|
| 1 | +{ |
| 2 | + "cells": [ |
| 3 | + { |
| 4 | + "cell_type": "markdown", |
| 5 | + "id": "google", |
| 6 | + "metadata": {}, |
| 7 | + "source": [ |
| 8 | + "##### Copyright 2023 Google LLC." |
| 9 | + ] |
| 10 | + }, |
| 11 | + { |
| 12 | + "cell_type": "markdown", |
| 13 | + "id": "apache", |
| 14 | + "metadata": {}, |
| 15 | + "source": [ |
| 16 | + "Licensed under the Apache License, Version 2.0 (the \"License\");\n", |
| 17 | + "you may not use this file except in compliance with the License.\n", |
| 18 | + "You may obtain a copy of the License at\n", |
| 19 | + "\n", |
| 20 | + " http://www.apache.org/licenses/LICENSE-2.0\n", |
| 21 | + "\n", |
| 22 | + "Unless required by applicable law or agreed to in writing, software\n", |
| 23 | + "distributed under the License is distributed on an \"AS IS\" BASIS,\n", |
| 24 | + "WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n", |
| 25 | + "See the License for the specific language governing permissions and\n", |
| 26 | + "limitations under the License.\n" |
| 27 | + ] |
| 28 | + }, |
| 29 | + { |
| 30 | + "cell_type": "markdown", |
| 31 | + "id": "basename", |
| 32 | + "metadata": {}, |
| 33 | + "source": [ |
| 34 | + "# permutation_flow_shop" |
| 35 | + ] |
| 36 | + }, |
| 37 | + { |
| 38 | + "cell_type": "markdown", |
| 39 | + "id": "link", |
| 40 | + "metadata": {}, |
| 41 | + "source": [ |
| 42 | + "<table align=\"left\">\n", |
| 43 | + "<td>\n", |
| 44 | + "<a href=\"https://colab.research.google.com/github/google/or-tools/blob/main/examples/notebook/contrib/permutation_flow_shop.ipynb\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/colab_32px.png\"/>Run in Google Colab</a>\n", |
| 45 | + "</td>\n", |
| 46 | + "<td>\n", |
| 47 | + "<a href=\"https://github.com/google/or-tools/blob/main/examples/contrib/permutation_flow_shop.py\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/github_32px.png\"/>View source on GitHub</a>\n", |
| 48 | + "</td>\n", |
| 49 | + "</table>" |
| 50 | + ] |
| 51 | + }, |
| 52 | + { |
| 53 | + "cell_type": "markdown", |
| 54 | + "id": "doc", |
| 55 | + "metadata": {}, |
| 56 | + "source": [ |
| 57 | + "First, you must install [ortools](https://pypi.org/project/ortools/) package in this colab." |
| 58 | + ] |
| 59 | + }, |
| 60 | + { |
| 61 | + "cell_type": "code", |
| 62 | + "execution_count": null, |
| 63 | + "id": "install", |
| 64 | + "metadata": {}, |
| 65 | + "outputs": [], |
| 66 | + "source": [ |
| 67 | + "%pip install ortools" |
| 68 | + ] |
| 69 | + }, |
| 70 | + { |
| 71 | + "cell_type": "markdown", |
| 72 | + "id": "description", |
| 73 | + "metadata": {}, |
| 74 | + "source": [ |
| 75 | + "\n", |
| 76 | + "This model implements the permutation flow shop problem (PFSP).\n", |
| 77 | + "\n", |
| 78 | + "In the PFSP, a set of jobs has to be processed on a set of machines. Each job\n", |
| 79 | + "must be processed on each machine in sequence and all jobs have to be processed\n", |
| 80 | + "in the same order on every machine. The objective is to minimize the makespan.\n", |
| 81 | + "\n" |
| 82 | + ] |
| 83 | + }, |
| 84 | + { |
| 85 | + "cell_type": "code", |
| 86 | + "execution_count": null, |
| 87 | + "id": "code", |
| 88 | + "metadata": {}, |
| 89 | + "outputs": [], |
| 90 | + "source": [ |
| 91 | + "from typing import Sequence\n", |
| 92 | + "from dataclasses import dataclass\n", |
| 93 | + "from itertools import product\n", |
| 94 | + "\n", |
| 95 | + "import numpy as np\n", |
| 96 | + "\n", |
| 97 | + "from ortools.sat.colab import flags\n", |
| 98 | + "from google.protobuf import text_format\n", |
| 99 | + "from ortools.sat.python import cp_model\n", |
| 100 | + "\n", |
| 101 | + "_PARAMS = flags.define_string(\n", |
| 102 | + " \"params\",\n", |
| 103 | + " \"num_search_workers:16\",\n", |
| 104 | + " \"Sat solver parameters.\",\n", |
| 105 | + ")\n", |
| 106 | + "\n", |
| 107 | + "_TIME_LIMIT = flags.define_float(\n", |
| 108 | + " \"time_limit\",\n", |
| 109 | + " 60.0,\n", |
| 110 | + " \"Time limit in seconds. Default is 60s.\",\n", |
| 111 | + ")\n", |
| 112 | + "\n", |
| 113 | + "_LOG = flags.define_boolean(\n", |
| 114 | + " \"log\",\n", |
| 115 | + " False,\n", |
| 116 | + " \"Whether to log the solver output.\",\n", |
| 117 | + ")\n", |
| 118 | + "\n", |
| 119 | + "\n", |
| 120 | + "@dataclass\n", |
| 121 | + "class TaskType:\n", |
| 122 | + " \"\"\"\n", |
| 123 | + " Small wrapper to hold the start, end, and interval variables of a task.\n", |
| 124 | + " \"\"\"\n", |
| 125 | + "\n", |
| 126 | + " start: cp_model.IntVar\n", |
| 127 | + " end: cp_model.IntVar\n", |
| 128 | + " interval: cp_model.IntervalVar\n", |
| 129 | + "\n", |
| 130 | + "\n", |
| 131 | + "def permutation_flow_shop(\n", |
| 132 | + " processing_times: np.ndarray,\n", |
| 133 | + " time_limit: float,\n", |
| 134 | + " log: bool,\n", |
| 135 | + " params: str\n", |
| 136 | + "):\n", |
| 137 | + " \"\"\"\n", |
| 138 | + " Solves the given permutation flow shop problem instance with OR-Tools.\n", |
| 139 | + "\n", |
| 140 | + " Parameters\n", |
| 141 | + " ----------\n", |
| 142 | + " processing_times\n", |
| 143 | + " An n-by-m matrix of processing times of the jobs on the machines.\n", |
| 144 | + " time_limit\n", |
| 145 | + " The time limit in seconds. If not set, the solver runs until an\n", |
| 146 | + " optimal solution is found.\n", |
| 147 | + " log\n", |
| 148 | + " Whether to log the solver output. Default is False.\n", |
| 149 | + "\n", |
| 150 | + " Raises\n", |
| 151 | + " ------\n", |
| 152 | + " ValueError\n", |
| 153 | + " If the number of lines is greater than 1, i.e., the instance is a\n", |
| 154 | + " distributed permutation flow shop problem.\n", |
| 155 | + " \"\"\"\n", |
| 156 | + " m = cp_model.CpModel()\n", |
| 157 | + " num_jobs, num_machines = processing_times.shape\n", |
| 158 | + " horizon = processing_times.sum()\n", |
| 159 | + "\n", |
| 160 | + " # Create interval variables for all tasks (each job/machine pair).\n", |
| 161 | + " tasks = {}\n", |
| 162 | + " for job, machine in product(range(num_jobs), range(num_machines)):\n", |
| 163 | + " start = m.new_int_var(0, horizon, \"\")\n", |
| 164 | + " end = m.new_int_var(0, horizon, \"\")\n", |
| 165 | + " duration = processing_times[job][machine]\n", |
| 166 | + " interval = m.new_interval_var(start, duration, end, \"\")\n", |
| 167 | + " tasks[job, machine] = TaskType(start, end, interval)\n", |
| 168 | + "\n", |
| 169 | + " # No overlap for all job intervals on this machine.\n", |
| 170 | + " for machine in range(num_machines):\n", |
| 171 | + " intervals = [tasks[job, machine].interval for job in range(num_jobs)]\n", |
| 172 | + " m.add_no_overlap(intervals)\n", |
| 173 | + "\n", |
| 174 | + " # Add precedence constraints between tasks of the same job.\n", |
| 175 | + " for job, machine in product(range(num_jobs), range(num_machines - 1)):\n", |
| 176 | + " pred = tasks[job, machine]\n", |
| 177 | + " succ = tasks[job, machine + 1]\n", |
| 178 | + " m.add(pred.end <= succ.start)\n", |
| 179 | + "\n", |
| 180 | + " # Create arcs for circuit constraints.\n", |
| 181 | + " arcs = []\n", |
| 182 | + " for idx1 in range(num_jobs):\n", |
| 183 | + " arcs.append((0, idx1 + 1, m.new_bool_var(\"start\")))\n", |
| 184 | + " arcs.append((idx1 + 1, 0, m.new_bool_var(\"end\")))\n", |
| 185 | + "\n", |
| 186 | + " lits = {}\n", |
| 187 | + " for idx1, idx2 in product(range(num_jobs), repeat=2):\n", |
| 188 | + " if idx1 != idx2:\n", |
| 189 | + " lit = m.new_bool_var(f\"{idx1} -> {idx2}\")\n", |
| 190 | + " lits[idx1, idx2] = lit\n", |
| 191 | + " arcs.append((idx1 + 1, idx2 + 1, lit))\n", |
| 192 | + "\n", |
| 193 | + " m.add_circuit(arcs)\n", |
| 194 | + "\n", |
| 195 | + " # Enforce that the permutation of jobs is the same on all machines.\n", |
| 196 | + " for machine in range(num_machines):\n", |
| 197 | + " starts = [tasks[job, machine].start for job in range(num_jobs)]\n", |
| 198 | + " ends = [tasks[job, machine].end for job in range(num_jobs)]\n", |
| 199 | + "\n", |
| 200 | + " for idx1, idx2 in product(range(num_jobs), repeat=2):\n", |
| 201 | + " if idx1 == idx2:\n", |
| 202 | + " continue\n", |
| 203 | + "\n", |
| 204 | + " # Since all machines share the same arc literals, if the literal\n", |
| 205 | + " # i -> j is True, this enforces that job i is always scheduled\n", |
| 206 | + " # before job j on all machines.\n", |
| 207 | + " lit = lits[idx1, idx2]\n", |
| 208 | + " m.add(ends[idx1] <= starts[idx2]).only_enforce_if(lit)\n", |
| 209 | + "\n", |
| 210 | + " # Set minimizing makespan as objective.\n", |
| 211 | + " obj_var = m.new_int_var(0, horizon, \"makespan\")\n", |
| 212 | + " completion_times = [\n", |
| 213 | + " tasks[(job, num_machines - 1)].end for job in range(num_jobs)\n", |
| 214 | + " ]\n", |
| 215 | + " m.add_max_equality(obj_var, completion_times)\n", |
| 216 | + " m.minimize(obj_var)\n", |
| 217 | + "\n", |
| 218 | + " solver = cp_model.CpSolver()\n", |
| 219 | + " if params:\n", |
| 220 | + " text_format.Parse(params, solver.parameters)\n", |
| 221 | + " solver.parameters.log_search_progress = log\n", |
| 222 | + " solver.parameters.max_time_in_seconds = time_limit\n", |
| 223 | + "\n", |
| 224 | + " status_code = solver.Solve(m)\n", |
| 225 | + " status = solver.StatusName(status_code)\n", |
| 226 | + "\n", |
| 227 | + " print(f\"Status: {status}\")\n", |
| 228 | + " print(f\"Makespan: {solver.ObjectiveValue()}\")\n", |
| 229 | + "\n", |
| 230 | + " if status in [\"OPTIMAL\", \"FEASIBLE\"]:\n", |
| 231 | + " start = [solver.Value(tasks[job, 0].start) for job in range(num_jobs)]\n", |
| 232 | + " solution = np.argsort(start) + 1\n", |
| 233 | + " print(f\"Solution: {solution}\")\n", |
| 234 | + "\n", |
| 235 | + "\n", |
| 236 | + "def main(argv: Sequence[str]) -> None:\n", |
| 237 | + " \"\"\"Creates the data and calls the solving procedure.\"\"\"\n", |
| 238 | + " # VRF_10_5_2 instance from http://soa.iti.es/problem-instances.\n", |
| 239 | + " # Optimal makespan is 698.\n", |
| 240 | + " processing_times = [\n", |
| 241 | + " [79, 67, 10, 48, 52],\n", |
| 242 | + " [40, 40, 57, 21, 54],\n", |
| 243 | + " [48, 93, 49, 11, 79],\n", |
| 244 | + " [16, 23, 19, 2, 38],\n", |
| 245 | + " [38, 90, 57, 73, 3],\n", |
| 246 | + " [76, 13, 99, 98, 55],\n", |
| 247 | + " [73, 85, 40, 20, 85],\n", |
| 248 | + " [34, 6, 27, 53, 21],\n", |
| 249 | + " [38, 6, 35, 28, 44],\n", |
| 250 | + " [32, 11, 11, 34, 27],\n", |
| 251 | + " ]\n", |
| 252 | + "\n", |
| 253 | + " permutation_flow_shop(\n", |
| 254 | + " np.array(processing_times), _TIME_LIMIT.value, _LOG.value, _PARAMS.value\n", |
| 255 | + " )\n", |
| 256 | + "\n", |
| 257 | + "\n", |
| 258 | + "app.run(main) \n", |
| 259 | + "\n" |
| 260 | + ] |
| 261 | + } |
| 262 | + ], |
| 263 | + "metadata": {}, |
| 264 | + "nbformat": 4, |
| 265 | + "nbformat_minor": 5 |
| 266 | +} |
0 commit comments