linear_solver: Add assignment_task_sizes_mip.py

ortools/linear_solver/samples/assignment_task_sizes_mip.py

@@ -0,0 +1,106 @@
+#!/usr/bin/env python3
+# 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]
+"""MIP example that solves an assignment problem."""
+# [START import]
+from ortools.linear_solver import pywraplp
+# [END import]
+
+
+def main():
+    # Data
+    # [START data]
+    costs = [
+        [90, 76, 75, 70, 50, 74, 12, 68],
+        [35, 85, 55, 65, 48, 101, 70, 83],
+        [125, 95, 90, 105, 59, 120, 36, 73],
+        [45, 110, 95, 115, 104, 83, 37, 71],
+        [60, 105, 80, 75, 59, 62, 93, 88],
+        [45, 65, 110, 95, 47, 31, 81, 34],
+        [38, 51, 107, 41, 69, 99, 115, 48],
+        [47, 85, 57, 71, 92, 77, 109, 36],
+        [39, 63, 97, 49, 118, 56, 92, 61],
+        [47, 101, 71, 60, 88, 109, 52, 90],
+    ]
+    num_workers = len(costs)
+    num_tasks = len(costs[0])
+
+    task_sizes = [10, 7, 3, 12, 15, 4, 11, 5]
+    # Maximum total of task sizes for any worker
+    total_size_max = 15
+    # [END data]
+
+    # Solver
+    # [START solver]
+    # Create the mip solver with the SCIP backend.
+    solver = pywraplp.Solver.CreateSolver('SCIP')
+
+    # [END solver]
+
+    # Variables
+    # [START variables]
+    # x[i, j] is an array of 0-1 variables, which will be 1
+    # if worker i is assigned to task j.
+    x = {}
+    for worker in range(num_workers):
+        for task in range(num_tasks):
+            x[worker, task] = solver.IntVar(0, 1, f'x[{worker},{task}]')
+    # [END variables]
+
+    # Constraints
+    # [START constraints]
+    # The total size of the tasks each worker takes on is at most total_size_max.
+    for worker in range(num_workers):
+        solver.Add(
+            solver.Sum([
+                task_sizes[task] * x[worker, task] for task in range(num_tasks)
+            ]) <= total_size_max)
+
+    # Each task is assigned to exactly one worker.
+    for task in range(num_tasks):
+        solver.Add(
+            solver.Sum([x[worker, task] for worker in range(num_workers)]) == 1)
+    # [END constraints]
+
+    # Objective
+    # [START objective]
+    objective_terms = []
+    for worker in range(num_workers):
+        for task in range(num_tasks):
+            objective_terms.append(costs[worker][task] * x[worker, task])
+    solver.Minimize(solver.Sum(objective_terms))
+    # [END objective]
+
+    # Solve
+    # [START solve]
+    status = solver.Solve()
+    # [END solve]
+
+    # Print solution.
+    # [START print_solution]
+    if status == pywraplp.Solver.OPTIMAL or status == pywraplp.Solver.FEASIBLE:
+        print(f'Total cost = {solver.Objective().Value()}\n')
+        for worker in range(num_workers):
+            for task in range(num_tasks):
+                if x[worker, task].solution_value() > 0.5:
+                    print(f'Worker {worker} assigned to task {task}.' +
+                          f' Cost = {costs[worker][task]}')
+    else:
+        print('No solution found.')
+    # [END print_solution]
+
+
+if __name__ == '__main__':
+    main()
+# [END program]