220 lines
7.3 KiB
Plaintext
220 lines
7.3 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "be201470",
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"metadata": {},
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"source": [
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"##### Copyright 2021 Google LLC."
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]
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},
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{
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"cell_type": "markdown",
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"id": "e3803804",
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"metadata": {},
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"source": [
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"Licensed under the Apache License, Version 2.0 (the \"License\");\n",
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"you may not use this file except in compliance with the License.\n",
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"You may obtain a copy of the License at\n",
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"\n",
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" http://www.apache.org/licenses/LICENSE-2.0\n",
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"\n",
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"Unless required by applicable law or agreed to in writing, software\n",
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"distributed under the License is distributed on an \"AS IS\" BASIS,\n",
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"WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
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"See the License for the specific language governing permissions and\n",
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"limitations under the License.\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "c54bc54c",
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"metadata": {},
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"source": [
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"# assignment_groups_sat"
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]
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},
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{
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"cell_type": "markdown",
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"id": "fd3f9a16",
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"metadata": {},
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"source": [
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"<table align=\"left\">\n",
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"<td>\n",
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"<a href=\"https://colab.research.google.com/github/google/or-tools/blob/master/examples/notebook/sat/assignment_groups_sat.ipynb\"><img src=\"https://raw.githubusercontent.com/google/or-tools/master/tools/colab_32px.png\"/>Run in Google Colab</a>\n",
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"</td>\n",
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"<td>\n",
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"<a href=\"https://github.com/google/or-tools/blob/master/ortools/sat/samples/assignment_groups_sat.py\"><img src=\"https://raw.githubusercontent.com/google/or-tools/master/tools/github_32px.png\"/>View source on GitHub</a>\n",
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"</td>\n",
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"</table>"
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]
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},
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{
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"cell_type": "markdown",
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"id": "5c2119e2",
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"metadata": {},
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"source": [
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"First, you must install [ortools](https://pypi.org/project/ortools/) package in this colab."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "ca65dd32",
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"metadata": {},
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"outputs": [],
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"source": [
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"!pip install ortools"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "b6bc35ee",
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"metadata": {},
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"outputs": [],
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"source": [
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"#!/usr/bin/env python3\n",
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"# Copyright 2010-2021 Google LLC\n",
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"# Licensed under the Apache License, Version 2.0 (the \"License\");\n",
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"# you may not use this file except in compliance with the License.\n",
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"# You may obtain a copy of the License at\n",
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"#\n",
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"# http://www.apache.org/licenses/LICENSE-2.0\n",
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"#\n",
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"# Unless required by applicable law or agreed to in writing, software\n",
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"# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
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"# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
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"# See the License for the specific language governing permissions and\n",
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"# limitations under the License.\n",
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"# [START program]\n",
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"\"\"\"Solve assignment problem for given group of workers.\"\"\"\n",
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"# [START import]\n",
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"from ortools.sat.python import cp_model\n",
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"# [END import]\n",
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"\n",
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"\n",
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"# Data\n",
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"# [START data]\n",
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"costs = [\n",
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" [90, 76, 75, 70, 50, 74],\n",
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" [35, 85, 55, 65, 48, 101],\n",
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" [125, 95, 90, 105, 59, 120],\n",
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" [45, 110, 95, 115, 104, 83],\n",
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" [60, 105, 80, 75, 59, 62],\n",
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" [45, 65, 110, 95, 47, 31],\n",
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" [38, 51, 107, 41, 69, 99],\n",
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" [47, 85, 57, 71, 92, 77],\n",
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" [39, 63, 97, 49, 118, 56],\n",
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" [47, 101, 71, 60, 88, 109],\n",
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" [17, 39, 103, 64, 61, 92],\n",
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" [101, 45, 83, 59, 92, 27],\n",
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"]\n",
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"num_workers = len(costs)\n",
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"num_tasks = len(costs[0])\n",
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"# [END data]\n",
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"\n",
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"# Allowed groups of workers:\n",
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"# [START allowed_groups]\n",
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"group1 = [\n",
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" [0, 0, 1, 1], # Workers 2, 3\n",
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" [0, 1, 0, 1], # Workers 1, 3\n",
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" [0, 1, 1, 0], # Workers 1, 2\n",
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" [1, 1, 0, 0], # Workers 0, 1\n",
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" [1, 0, 1, 0], # Workers 0, 2\n",
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"]\n",
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"\n",
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"group2 = [\n",
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" [0, 0, 1, 1], # Workers 6, 7\n",
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" [0, 1, 0, 1], # Workers 5, 7\n",
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" [0, 1, 1, 0], # Workers 5, 6\n",
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" [1, 1, 0, 0], # Workers 4, 5\n",
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" [1, 0, 0, 1], # Workers 4, 7\n",
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"]\n",
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"\n",
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"group3 = [\n",
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" [0, 0, 1, 1], # Workers 10, 11\n",
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" [0, 1, 0, 1], # Workers 9, 11\n",
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" [0, 1, 1, 0], # Workers 9, 10\n",
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" [1, 0, 1, 0], # Workers 8, 10\n",
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" [1, 0, 0, 1], # Workers 8, 11\n",
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"]\n",
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"# [END allowed_groups]\n",
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"\n",
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"# Model\n",
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"# [START model]\n",
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"model = cp_model.CpModel()\n",
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"# [END model]\n",
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"\n",
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"# Variables\n",
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"# [START variables]\n",
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"x = {}\n",
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"for worker in range(num_workers):\n",
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" for task in range(num_tasks):\n",
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" x[worker, task] = model.NewBoolVar(f'x[{worker},{task}]')\n",
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"# [END variables]\n",
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"\n",
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"# Constraints\n",
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"# [START constraints]\n",
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"# Each worker is assigned to at most one task.\n",
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"for worker in range(num_workers):\n",
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" model.Add(sum(x[worker, task] for task in range(num_tasks)) <= 1)\n",
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"\n",
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"# Each task is assigned to exactly one worker.\n",
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"for task in range(num_tasks):\n",
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" model.Add(sum(x[worker, task] for worker in range(num_workers)) == 1)\n",
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"# [END constraints]\n",
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"\n",
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"# [START assignments]\n",
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"# Create variables for each worker, indicating whether they work on some task.\n",
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"work = {}\n",
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"for worker in range(num_workers):\n",
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" work[worker] = model.NewBoolVar(f'work[{worker}]')\n",
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"\n",
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"for worker in range(num_workers):\n",
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" for task in range(num_tasks):\n",
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" model.Add(work[worker] == sum(\n",
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" x[worker, task] for task in range(num_tasks)))\n",
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"\n",
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"# Define the allowed groups of worders\n",
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"model.AddAllowedAssignments([work[0], work[1], work[2], work[3]], group1)\n",
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"model.AddAllowedAssignments([work[4], work[5], work[6], work[7]], group2)\n",
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"model.AddAllowedAssignments([work[8], work[9], work[10], work[11]], group3)\n",
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"# [END assignments]\n",
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"\n",
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"# Objective\n",
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"# [START objective]\n",
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"objective_terms = []\n",
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"for worker in range(num_workers):\n",
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" for task in range(num_tasks):\n",
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" objective_terms.append(costs[worker][task] * x[worker, task])\n",
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"model.Minimize(sum(objective_terms))\n",
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"# [END objective]\n",
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"\n",
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"# Solve\n",
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"# [START solve]\n",
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"solver = cp_model.CpSolver()\n",
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"status = solver.Solve(model)\n",
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"# [END solve]\n",
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"\n",
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"# Print solution.\n",
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"# [START print_solution]\n",
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"if status == cp_model.OPTIMAL or status == cp_model.FEASIBLE:\n",
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" print(f'Total cost = {solver.ObjectiveValue()}\\n')\n",
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" for worker in range(num_workers):\n",
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" for task in range(num_tasks):\n",
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" if solver.BooleanValue(x[worker, task]):\n",
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" print(f'Worker {worker} assigned to task {task}.' +\n",
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" f' Cost = {costs[worker][task]}')\n",
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"else:\n",
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" print('No solution found.')\n",
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"# [END print_solution]\n",
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"\n"
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]
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}
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],
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"metadata": {},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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