AssignmentSat.cs

// Copyright 2010-2018 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
{
  static void Main()
  {
    // 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]