ortools-clone/ortools/linear_solver/samples/BinPackingMip.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]

// [START program_part1]
public class BinPackingMip {
  // [START data_model]
  class DataModel {
    public static double[] Weights = { 48, 30, 19, 36, 36, 27, 42, 42, 36, 24, 30 };
    public int NumItems = Weights.Length;
    public int NumBins = Weights.Length;
    public double BinCapacity = 100.0;
  }
  // [END data_model]
  public static void Main() {
    // [START data]
    DataModel data = new DataModel();
    // [END data]
    // [END program_part1]

    // [START solver]
    // Create the linear solver with the SCIP backend.
    Solver solver = Solver.CreateSolver("SCIP");
    // [END solver]

    // [START program_part2]
    // [START variables]
    Variable[,] x = new Variable[data.NumItems, data.NumBins];
    for (int i = 0; i < data.NumItems; i++) {
      for (int j = 0; j < data.NumBins; j++) {
        x[i, j] = solver.MakeIntVar(0, 1, $"x_{i}_{j}");
      }
    }
    Variable[] y = new Variable[data.NumBins];
    for (int j = 0; j < data.NumBins; j++) {
      y[j] = solver.MakeIntVar(0, 1, $"y_{j}");
    }
    // [END variables]

    // [START constraints]
    for (int i = 0; i < data.NumItems; ++i) {
      Constraint constraint = solver.MakeConstraint(1, 1, "");
      for (int j = 0; j < data.NumBins; ++j) {
        constraint.SetCoefficient(x[i, j], 1);
      }
    }

    for (int j = 0; j < data.NumBins; ++j) {
      Constraint constraint = solver.MakeConstraint(0, Double.PositiveInfinity, "");
      constraint.SetCoefficient(y[j], data.BinCapacity);
      for (int i = 0; i < data.NumItems; ++i) {
        constraint.SetCoefficient(x[i, j], -DataModel.Weights[i]);
      }
    }
    // [END constraints]

    // [START objective]
    Objective objective = solver.Objective();
    for (int j = 0; j < data.NumBins; ++j) {
      objective.SetCoefficient(y[j], 1);
    }
    objective.SetMinimization();
    // [END objective]

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

    // [START print_solution]
    // Check that the problem has an optimal solution.
    if (resultStatus != Solver.ResultStatus.OPTIMAL) {
      Console.WriteLine("The problem does not have an optimal solution!");
      return;
    }
    Console.WriteLine($"Number of bins used: {solver.Objective().Value()}");
    double TotalWeight = 0.0;
    for (int j = 0; j < data.NumBins; ++j) {
      double BinWeight = 0.0;
      if (y[j].SolutionValue() == 1) {
        Console.WriteLine($"Bin {j}");
        for (int i = 0; i < data.NumItems; ++i) {
          if (x[i, j].SolutionValue() == 1) {
            Console.WriteLine($"Item {i} weight: {DataModel.Weights[i]}");
            BinWeight += DataModel.Weights[i];
          }
        }
        Console.WriteLine($"Packed bin weight: {BinWeight}");
        TotalWeight += BinWeight;
      }
    }
    Console.WriteLine($"Total packed weight: {TotalWeight}");
    // [END print_solution]
  }
}
// [END program_part2]
// [END program]