examples/notebook/contrib/post_office_problem2.ipynb
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First, you must install ortools package in this colab.
%pip install ortools
Post office problem in Google CP Solver.
Problem statement: http://www-128.ibm.com/developerworks/linux/library/l-glpk2/
From Winston 'Operations Research: Applications and Algorithms': ''' A post office requires a different number of full-time employees working on different days of the week [summarized below]. Union rules state that each full-time employee must work for 5 consecutive days and then receive two days off. For example, an employee who works on Monday to Friday must be off on Saturday and Sunday. The post office wants to meet its daily requirements using only full-time employees. Minimize the number of employees that must be hired.
To summarize the important information about the problem:
* Every full-time worker works for 5 consecutive days and takes 2 days off
* Day 1 (Monday): 17 workers needed
* Day 2 : 13 workers needed
* Day 3 : 15 workers needed
* Day 4 : 19 workers needed
* Day 5 : 14 workers needed
* Day 6 : 16 workers needed
* Day 7 (Sunday) : 11 workers needed
The post office needs to minimize the number of employees it needs to hire to meet its demand. '''
This model was created by Hakan Kjellerstrand ([email protected]) Also see my other Google CP Solver models: http://www.hakank.org/google_or_tools/
from ortools.constraint_solver import pywrapcp
def main():
# Create the solver.
solver = pywrapcp.Solver('Post office problem')
#
# data
#
# days 0..6, monday 0
n = 7
days = list(range(n))
need = [17, 13, 15, 19, 14, 16, 11]
# Total cost for the 5 day schedule.
# Base cost per day is 100.
# Working saturday is 100 extra
# Working sunday is 200 extra.
cost = [500, 600, 800, 800, 800, 800, 700]
#
# variables
#
# No. of workers starting at day i
x = [solver.IntVar(0, 100, 'x[%i]' % i) for i in days]
total_cost = solver.IntVar(0, 20000, 'total_cost')
num_workers = solver.IntVar(0, 100, 'num_workers')
#
# constraints
#
solver.Add(total_cost == solver.ScalProd(x, cost))
solver.Add(num_workers == solver.Sum(x))
for i in days:
s = solver.Sum(
[x[j] for j in days if j != (i + 5) % n and j != (i + 6) % n])
solver.Add(s >= need[i])
# objective
objective = solver.Minimize(total_cost, 1)
#
# search and result
#
db = solver.Phase(x, solver.CHOOSE_MIN_SIZE_LOWEST_MIN,
solver.ASSIGN_MIN_VALUE)
solver.NewSearch(db, [objective])
num_solutions = 0
while solver.NextSolution():
num_solutions += 1
print('num_workers:', num_workers.Value())
print('total_cost:', total_cost.Value())
print('x:', [x[i].Value() for i in days])
solver.EndSearch()
print()
print('num_solutions:', num_solutions)
print('failures:', solver.Failures())
print('branches:', solver.Branches())
print('WallTime:', solver.WallTime())
main()