80 lines
2.9 KiB
C#
80 lines
2.9 KiB
C#
// 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.
|
|
|
|
// """From Bradley, Hax, and Magnanti, 'Applied Mathematical Programming',
|
|
// figure 8.1.""" [START program]
|
|
using System;
|
|
using Google.OrTools.Graph;
|
|
|
|
public class SimpleMinCostFlowProgram {
|
|
static void Main() {
|
|
// [START data]
|
|
// Define four parallel arrays: sources, destinations, capacities, and unit
|
|
// costs between each pair. For instance, the arc from node 0 to node 1 has
|
|
// a capacity of 15. Problem taken From Taha's 'Introduction to Operations
|
|
// Research', example 6.4-2.
|
|
int[] startNodes = {0, 0, 1, 1, 1, 2, 2, 3, 4};
|
|
int[] endNodes = {1, 2, 2, 3, 4, 3, 4, 4, 2};
|
|
int[] capacities = {15, 8, 20, 4, 10, 15, 4, 20, 5};
|
|
int[] unitCosts = {4, 4, 2, 2, 6, 1, 3, 2, 3};
|
|
|
|
// Define an array of supplies at each node.
|
|
int[] supplies = {20, 0, 0, -5, -15};
|
|
// [END data]
|
|
|
|
// [START constraints]
|
|
// Instantiate a SimpleMinCostFlow solver.
|
|
MinCostFlow minCostFlow = new MinCostFlow();
|
|
|
|
// Add each arc.
|
|
for (int i = 0; i < startNodes.Length; ++i) {
|
|
int arc = minCostFlow.AddArcWithCapacityAndUnitCost(
|
|
startNodes[i], endNodes[i], capacities[i], unitCosts[i]);
|
|
if (arc != i) throw new Exception("Internal error");
|
|
}
|
|
|
|
// Add node supplies.
|
|
for (int i = 0; i < supplies.Length; ++i) {
|
|
minCostFlow.SetNodeSupply(i, supplies[i]);
|
|
}
|
|
|
|
// [END constraints]
|
|
|
|
// [START solve]
|
|
// Find the min cost flow.
|
|
MinCostFlow.Status solveStatus = minCostFlow.Solve();
|
|
// [END solve]
|
|
|
|
// [START print_solution]
|
|
if (solveStatus == MinCostFlow.Status.OPTIMAL) {
|
|
Console.WriteLine("Minimum cost: " + minCostFlow.OptimalCost());
|
|
Console.WriteLine("");
|
|
Console.WriteLine(" Edge Flow / Capacity Cost");
|
|
for (int i = 0; i < minCostFlow.NumArcs(); ++i) {
|
|
long cost = minCostFlow.Flow(i) * minCostFlow.UnitCost(i);
|
|
Console.WriteLine(minCostFlow.Tail(i) + " -> " + minCostFlow.Head(i) +
|
|
" " + string.Format("{0,3}", minCostFlow.Flow(i)) +
|
|
" / " +
|
|
string.Format("{0,3}", minCostFlow.Capacity(i)) +
|
|
" " + string.Format("{0,3}", cost));
|
|
}
|
|
} else {
|
|
Console.WriteLine(
|
|
"Solving the min cost flow problem failed. Solver status: " +
|
|
solveStatus);
|
|
}
|
|
// [END print_solution]
|
|
}
|
|
}
|
|
// [END program]
|