78 lines
2.9 KiB
C#
78 lines
2.9 KiB
C#
// Copyright 2010-2018 Google LLC
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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// """From Bradley, Hax, and Magnanti, 'Applied Mathematical Programming',
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// figure 8.1.""" [START program]
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using System;
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using Google.OrTools.Graph;
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public class SimpleMinCostFlowProgram {
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static void Main() {
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// [START data]
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// Define four parallel arrays: sources, destinations, capacities, and unit
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// costs between each pair. For instance, the arc from node 0 to node 1 has
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// a capacity of 15. Problem taken From Taha's 'Introduction to Operations
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// Research', example 6.4-2.
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int[] startNodes = { 0, 0, 1, 1, 1, 2, 2, 3, 4 };
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int[] endNodes = { 1, 2, 2, 3, 4, 3, 4, 4, 2 };
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int[] capacities = { 15, 8, 20, 4, 10, 15, 4, 20, 5 };
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int[] unitCosts = { 4, 4, 2, 2, 6, 1, 3, 2, 3 };
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// Define an array of supplies at each node.
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int[] supplies = { 20, 0, 0, -5, -15 };
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// [END data]
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// [START constraints]
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// Instantiate a SimpleMinCostFlow solver.
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MinCostFlow minCostFlow = new MinCostFlow();
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// Add each arc.
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for (int i = 0; i < startNodes.Length; ++i) {
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int arc = minCostFlow.AddArcWithCapacityAndUnitCost(startNodes[i], endNodes[i], capacities[i],
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unitCosts[i]);
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if (arc != i)
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throw new Exception("Internal error");
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}
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// Add node supplies.
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for (int i = 0; i < supplies.Length; ++i) {
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minCostFlow.SetNodeSupply(i, supplies[i]);
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}
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// [END constraints]
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// [START solve]
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// Find the min cost flow.
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MinCostFlow.Status solveStatus = minCostFlow.Solve();
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// [END solve]
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// [START print_solution]
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if (solveStatus == MinCostFlow.Status.OPTIMAL) {
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Console.WriteLine("Minimum cost: " + minCostFlow.OptimalCost());
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Console.WriteLine("");
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Console.WriteLine(" Edge Flow / Capacity Cost");
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for (int i = 0; i < minCostFlow.NumArcs(); ++i) {
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long cost = minCostFlow.Flow(i) * minCostFlow.UnitCost(i);
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Console.WriteLine(minCostFlow.Tail(i) + " -> " + minCostFlow.Head(i) + " " +
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string.Format("{0,3}", minCostFlow.Flow(i)) + " / " +
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string.Format("{0,3}", minCostFlow.Capacity(i)) + " " +
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string.Format("{0,3}", cost));
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}
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} else {
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Console.WriteLine("Solving the min cost flow problem failed. Solver status: " + solveStatus);
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}
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// [END print_solution]
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}
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}
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// [END program]
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