234 lines
6.9 KiB
C++
234 lines
6.9 KiB
C++
// Copyright 2010-2021 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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// [START program]
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// Solve a simple assignment problem.
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// [START import]
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#include <cstdint>
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#include <numeric>
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#include <utility>
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#include <vector>
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#include "absl/strings/str_format.h"
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#include "ortools/base/logging.h"
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#include "ortools/linear_solver/linear_solver.h"
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// [END import]
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namespace operations_research {
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void AssignmentTeamsMip() {
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// Data
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// [START data]
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const std::vector<std::vector<int64_t>> costs = {{
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{{90, 76, 75, 70, 50, 74}},
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{{35, 85, 55, 65, 48, 101}},
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{{125, 95, 90, 105, 59, 120}},
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{{45, 110, 95, 115, 104, 83}},
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{{60, 105, 80, 75, 59, 62}},
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{{45, 65, 110, 95, 47, 31}},
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{{38, 51, 107, 41, 69, 99}},
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{{47, 85, 57, 71, 92, 77}},
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{{39, 63, 97, 49, 118, 56}},
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{{47, 101, 71, 60, 88, 109}},
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{{17, 39, 103, 64, 61, 92}},
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{{101, 45, 83, 59, 92, 27}},
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}};
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const int num_workers = costs.size();
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std::vector<int> all_workers(num_workers);
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std::iota(all_workers.begin(), all_workers.end(), 0);
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const int num_tasks = costs[0].size();
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std::vector<int> all_tasks(num_tasks);
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std::iota(all_tasks.begin(), all_tasks.end(), 0);
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// [END data]
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// Allowed groups of workers:
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// [START allowed_groups]
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using WorkerIndex = int;
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using Binome = std::pair<WorkerIndex, WorkerIndex>;
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using AllowedBinomes = std::vector<Binome>;
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const AllowedBinomes group1 = {{ // group of worker 0-3
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{2, 3},
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{1, 3},
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{1, 2},
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{0, 1},
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{0, 2},
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}};
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const AllowedBinomes group2 = {{ // group of worker 4-7
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{6, 7},
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{5, 7},
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{5, 6},
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{4, 5},
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{4, 7},
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}};
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const AllowedBinomes group3 = {{ // group of worker 8-11
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{10, 11},
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{9, 11},
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{9, 10},
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{8, 10},
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{8, 11},
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}};
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// [END allowed_groups]
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// Solver
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// [START solver]
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// Create the mip solver with the SCIP backend.
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std::unique_ptr<MPSolver> solver(MPSolver::CreateSolver("SCIP"));
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if (!solver) {
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LOG(WARNING) << "SCIP solver unavailable.";
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return;
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}
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// [END solver]
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// Variables
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// [START variables]
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// x[i][j] is an array of 0-1 variables, which will be 1
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// if worker i is assigned to task j.
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std::vector<std::vector<const MPVariable*>> x(
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num_workers, std::vector<const MPVariable*>(num_tasks));
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for (int worker : all_workers) {
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for (int task : all_tasks) {
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x[worker][task] =
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solver->MakeBoolVar(absl::StrFormat("x[%d,%d]", worker, task));
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}
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}
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// [END variables]
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// Constraints
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// [START constraints]
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// Each worker is assigned to at most one task.
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for (int worker : all_workers) {
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LinearExpr worker_sum;
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for (int task : all_tasks) {
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worker_sum += x[worker][task];
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}
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solver->MakeRowConstraint(worker_sum <= 1.0);
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}
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// Each task is assigned to exactly one worker.
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for (int task : all_tasks) {
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LinearExpr task_sum;
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for (int worker : all_workers) {
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task_sum += x[worker][task];
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}
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solver->MakeRowConstraint(task_sum == 1.0);
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}
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// [END constraints]
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// [START assignments]
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// Create variables for each worker, indicating whether they work on some
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// task.
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std::vector<const MPVariable*> work(num_workers);
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for (int worker : all_workers) {
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work[worker] =
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solver->MakeBoolVar(absl::StrFormat("work[%d]", worker));
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}
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for (int worker : all_workers) {
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LinearExpr task_sum;
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for (int task : all_tasks) {
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task_sum += x[worker][task];
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}
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solver->MakeRowConstraint(work[worker] == task_sum);
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}
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// Group1
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{
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MPConstraint* g1 = solver->MakeRowConstraint(1, 1);
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for (int i=0; i < group1.size(); ++i) {
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// a*b can be transformed into 0 <= a + b - 2*p <= 1 with p in [0,1]
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// p is true if a AND b, false otherwise
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MPConstraint* tmp = solver->MakeRowConstraint(0, 1);
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tmp->SetCoefficient(work[group1[i].first], 1);
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tmp->SetCoefficient(work[group1[i].second], 1);
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MPVariable* p = solver->MakeBoolVar(absl::StrFormat("g1_p%d", i));
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tmp->SetCoefficient(p, -2);
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g1->SetCoefficient(p, 1);
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}
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}
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// Group2
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{
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MPConstraint* g2 = solver->MakeRowConstraint(1, 1);
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for (int i=0; i < group2.size(); ++i) {
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// a*b can be transformed into 0 <= a + b - 2*p <= 1 with p in [0,1]
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// p is true if a AND b, false otherwise
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MPConstraint* tmp = solver->MakeRowConstraint(0, 1);
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tmp->SetCoefficient(work[group2[i].first], 1);
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tmp->SetCoefficient(work[group2[i].second], 1);
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MPVariable* p = solver->MakeBoolVar(absl::StrFormat("g2_p%d", i));
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tmp->SetCoefficient(p, -2);
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g2->SetCoefficient(p, 1);
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}
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}
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// Group3
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{
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MPConstraint* g3 = solver->MakeRowConstraint(1, 1);
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for (int i=0; i < group3.size(); ++i) {
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// a*b can be transformed into 0 <= a + b - 2*p <= 1 with p in [0,1]
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// p is true if a AND b, false otherwise
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MPConstraint* tmp = solver->MakeRowConstraint(0, 1);
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tmp->SetCoefficient(work[group3[i].first], 1);
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tmp->SetCoefficient(work[group3[i].second], 1);
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MPVariable* p = solver->MakeBoolVar(absl::StrFormat("g3_p%d", i));
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tmp->SetCoefficient(p, -2);
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g3->SetCoefficient(p, 1);
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}
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}
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// [END assignments]
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// Objective.
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// [START objective]
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MPObjective* const objective = solver->MutableObjective();
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for (int worker : all_workers) {
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for (int task : all_tasks) {
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objective->SetCoefficient(x[worker][task], costs[worker][task]);
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}
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}
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objective->SetMinimization();
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// [END objective]
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// Solve
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// [START solve]
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const MPSolver::ResultStatus result_status = solver->Solve();
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// [END solve]
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// Print solution.
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// [START print_solution]
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// Check that the problem has a feasible solution.
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if (result_status != MPSolver::OPTIMAL &&
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result_status != MPSolver::FEASIBLE) {
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LOG(FATAL) << "No solution found.";
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}
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LOG(INFO) << "Total cost = " << objective->Value() << "\n\n";
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for (int worker : all_workers) {
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for (int task : all_tasks) {
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// Test if x[i][j] is 0 or 1 (with tolerance for floating point
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// arithmetic).
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if (x[worker][task]->solution_value() > 0.5) {
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LOG(INFO) << "Worker " << worker << " assigned to task " << task
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<< ". Cost: " << costs[worker][task];
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}
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}
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}
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// [END print_solution]
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}
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} // namespace operations_research
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int main(int argc, char** argv) {
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operations_research::AssignmentTeamsMip();
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return EXIT_SUCCESS;
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}
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// [END program]
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