AssignmentMip.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.LinearSolver;
// [END import]

public class AssignmentMip
{
  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]
    Solver solver = Solver.CreateSolver("AssignmentMip", "CBC_MIXED_INTEGER_PROGRAMMING");
    // [END model]

    // Variables.
    // [START variables]
    // x[i, j] is an array of 0-1 variables, which will be 1
    // if worker i is assigned to task j.
    Variable[,] x = new Variable[numWorkers, numTasks];
    for (int i = 0; i < numWorkers; ++i)
    {
      for (int j = 0; j < numTasks; ++j)
      {
        x[i, j] = solver.MakeIntVar(0, 1, $"worker_{i}_task_{j}");
      }
    }
    // [END variables]

    // Constraints
    // [START constraints]
    // Each worker is assigned to at most one task.
    for (int i = 0; i < numWorkers; ++i)
    {
      Constraint constraint = solver.MakeConstraint(0, 1, "");
      for (int j = 0; j < numTasks; ++j)
      {
        constraint.SetCoefficient(x[i, j], 1);
      }
    }
    // Each task is assigned to exactly one worker.
    for (int j = 0; j < numTasks; ++j)
    {
      Constraint constraint = solver.MakeConstraint(1, 1, "");
      for (int i = 0; i < numWorkers; ++i)
      {
        constraint.SetCoefficient(x[i, j], 1);
      }
    }
    // [END constraints]

    // Objective
    // [START objective]
    Objective objective = solver.Objective();
    for (int i = 0; i < numWorkers; ++i)
    {
      for (int j = 0; j < numTasks; ++j)
      {
        objective.SetCoefficient(x[i, j], 1);
      }
    }
    objective.SetMinimization();
    // [END objective]

    // Solve
    // [START solve]
    Solver.ResultStatus resultStatus = solver.Solve();
    // [END solve]

    // Print solution.
    // [START print_solution]
    // Check that the problem has a feasible solution.
    if (resultStatus == Solver.ResultStatus.OPTIMAL || resultStatus == Solver.ResultStatus.FEASIBLE)
    {
      Console.WriteLine($"Total cost: {solver.Objective().Value()}\n");
      for (int i = 0; i < numWorkers; ++i)
      {
        for (int j = 0; j < numTasks; ++j)
        {
          // Test if x[i, j] is 0 or 1 (with tolerance for floating point
          // arithmetic).
          if (x[i, j].SolutionValue() > 0.5)
          {
            Console.WriteLine($"Worker {i} assigned to task {j}. Cost: {costs[i, j]}");
          }
        }
      }
    } else {
      Console.WriteLine("No solution found.");
    }
    // [END print_solution]
  }
}
// [END program]