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AssignmentSat.cs
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AssignmentSat.cs
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// Copyright 2010-2021 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 Google.OrTools.Sat;
// [END import]
public class AssignmentSat
{
public static void Main(String[] args)
{
// Data.
// [START data_model]
int[,] costs = {
{ 90, 80, 75, 70 }, { 35, 85, 55, 65 }, { 125, 95, 90, 95 }, { 45, 110, 95, 115 }, { 50, 100, 90, 100 },
};
int numWorkers = costs.GetLength(0);
int numTasks = costs.GetLength(1);
// [END data_model]
// Model.
// [START model]
CpModel model = new CpModel();
// [END model]
// Variables.
// [START variables]
IntVar[,] x = new IntVar[numWorkers, numTasks];
// Variables in a 1-dim array.
IntVar[] xFlat = new IntVar[numWorkers * numTasks];
int[] costsFlat = new int[numWorkers * numTasks];
for (int i = 0; i < numWorkers; ++i)
{
for (int j = 0; j < numTasks; ++j)
{
x[i, j] = model.NewIntVar(0, 1, $"worker_{i}_task_{j}");
int k = i * numTasks + j;
xFlat[k] = x[i, j];
costsFlat[k] = costs[i, j];
}
}
// [END variables]
// Constraints
// [START constraints]
// Each worker is assigned to at most one task.
for (int i = 0; i < numWorkers; ++i)
{
IntVar[] vars = new IntVar[numTasks];
for (int j = 0; j < numTasks; ++j)
{
vars[j] = x[i, j];
}
model.Add(LinearExpr.Sum(vars) <= 1);
}
// Each task is assigned to exactly one worker.
for (int j = 0; j < numTasks; ++j)
{
IntVar[] vars = new IntVar[numWorkers];
for (int i = 0; i < numWorkers; ++i)
{
vars[i] = x[i, j];
}
model.Add(LinearExpr.Sum(vars) == 1);
}
// [END constraints]
// Objective
// [START objective]
model.Minimize(LinearExpr.ScalProd(xFlat, costsFlat));
// [END objective]
// Solve
// [START solve]
CpSolver solver = new CpSolver();
CpSolverStatus status = solver.Solve(model);
Console.WriteLine($"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($"Total cost: {solver.ObjectiveValue}\n");
for (int i = 0; i < numWorkers; ++i)
{
for (int j = 0; j < numTasks; ++j)
{
if (solver.Value(x[i, j]) > 0.5)
{
Console.WriteLine($"Worker {i} assigned to task {j}. Cost: {costs[i, j]}");
}
}
}
}
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]