MultipleKnapsackMip.cs

// 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.LinearSolver;
// [END import]

// [START program_part1]
public class MultipleKnapsackMip
{
    // [START data_model]
    class DataModel
    {
        public static double[] Weights = { 48, 30, 42, 36, 36, 48, 42, 42, 36, 24, 30, 30, 42, 36, 36 };
        public static double[] Values = { 10, 30, 25, 50, 35, 30, 15, 40, 30, 35, 45, 10, 20, 30, 25 };
        public double[] BinCapacities = { 100, 100, 100, 100, 100 };
        public int NumItems = Weights.Length;
        public int NumBins = 5;
    }
    // [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}");
            }
        }
        // [END variables]

        // [START constraints]
        for (int i = 0; i < data.NumItems; ++i)
        {
            Constraint constraint = solver.MakeConstraint(0, 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, data.BinCapacities[j], "");
            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 i = 0; i < data.NumItems; ++i)
        {
            for (int j = 0; j < data.NumBins; ++j)
            {
                objective.SetCoefficient(x[i, j], DataModel.Values[i]);
            }
        }
        objective.SetMaximization();
        // [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("Total packed value: " + solver.Objective().Value());
        double TotalWeight = 0.0;
        for (int j = 0; j < data.NumBins; ++j)
        {
            double BinWeight = 0.0;
            double BinValue = 0.0;
            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]} values: {DataModel.Values[i]}");
                    BinWeight += DataModel.Weights[i];
                    BinValue += DataModel.Values[i];
                }
            }
            Console.WriteLine("Packed bin weight: " + BinWeight);
            Console.WriteLine("Packed bin value: " + BinValue);
            TotalWeight += BinWeight;
        }
        Console.WriteLine("Total packed weight: " + TotalWeight);
        // [END print_solution]
    }
}
// [END program_part2]
// [END program]