BinPackingProblemSat.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.

using System;
using Google.OrTools.Sat;

public class BinPackingProblemSat
{
  static void Main()
  {
    // Data.
    int bin_capacity = 100;
    int slack_capacity = 20;
    int num_bins = 5;

    int[,] items = new int[,] { { 20, 6 }, { 15, 6 }, { 30, 4 }, { 45, 3 } };
    int num_items = items.GetLength(0);

    // Model.
    CpModel model = new CpModel();

    // Main variables.
    IntVar[,] x = new IntVar[num_items, num_bins];
    for (int i = 0; i < num_items; ++i)
    {
      int num_copies = items[i, 1];
      for (int b = 0; b < num_bins; ++b)
      {
        x[i, b] = model.NewIntVar(0, num_copies, String.Format("x_{0}_{1}", i, b));
      }
    }

    // Load variables.
    IntVar[] load = new IntVar[num_bins];
    for (int b = 0; b < num_bins; ++b)
    {
      load[b] = model.NewIntVar(0, bin_capacity, String.Format("load_{0}", b));
    }

    // Slack variables.
    IntVar[] slacks = new IntVar[num_bins];
    for (int b = 0; b < num_bins; ++b)
    {
      slacks[b] = model.NewBoolVar(String.Format("slack_{0}", b));
    }

    // Links load and x.
    int[] sizes = new int[num_items];
    for (int i = 0; i < num_items; ++i)
    {
      sizes[i] = items[i, 0];
    }
    for (int b = 0; b < num_bins; ++b)
    {
      IntVar[] tmp = new IntVar[num_items];
      for (int i = 0; i < num_items; ++i)
      {
        tmp[i] = x[i, b];
      }
      model.Add(load[b] == LinearExpr.ScalProd(tmp, sizes));
    }

    // Place all items.
    for (int i = 0; i < num_items; ++i)
    {
      IntVar[] tmp = new IntVar[num_bins];
      for (int b = 0; b < num_bins; ++b)
      {
        tmp[b] = x[i, b];
      }
      model.Add(LinearExpr.Sum(tmp) == items[i, 1]);
    }

    // Links load and slack.
    int safe_capacity = bin_capacity - slack_capacity;
    for (int b = 0; b < num_bins; ++b)
    {
      //  slack[b] => load[b] <= safe_capacity.
      model.Add(load[b] <= safe_capacity).OnlyEnforceIf(slacks[b]);
      // not(slack[b]) => load[b] > safe_capacity.
      model.Add(load[b] > safe_capacity).OnlyEnforceIf(slacks[b].Not());
    }

    // Maximize sum of slacks.
    model.Maximize(LinearExpr.Sum(slacks));

    // Solves and prints out the solution.
    CpSolver solver = new CpSolver();
    CpSolverStatus status = solver.Solve(model);
    Console.WriteLine(String.Format("Solve status: {0}", status));
    if (status == CpSolverStatus.Optimal) {
      Console.WriteLine(String.Format("Optimal objective value: {0}",
                                      solver.ObjectiveValue));
      for (int b = 0; b < num_bins; ++b)
      {
        Console.WriteLine(String.Format("load_{0} = {1}",
                                        b, solver.Value(load[b])));
        for (int i = 0; i < num_items; ++i)
        {
          Console.WriteLine(string.Format("  item_{0}_{1} = {2}",
                                          i, b, solver.Value(x[i, b])));
        }
      }
    }
    Console.WriteLine("Statistics");
    Console.WriteLine(String.Format("  - conflicts : {0}",
                                    solver.NumConflicts()));
    Console.WriteLine(String.Format("  - branches  : {0}",
                                    solver.NumBranches()));
    Console.WriteLine(String.Format("  - wall time : {0} s",
                                    solver.WallTime()));
  }
}