ortools-clone/examples/cpp/min_cost_flow.cc

// Copyright 2010-2025 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.

#include "ortools/graph/min_cost_flow.h"

#include <cstdlib>
#include <utility>
#include <vector>

#include "absl/base/log_severity.h"
#include "absl/log/globals.h"
#include "absl/log/log.h"
#include "ortools/base/init_google.h"

namespace operations_research {
struct Arc {
  std::pair<SimpleMinCostFlow::NodeIndex, SimpleMinCostFlow::NodeIndex> nodes;
  SimpleMinCostFlow::FlowQuantity capacity;
  SimpleMinCostFlow::FlowQuantity unit_cost;
};

void SolveMinCostFlow() {
  // Define supply of each node.
  const std::vector<
      std::pair<SimpleMinCostFlow::NodeIndex, SimpleMinCostFlow::FlowQuantity> >
      supplies = {{0, 20}, {1, 0}, {2, 0}, {3, -5}, {4, -15}};

  // Define each arc
  // Can't use std::tuple<NodeIndex, NodeIndex, FlowQuantity>
  // Initialization list is not working on std:tuple cf. N4387
  // Arc are stored as {{begin_node, end_node}, capacity}
  const std::vector<Arc> arcs = {
      {{0, 1}, 15, 4}, {{0, 2}, 8, 4},  {{1, 2}, 20, 2},
      {{1, 3}, 4, 2},  {{1, 4}, 10, 6}, {{2, 3}, 15, 1},
      {{2, 4}, 4, 3},  {{3, 4}, 20, 2}, {{4, 2}, 5, 3}};

  SimpleMinCostFlow min_cost_flow;
  for (const auto& it : arcs) {
    min_cost_flow.AddArcWithCapacityAndUnitCost(it.nodes.first, it.nodes.second,
                                                it.capacity, it.unit_cost);
  }
  for (const auto& it : supplies) {
    min_cost_flow.SetNodeSupply(it.first, it.second);
  }

  LOG(INFO) << "Solving min cost flow with: " << min_cost_flow.NumNodes()
            << " nodes, and " << min_cost_flow.NumArcs() << " arcs.";

  // Find the maximum flow between node 0 and node 4.
  const auto status = min_cost_flow.Solve();
  if (status != SimpleMinCostFlow::OPTIMAL) {
    LOG(FATAL) << "Solving the max flow is not optimal!";
  }
  SimpleMinCostFlow::FlowQuantity total_flow_cost = min_cost_flow.OptimalCost();
  LOG(INFO) << "Minimum cost flow: " << total_flow_cost;
  LOG(INFO) << "";
  LOG(INFO) << "Arc   : Flow / Capacity / Cost";
  for (int i = 0; i < arcs.size(); ++i) {
    LOG(INFO) << min_cost_flow.Tail(i) << " -> " << min_cost_flow.Head(i)
              << ": " << min_cost_flow.Flow(i) << " / "
              << min_cost_flow.Capacity(i) << " / "
              << min_cost_flow.UnitCost(i);
  }
}
}  // namespace operations_research

int main(int argc, char** argv) {
  absl::SetStderrThreshold(absl::LogSeverityAtLeast::kInfo);
  InitGoogle(argv[0], &argc, &argv, true);
  operations_research::SolveMinCostFlow();
  return EXIT_SUCCESS;
}