flexible job shop scheduling problem

Untitled-1.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solution 0, time = 0.004457 s, objective = 15\n",
      "Solution 1, time = 0.006655 s, objective = 11\n",
      "\n",
      "solve status: OPTIMAL\n",
      "Optimal objective value: 11\n",
      "Statistics\n",
      "  - conflicts : 0\n",
      "  - branches  : 0\n",
      "  - wall time : 0.012622 s\n"
     ]
    }
   ],
   "source": [
    "from ortools.sat.python import cp_model\n",
    "import collections\n",
    "\n",
    "class SolutionPrinter(cp_model.CpSolverSolutionCallback):\n",
    "    \"\"\"Print intermediate solutions.\"\"\"\n",
    "\n",
    "    def __init__(self):\n",
    "        cp_model.CpSolverSolutionCallback.__init__(self)\n",
    "        self.__solution_count = 0\n",
    "\n",
    "    def on_solution_callback(self):\n",
    "        \"\"\"Called at each new solution.\"\"\"\n",
    "        print(\n",
    "            \"Solution %i, time = %f s, objective = %i\"\n",
    "            % (self.__solution_count, self.wall_time, self.objective_value)\n",
    "        )\n",
    "        self.__solution_count += 1\n",
    "\n",
    "\n",
    "task_type = collections.namedtuple(\"task_type\", \"start end interval machine\")\n",
    "\n",
    "\n",
    "machine = 5\n",
    "tasks=[\n",
    " {'id': 1, 'name': 'Job 1', 'machine': [5], 'duration': 4, 'dependent': [2]},\n",
    " {'id': 2, 'name': 'Cheese', 'machine': [3,4], 'duration': 2, 'dependent': [3,4]},\n",
    " {'id': 3, 'name': 'Milk', 'machine': [3,4], 'duration': 2, 'dependent': [5,6,7,8]},\n",
    " {'id': 4, 'name': 'Milk', 'machine': [3,4], 'duration': 3, 'dependent': [5,6,7,8]},\n",
    " {'id': 5, 'name': 'Wheat 1','machine': [1,2],'duration': 1,'dependent': []},\n",
    " {'id': 6, 'name': 'Wheat 2','machine': [1,2],'duration': 1,'dependent': []},\n",
    " {'id': 7, 'name': 'Wheat 3','machine': [1,2],'duration': 1,'dependent': []},\n",
    "  {'id': 8, 'name': 'Wheat 4','machine': [1,2],'duration': 1,'dependent': []}]\n",
    "\n",
    "duration = {task['id']: task['duration'] for task in tasks}\n",
    "horizon = sum(task['duration'] for task in tasks)\n",
    "times = range(horizon)\n",
    "\n",
    "model = cp_model.CpModel()\n",
    "\n",
    "all_tasks = {}\n",
    "intervals_per_resources = collections.defaultdict(list)\n",
    "\n",
    "for task in tasks:\n",
    "    start_var = model.new_int_var(0, horizon, 'start_%i' % task['id'])\n",
    "    end_var = model.new_int_var(0, horizon, 'end_%i' % task['id'])\n",
    "    interval_var = model.new_interval_var(start_var, duration[task['id']], end_var, 'interval_%i' % task['id'])\n",
    "    machine_var = model.new_int_var_from_domain(cp_model.Domain.FromValues(task['machine']), 'machine_%i' % task['id'])\n",
    "    all_tasks[task['id']] = task_type(\n",
    "        start=start_var, end=end_var, interval=interval_var, machine=machine_var\n",
    "    )\n",
    "\n",
    "    if len(task['machine']) == 1:\n",
    "        intervals_per_resources[task['machine'][0]].append(interval_var)\n",
    "    else:\n",
    "        l_presences = []\n",
    "        for machine_id in task['machine']:\n",
    "            l_presence = model.new_bool_var('presence_%i_%i' % (task['id'], machine_id))\n",
    "            l_start = model.new_int_var(0, horizon, 'start_%i_%i' % (task['id'], machine_id))\n",
    "            l_end = model.new_int_var(0, horizon, 'end_%i_%i' % (task['id'], machine_id))   \n",
    "            l_interval = model.new_optional_interval_var(l_start, duration[task['id']], l_end, l_presence, 'interval_%i_%i' % (task['id'], machine_id))\n",
    "            l_presences.append(l_presence)\n",
    "\n",
    "            model.add(start_var == l_start).only_enforce_if(l_presence)\n",
    "            model.add(end_var == l_end).only_enforce_if(l_presence)\n",
    "            model.add(machine_var == machine_id).only_enforce_if(l_presence)\n",
    "            intervals_per_resources[machine_id].append(l_interval)\n",
    "        model.add_exactly_one(l_presences)\n",
    "\n",
    "for machine_id in range(machine):\n",
    "    intervals = intervals_per_resources[machine_id]\n",
    "    if len(intervals) > 1:\n",
    "        model.add_no_overlap(intervals)\n",
    "\n",
    "for task in tasks:\n",
    "    for dependency in task['dependent']:\n",
    "        model.Add(all_tasks[task['id']].start >= all_tasks[dependency].end)\n",
    "\n",
    "\n",
    "\n",
    "obj_var = model.new_int_var(0, horizon, 'makespan')\n",
    "model.add_max_equality(obj_var, [all_tasks[task['id']].end for task in tasks])\n",
    "model.minimize(obj_var)\n",
    "solver = cp_model.CpSolver()\n",
    "solution_printer = SolutionPrinter()\n",
    "status = solver.solve(model,solution_printer)\n",
    "print()\n",
    "print(\"solve status: %s\" % solver.status_name(status))\n",
    "print(\"Optimal objective value: %i\" % solver.objective_value)\n",
    "print(\"Statistics\")\n",
    "print(\"  - conflicts : %i\" % solver.num_conflicts)\n",
    "print(\"  - branches  : %i\" % solver.num_branches)\n",
    "print(\"  - wall time : %f s\" % solver.wall_time)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "# solution to pandas dataframe\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "data = []\n",
    "for task in tasks:\n",
    "    task_id = task['id']\n",
    "    task_name = task['name']\n",
    "    start = solver.Value(all_tasks[task_id].start)\n",
    "    end = solver.Value(all_tasks[task_id].end)\n",
    "    machine = solver.Value(all_tasks[task_id].machine)\n",
    "    data.append([task_id, task_name, start, end, machine])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 1200x800 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "\n",
    "def visualize(data):\n",
    "    df = pd.DataFrame(data, columns=['id', 'task_name', 'start', 'end', 'machine'])\n",
    "    TASKS = sorted(list(df[\"task_name\"].unique()))\n",
    "    MACHINES = sorted(list(df[\"machine\"].unique()))\n",
    "    makespan = df[\"end\"].max()\n",
    "    df.sort_values(by=['task_name','start'])\n",
    "    df.set_index(['task_name','machine'], inplace=True)\n",
    "\n",
    "\n",
    "    bar_style = {\"alpha\": 1.0, \"lw\": 25, \"solid_capstyle\": \"butt\"}\n",
    "    text_style = {\"color\": \"white\", \"weight\": \"bold\", \"ha\": \"center\", \"va\": \"center\"}\n",
    "    colors = mpl.cm.Dark2.colors\n",
    "\n",
    "    fig, ax = plt.subplots(2, 1, figsize=(12, 5 + (len(TASKS ) + len(MACHINES)) / 4))\n",
    "    for jdx, j in enumerate(TASKS, 1):\n",
    "        for mdx, m in enumerate(MACHINES, 1):\n",
    "            if (j, m) in df.index:\n",
    "                xs = df.loc[(j, m), \"start\"]\n",
    "                xf = df.loc[(j, m), \"end\"]\n",
    "                ax[0].plot([xs, xf], [jdx] * 2, c=colors[mdx % 7], **bar_style)\n",
    "                ax[0].text((xs + xf) / 2, jdx, m, **text_style)\n",
    "                ax[1].plot([xs, xf], [mdx] * 2, c=colors[jdx % 7], **bar_style)\n",
    "                ax[1].text((xs + xf) / 2, mdx, j, **text_style)\n",
    "    ax[0].set_title(\"Job Schedule\")\n",
    "    ax[0].set_ylabel(\"Job\")\n",
    "    ax[1].set_title(\"Machine Schedule\")\n",
    "    ax[1].set_ylabel(\"Machine\")\n",
    "\n",
    "    for idx, s in enumerate([TASKS, MACHINES]):\n",
    "        ax[idx].set_ylim(0.5, len(s) + 0.5)\n",
    "        ax[idx].set_yticks(range(1, 1 + len(s)))\n",
    "        ax[idx].set_yticklabels(s)\n",
    "        ax[idx].text(\n",
    "            makespan,\n",
    "            ax[idx].get_ylim()[0] - 0.2,\n",
    "            \"{0:0.1f}\".format(makespan),\n",
    "            ha=\"center\",\n",
    "            va=\"top\",\n",
    "        )\n",
    "        ax[idx].plot([makespan] * 2, ax[idx].get_ylim(), \"r--\")\n",
    "        ax[idx].set_xlabel(\"Time\")\n",
    "        ax[idx].grid(True)\n",
    "\n",
    "    fig.tight_layout()\n",
    "visualize(data)"
   ]
  }
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