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assignment

examples/notebook/contrib/assignment.ipynb

2016-063.9 KB
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assignment

<table align="left"> <td> <a href="https://colab.research.google.com/github/google/or-tools/blob/main/examples/notebook/contrib/assignment.ipynb">Run in Google Colab</a> </td> <td> <a href="https://github.com/google/or-tools/blob/main/examples/contrib/assignment.py">View source on GitHub</a> </td> </table>

First, you must install ortools package in this colab.

python
%pip install ortools

Assignment problem in Google CP Solver.

Winston 'Operations Research', Assignment Problems, page 393f (generalized version with added test column)

Compare with the following models:

This model was created by Hakan Kjellerstrand ([email protected]) Also see my other Google CP Solver models: http://www.hakank.org/google_or_tools/

python
from ortools.constraint_solver import pywrapcp


def main(cost, rows, cols):
  # Create the solver.
  solver = pywrapcp.Solver("n-queens")

  #
  # data
  #

  # declare variables
  total_cost = solver.IntVar(0, 100, "total_cost")
  x = []
  for i in range(rows):
    t = []
    for j in range(cols):
      t.append(solver.IntVar(0, 1, "x[%i,%i]" % (i, j)))
    x.append(t)
  x_flat = [x[i][j] for i in range(rows) for j in range(cols)]

  #
  # constraints
  #

  # total_cost
  solver.Add(total_cost == solver.Sum(
      [solver.ScalProd(x_row, cost_row) for (x_row, cost_row) in zip(x, cost)]))

  # exacly one assignment per row, all rows must be assigned
  [
      solver.Add(solver.Sum([x[row][j]
                             for j in range(cols)]) == 1)
      for row in range(rows)
  ]

  # zero or one assignments per column
  [
      solver.Add(solver.Sum([x[i][col]
                             for i in range(rows)]) <= 1)
      for col in range(cols)
  ]

  objective = solver.Minimize(total_cost, 1)

  #
  # solution and search
  #
  solution = solver.Assignment()
  solution.Add(x_flat)
  solution.Add(total_cost)

  # db: DecisionBuilder
  db = solver.Phase(x_flat, solver.INT_VAR_SIMPLE, solver.ASSIGN_MIN_VALUE)

  solver.NewSearch(db, [objective])
  num_solutions = 0
  while solver.NextSolution():
    print("total_cost:", total_cost.Value())
    for i in range(rows):
      for j in range(cols):
        print(x[i][j].Value(), end=" ")
      print()
    print()

    for i in range(rows):
      print("Task:", i, end=" ")
      for j in range(cols):
        if x[i][j].Value() == 1:
          print(" is done by ", j)
    print()

    num_solutions += 1
  solver.EndSearch()

  print()
  print("num_solutions:", num_solutions)
  print("failures:", solver.Failures())
  print("branches:", solver.Branches())
  print("WallTime:", solver.WallTime())


# Problem instance
# hakank: I added the fifth column to make it more
#         interesting
rows = 4
cols = 5
cost = [[14, 5, 8, 7, 15], [2, 12, 6, 5, 3], [7, 8, 3, 9, 7], [2, 4, 6, 10, 1]]

main(cost, rows, cols)