134 lines
4.3 KiB
Python
134 lines
4.3 KiB
Python
#!/usr/bin/env python3
|
|
# Copyright 2010-2022 Google LLC
|
|
# 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.
|
|
|
|
"""Tasks and workers to group assignment to average sum(cost) / #workers."""
|
|
|
|
from typing import Sequence
|
|
from absl import app
|
|
from ortools.sat.python import cp_model
|
|
|
|
|
|
class ObjectivePrinter(cp_model.CpSolverSolutionCallback):
|
|
"""Print intermediate solutions."""
|
|
|
|
def __init__(self):
|
|
cp_model.CpSolverSolutionCallback.__init__(self)
|
|
self.__solution_count = 0
|
|
|
|
def on_solution_callback(self):
|
|
print(
|
|
"Solution %i, time = %f s, objective = %i"
|
|
% (self.__solution_count, self.WallTime(), self.ObjectiveValue())
|
|
)
|
|
self.__solution_count += 1
|
|
|
|
|
|
def tasks_and_workers_assignment_sat():
|
|
"""Solve the assignment problem."""
|
|
model = cp_model.CpModel()
|
|
|
|
# CP-SAT solver is integer only.
|
|
task_cost = [24, 10, 7, 2, 11, 16, 1, 13, 9, 27]
|
|
num_tasks = len(task_cost)
|
|
num_workers = 3
|
|
num_groups = 2
|
|
all_workers = range(num_workers)
|
|
all_groups = range(num_groups)
|
|
all_tasks = range(num_tasks)
|
|
|
|
# Variables
|
|
|
|
## x_ij = 1 if worker i is assigned to group j
|
|
x = {}
|
|
for i in all_workers:
|
|
for j in all_groups:
|
|
x[i, j] = model.NewBoolVar("x[%i,%i]" % (i, j))
|
|
|
|
## y_kj is 1 if task k is assigned to group j
|
|
y = {}
|
|
for k in all_tasks:
|
|
for j in all_groups:
|
|
y[k, j] = model.NewBoolVar("x[%i,%i]" % (k, j))
|
|
|
|
# Constraints
|
|
|
|
# Each task k is assigned to a group and only one.
|
|
for k in all_tasks:
|
|
model.Add(sum(y[k, j] for j in all_groups) == 1)
|
|
|
|
# Each worker i is assigned to a group and only one.
|
|
for i in all_workers:
|
|
model.Add(sum(x[i, j] for j in all_groups) == 1)
|
|
|
|
# cost per group
|
|
sum_of_costs = sum(task_cost)
|
|
averages = []
|
|
num_workers_in_group = []
|
|
scaled_sum_of_costs_in_group = []
|
|
scaling = 1000 # We introduce scaling to deal with floating point average.
|
|
for j in all_groups:
|
|
n = model.NewIntVar(1, num_workers, "num_workers_in_group_%i" % j)
|
|
model.Add(n == sum(x[i, j] for i in all_workers))
|
|
c = model.NewIntVar(0, sum_of_costs * scaling, "sum_of_costs_of_group_%i" % j)
|
|
model.Add(c == sum(y[k, j] * task_cost[k] * scaling for k in all_tasks))
|
|
a = model.NewIntVar(0, sum_of_costs * scaling, "average_cost_of_group_%i" % j)
|
|
model.AddDivisionEquality(a, c, n)
|
|
|
|
averages.append(a)
|
|
num_workers_in_group.append(n)
|
|
scaled_sum_of_costs_in_group.append(c)
|
|
|
|
# All workers are assigned.
|
|
model.Add(sum(num_workers_in_group) == num_workers)
|
|
|
|
# Objective.
|
|
obj = model.NewIntVar(0, sum_of_costs * scaling, "obj")
|
|
model.AddMaxEquality(obj, averages)
|
|
model.Minimize(obj)
|
|
|
|
# Solve and print out the solution.
|
|
solver = cp_model.CpSolver()
|
|
solver.parameters.max_time_in_seconds = 60 * 60 * 2
|
|
objective_printer = ObjectivePrinter()
|
|
status = solver.Solve(model, objective_printer)
|
|
print(solver.ResponseStats())
|
|
|
|
if status == cp_model.OPTIMAL:
|
|
for j in all_groups:
|
|
print("Group %i" % j)
|
|
for i in all_workers:
|
|
if solver.BooleanValue(x[i, j]):
|
|
print(" - worker %i" % i)
|
|
for k in all_tasks:
|
|
if solver.BooleanValue(y[k, j]):
|
|
print(" - task %i with cost %i" % (k, task_cost[k]))
|
|
print(
|
|
" - sum_of_costs = %i"
|
|
% (solver.Value(scaled_sum_of_costs_in_group[j]) // scaling)
|
|
)
|
|
print(" - average cost = %f" % (solver.Value(averages[j]) * 1.0 / scaling))
|
|
|
|
|
|
tasks_and_workers_assignment_sat()
|
|
|
|
|
|
def main(argv: Sequence[str]) -> None:
|
|
if len(argv) > 1:
|
|
raise app.UsageError("Too many command-line arguments.")
|
|
tasks_and_workers_assignment_sat()
|
|
|
|
|
|
if __name__ == "__main__":
|
|
app.run(main)
|