120 lines
4.1 KiB
Python
120 lines
4.1 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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"""Tasks and workers to group assignment to average sum(cost) / #workers"""
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from ortools.sat.python import cp_model
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class ObjectivePrinter(cp_model.CpSolverSolutionCallback):
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"""Print intermediate solutions."""
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def __init__(self):
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cp_model.CpSolverSolutionCallback.__init__(self)
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self.__solution_count = 0
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def OnSolutionCallback(self):
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print('Solution %i, time = %f s, objective = %i' %
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(self.__solution_count, self.WallTime(), self.ObjectiveValue()))
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self.__solution_count += 1
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def tasks_and_workers_assignment_sat():
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"""Solve the assignment problem."""
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model = cp_model.CpModel()
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# CP-SAT solver is integer only.
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task_cost = [24, 10, 7, 2, 11, 16, 1, 13, 9, 27]
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num_tasks = len(task_cost)
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num_workers = 3
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num_groups = 2
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all_workers = range(num_workers)
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all_groups = range(num_groups)
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all_tasks = range(num_tasks)
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# Variables
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## x_ij = 1 if worker i is assigned to group j
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x = {}
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for i in all_workers:
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for j in all_groups:
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x[i, j] = model.NewBoolVar('x[%i,%i]' % (i, j))
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## y_kj is 1 if task k is assigned to group j
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y = {}
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for k in all_tasks:
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for j in all_groups:
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y[k, j] = model.NewBoolVar('x[%i,%i]' % (k, j))
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# Constraints
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# Each task k is assigned to a group and only one.
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for k in all_tasks:
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model.Add(sum(y[k, j] for j in all_groups) == 1)
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# Each worker i is assigned to a group and only one.
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for i in all_workers:
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model.Add(sum(x[i, j] for j in all_groups) == 1)
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# cost per group
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sum_of_costs = sum(task_cost)
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averages = []
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num_workers_in_group = []
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scaled_sum_of_costs_in_group = []
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scaling = 1000 # We introduce scaling to deal with floating point average.
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for j in all_groups:
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n = model.NewIntVar(1, num_workers, 'num_workers_in_group_%i' % j)
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model.Add(n == sum(x[i, j] for i in all_workers))
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c = model.NewIntVar(0, sum_of_costs * scaling,
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'sum_of_costs_of_group_%i' % j)
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model.Add(c == sum(
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y[k, j] * task_cost[k] * scaling for k in all_tasks))
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a = model.NewIntVar(0, sum_of_costs * scaling,
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'average_cost_of_group_%i' % j)
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model.AddDivisionEquality(a, c, n)
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averages.append(a)
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num_workers_in_group.append(n)
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scaled_sum_of_costs_in_group.append(c)
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# All workers are assigned.
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model.Add(sum(num_workers_in_group) == num_workers)
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# Objective.
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obj = model.NewIntVar(0, sum_of_costs * scaling, 'obj')
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model.AddMaxEquality(obj, averages)
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model.Minimize(obj)
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# Solve and print out the solution.
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solver = cp_model.CpSolver()
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solver.parameters.max_time_in_seconds = 60 * 60 * 2
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objective_printer = ObjectivePrinter()
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status = solver.SolveWithSolutionCallback(model, objective_printer)
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print(solver.ResponseStats())
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if status == cp_model.OPTIMAL:
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for j in all_groups:
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print('Group %i' % j)
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for i in all_workers:
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if solver.BooleanValue(x[i, j]):
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print(' - worker %i' % i)
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for k in all_tasks:
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if solver.BooleanValue(y[k, j]):
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print(' - task %i with cost %i' % (k, task_cost[k]))
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print(' - sum_of_costs = %i' %
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(solver.Value(scaled_sum_of_costs_in_group[j]) // scaling))
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print(' - average cost = %f' %
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(solver.Value(averages[j]) * 1.0 / scaling))
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tasks_and_workers_assignment_sat()
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