global constraint regular
#
# This is a translation of MiniZinc's regular constraint (defined in
# lib/zinc/globals.mzn), via the Comet code refered above.
# All comments are from the MiniZinc code.
# '''
# The sequence of values in array 'x' (which must all be in the range 1..S)
# is accepted by the DFA of 'Q' states with input 1..S and transition
# function 'd' (which maps (1..Q, 1..S) -> 0..Q)) and initial state 'q0'
# (which must be in 1..Q) and accepting states 'F' (which all must be in
# 1..Q). We reserve state 0 to be an always failing state.
# '''
#
# x : IntVar array
# Q : number of states
# S : input_max
# d : transition matrix
# q0: initial state
# F : accepting states
def regular(x, Q, S, d, q0, F):
solver = x[0].solver()
assert Q > 0, 'regular: "Q" must be greater than zero'
assert S > 0, 'regular: "S" must be greater than zero'
# d2 is the same as d, except we add one extra transition for
# each possible input; each extra transition is from state zero
# to state zero. This allows us to continue even if we hit a
# non-accepted input.
# Comet: int d2[0..Q, 1..S]
d2 = []
for i in range(Q + 1):
row = []
for j in range(S):
if i == 0:
row.append(0)
else:
row.append(d[i - 1][j])
d2.append(row)
d2_flatten = [d2[i][j] for i in range(Q + 1) for j in range(S)]
# If x has index set m..n, then a[m-1] holds the initial state
# (q0), and a[i+1] holds the state we're in after processing
# x[i]. If a[n] is in F, then we succeed (ie. accept the
# string).
x_range = range(0, len(x))
m = 0
n = len(x)
a = [solver.IntVar(0, Q + 1, 'a[%i]' % i) for i in range(m, n + 1)]
# Check that the final state is in F
solver.Add(solver.MemberCt(a[-1], F))
# First state is q0
solver.Add(a[m] == q0)
for i in x_range:
solver.Add(x[i] >= 1)
solver.Add(x[i] <= S)
# Determine a[i+1]: a[i+1] == d2[a[i], x[i]]
solver.Add(
a[i + 1] == solver.Element(d2_flatten, ((a[i]) * S) + (x[i] - 1)))
def main():
# Create the solver.
solver = pywrapcp.Solver('Nurse rostering using regular')
#
# data
#
# Note: If you change num_nurses or num_days,
# please also change the constraints
# on nurse_stat and/or day_stat.
num_nurses = 7
num_days = 14
day_shift = 1
night_shift = 2
off_shift = 3
shifts = [day_shift, night_shift, off_shift]
# the DFA (for regular)
n_states = 6
input_max = 3
initial_state = 1 # 0 is for the failing state
accepting_states = [1, 2, 3, 4, 5, 6]
transition_fn = [
# d,n,o
[2, 3, 1], # state 1
[4, 4, 1], # state 2
[4, 5, 1], # state 3
[6, 6, 1], # state 4
[6, 0, 1], # state 5
[0, 0, 1] # state 6
]
days = ['d', 'n', 'o'] # for presentation
#
# declare variables
#
x = {}
for i in range(num_nurses):
for j in range(num_days):
x[i, j] = solver.IntVar(shifts, 'x[%i,%i]' % (i, j))
x_flat = [x[i, j] for i in range(num_nurses) for j in range(num_days)]
# summary of the nurses
nurse_stat = [solver.IntVar(0, num_days, 'nurse_stat[%i]' % i)
for i in range(num_nurses)]
# summary of the shifts per day
day_stat = {}
for i in range(num_days):
for j in shifts:
day_stat[i, j] = solver.IntVar(0, num_nurses, 'day_stat[%i,%i]' % (i, j))
day_stat_flat = [day_stat[i, j] for i in range(num_days) for j in shifts]
#
# constraints
#
for i in range(num_nurses):
reg_input = [x[i, j] for j in range(num_days)]
regular(reg_input, n_states, input_max, transition_fn,
initial_state, accepting_states)
#
# Statistics and constraints for each nurse
#
for i in range(num_nurses):
# number of worked days (day or night shift)
b = [solver.IsEqualCstVar(x[i, j], day_shift) +
solver.IsEqualCstVar(x[i, j], night_shift)
for j in range(num_days)]
solver.Add(nurse_stat[i] == solver.Sum(b))
# Each nurse must work between 7 and 10
# days during this period
solver.Add(nurse_stat[i] >= 7)
solver.Add(nurse_stat[i] <= 10)
#
# Statistics and constraints for each day
#
for j in range(num_days):
for t in shifts:
b = [solver.IsEqualCstVar(x[i, j], t)
for i in range(num_nurses)]
solver.Add(day_stat[j, t] == solver.Sum(b))
#
# Some constraints for this day:
#
# Note: We have a strict requirements of
# the number of shifts.
# Using atleast constraints is much harder
# in this model.
#
if j % 7 == 5 or j % 7 == 6:
# special constraints for the weekends
solver.Add(day_stat[j, day_shift] == 2)
solver.Add(day_stat[j, night_shift] == 1)
solver.Add(day_stat[j, off_shift] == 4)
else:
# workdays:
# - exactly 3 on day shift
solver.Add(day_stat[j, day_shift] == 3)
# - exactly 2 on night
solver.Add(day_stat[j, night_shift] == 2)
# - exactly 1 off duty
solver.Add(day_stat[j, off_shift] == 2)
#
# solution and search
#
db = solver.Phase(day_stat_flat + x_flat + nurse_stat,
solver.CHOOSE_FIRST_UNBOUND,
solver.ASSIGN_MIN_VALUE)
solver.NewSearch(db)
num_solutions = 0
while solver.NextSolution():
num_solutions += 1
for i in range(num_nurses):
print 'Nurse%i: ' % i,
this_day_stat = defaultdict(int)
for j in range(num_days):
d = days[x[i, j].Value() - 1]
this_day_stat[d] += 1
print d,
print ' day_stat:', [(d, this_day_stat[d]) for d in this_day_stat],
print 'total:', nurse_stat[i].Value(), 'workdays'
print
print 'Statistics per day:'
for j in range(num_days):
print 'Day%2i: ' % j,
for t in shifts:
print day_stat[j, t].Value(),
print
print
# We just show 2 solutions
if num_solutions >= 2:
break
solver.EndSearch()
print
print 'num_solutions:', num_solutions
print 'failures:', solver.Failures()
print 'branches:', solver.Branches()
print 'WallTime:', solver.WallTime(), 'ms'
if __name__ == '__main__':
main()