139 lines
4.6 KiB
C#
139 lines
4.6 KiB
C#
// 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.
|
|
|
|
// [START program]
|
|
// [START import]
|
|
using System;
|
|
using System.Collections.Generic;
|
|
using System.Linq;
|
|
using Google.OrTools.Sat;
|
|
// [END import]
|
|
|
|
public class AssignmentTaskSizesSat
|
|
{
|
|
public static void Main(String[] args)
|
|
{
|
|
// Data.
|
|
// [START data]
|
|
int[,] costs = {
|
|
{ 90, 76, 75, 70, 50, 74, 12, 68 }, { 35, 85, 55, 65, 48, 101, 70, 83 },
|
|
{ 125, 95, 90, 105, 59, 120, 36, 73 }, { 45, 110, 95, 115, 104, 83, 37, 71 },
|
|
{ 60, 105, 80, 75, 59, 62, 93, 88 }, { 45, 65, 110, 95, 47, 31, 81, 34 },
|
|
{ 38, 51, 107, 41, 69, 99, 115, 48 }, { 47, 85, 57, 71, 92, 77, 109, 36 },
|
|
{ 39, 63, 97, 49, 118, 56, 92, 61 }, { 47, 101, 71, 60, 88, 109, 52, 90 },
|
|
};
|
|
int numWorkers = costs.GetLength(0);
|
|
int numTasks = costs.GetLength(1);
|
|
|
|
int[] allWorkers = Enumerable.Range(0, numWorkers).ToArray();
|
|
int[] allTasks = Enumerable.Range(0, numTasks).ToArray();
|
|
|
|
int[] taskSizes = { 10, 7, 3, 12, 15, 4, 11, 5 };
|
|
// Maximum total of task sizes for any worker
|
|
int totalSizeMax = 15;
|
|
// [END data]
|
|
|
|
// Model.
|
|
// [START model]
|
|
CpModel model = new CpModel();
|
|
// [END model]
|
|
|
|
// Variables.
|
|
// [START variables]
|
|
BoolVar[,] x = new BoolVar[numWorkers, numTasks];
|
|
foreach (int worker in allWorkers)
|
|
{
|
|
foreach (int task in allTasks)
|
|
{
|
|
x[worker, task] = model.NewBoolVar($"x[{worker},{task}]");
|
|
}
|
|
}
|
|
// [END variables]
|
|
|
|
// Constraints
|
|
// [START constraints]
|
|
// Each worker is assigned to at most max task size.
|
|
foreach (int worker in allWorkers)
|
|
{
|
|
BoolVar[] vars = new BoolVar[numTasks];
|
|
foreach (int task in allTasks)
|
|
{
|
|
vars[task] = x[worker, task];
|
|
}
|
|
model.Add(LinearExpr.WeightedSum(vars, taskSizes) <= totalSizeMax);
|
|
}
|
|
|
|
// Each task is assigned to exactly one worker.
|
|
foreach (int task in allTasks)
|
|
{
|
|
List<ILiteral> workers = new List<ILiteral>();
|
|
foreach (int worker in allWorkers)
|
|
{
|
|
workers.Add(x[worker, task]);
|
|
}
|
|
model.AddExactlyOne(workers);
|
|
}
|
|
// [END constraints]
|
|
|
|
// Objective
|
|
// [START objective]
|
|
LinearExprBuilder obj = LinearExpr.NewBuilder();
|
|
foreach (int worker in allWorkers)
|
|
{
|
|
foreach (int task in allTasks)
|
|
{
|
|
obj.AddTerm(x[worker, task], costs[worker, task]);
|
|
}
|
|
}
|
|
model.Minimize(obj);
|
|
// [END objective]
|
|
|
|
// Solve
|
|
// [START solve]
|
|
CpSolver solver = new CpSolver();
|
|
CpSolverStatus status = solver.Solve(model);
|
|
Console.WriteLine($"Solve status: {status}");
|
|
// [END solve]
|
|
|
|
// Print solution.
|
|
// [START print_solution]
|
|
// Check that the problem has a feasible solution.
|
|
if (status == CpSolverStatus.Optimal || status == CpSolverStatus.Feasible)
|
|
{
|
|
Console.WriteLine($"Total cost: {solver.ObjectiveValue}\n");
|
|
foreach (int worker in allWorkers)
|
|
{
|
|
foreach (int task in allTasks)
|
|
{
|
|
if (solver.Value(x[worker, task]) > 0.5)
|
|
{
|
|
Console.WriteLine($"Worker {worker} assigned to task {task}. " +
|
|
$"Cost: {costs[worker, task]}");
|
|
}
|
|
}
|
|
}
|
|
}
|
|
else
|
|
{
|
|
Console.WriteLine("No solution found.");
|
|
}
|
|
// [END print_solution]
|
|
|
|
Console.WriteLine("Statistics");
|
|
Console.WriteLine($" - conflicts : {solver.NumConflicts()}");
|
|
Console.WriteLine($" - branches : {solver.NumBranches()}");
|
|
Console.WriteLine($" - wall time : {solver.WallTime()}s");
|
|
}
|
|
}
|
|
// [END program]
|