{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "0f977a05-2365-410a-8d90-202374c2c5aa",
   "metadata": {},
   "source": [
    "```{index} disjunctive programming\n",
    "```\n",
    "```{index} single: application; scheduling\n",
    "```\n",
    "```{index} single: solver; HiGHS\n",
    "```\n",
    "```{index} single: Gantt charts\n",
    "```\n",
    "```{index} pandas dataframe\n",
    "```\n",
    "# 3.5 Machine Scheduling"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f3a9ec0b-dfc4-4576-83a5-1c7b289793df",
   "metadata": {},
   "source": [
    "## Preamble: Install Pyomo and a solver\n",
    "\n",
    "The following cell sets and verifies a global SOLVER for the notebook. If run on Google Colab, the cell installs Pyomo and the HiGHS solver, while, if run elsewhere, it assumes Pyomo and HiGHS have been previously installed. It then sets to use HiGHS as solver via the appsi module and a test is performed to verify that it is available. The solver interface is stored in a global object `SOLVER` for later use."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "351ce959-4e44-433d-ba31-a82521888c96",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "5ssUqKOaPVaE",
    "outputId": "38c1005a-39f4-4307-e305-19a4c9819396"
   },
   "outputs": [],
   "source": [
    "import sys\n",
    "\n",
    "if \"google.colab\" in sys.modules:\n",
    "    %pip install pyomo >/dev/null 2>/dev/null\n",
    "    %pip install highspy >/dev/null 2>/dev/null\n",
    "\n",
    "solver = \"appsi_highs\"\n",
    "\n",
    "import pyomo.environ as pyo\n",
    "\n",
    "SOLVER = pyo.SolverFactory(solver)\n",
    "\n",
    "assert SOLVER.available(), f\"Solver {solver} is not available.\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.lines import Line2D"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "47dbbe18-205b-430b-895e-ee51b15cf3ca",
   "metadata": {},
   "source": [
    "## Problem description\n",
    "\n",
    "\"Which job should be done next?\" is a question one face in modern life, whether for a busy student working on course assignments, a courier delivering packages, a server waiting on tables in a busy restaurant, a computer processing threads, or a machine on a complex assembly line. There are well-known empirical rules or heuristics to address to this question, among which \"first in, first out\", \"last in, first out\", or \"shortest job first\".  \n",
    "\n",
    "What we consider in this notebook is the modeling finding solutions to this class of problem using optimization techniques. This notebook demonstrates the formulation of a model for scheduling a single machine scheduling using disjunctive programming in Pyomo. Data for the example problem is from Chapter 5 of the book by Christelle Guéret, Christian Prins, Marc Sevaux titled [Applications of Optimization with Xpress-MP](https://www2.isye.gatech.edu/~sahmed/isye3133b/XpressBook.pdf) (Dash Optimization, 2000).\n",
    "\n",
    "Consider the problem of scheduling a set of jobs on a single machine given the release time, duration, and due time for each job. Our goal is to find a sequence of the jobs on the machine that meets the due dates. If no such schedule exists, then the objective is to find the least bad schedule that minimizes a designated performance metric. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "95641d22-b943-47a5-8e3a-303861877ebe",
   "metadata": {},
   "source": [
    "### Job data\n",
    "\n",
    "The data is given as a Pandas dataframe in which each row corresponds to a job, its release time, duration, and due date. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "825592dd-46e3-42b6-8c86-21071066617a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>release</th>\n",
       "      <th>duration</th>\n",
       "      <th>due</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C</th>\n",
       "      <td>4</td>\n",
       "      <td>8</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>D</th>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>E</th>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>F</th>\n",
       "      <td>8</td>\n",
       "      <td>3</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>G</th>\n",
       "      <td>9</td>\n",
       "      <td>2</td>\n",
       "      <td>22</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   release  duration  due\n",
       "A        2         5   10\n",
       "B        5         6   21\n",
       "C        4         8   15\n",
       "D        0         4   10\n",
       "E        0         2    5\n",
       "F        8         3   15\n",
       "G        9         2   22"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "jobs = pd.DataFrame(\n",
    "    {\n",
    "        \"A\": {\"release\": 2, \"duration\": 5, \"due\": 10},\n",
    "        \"B\": {\"release\": 5, \"duration\": 6, \"due\": 21},\n",
    "        \"C\": {\"release\": 4, \"duration\": 8, \"due\": 15},\n",
    "        \"D\": {\"release\": 0, \"duration\": 4, \"due\": 10},\n",
    "        \"E\": {\"release\": 0, \"duration\": 2, \"due\": 5},\n",
    "        \"F\": {\"release\": 8, \"duration\": 3, \"due\": 15},\n",
    "        \"G\": {\"release\": 9, \"duration\": 2, \"due\": 22},\n",
    "    }\n",
    ").T\n",
    "display(jobs)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7210c42-747f-4c4d-8649-923b543dcf17",
   "metadata": {},
   "source": [
    "### Schedule data\n",
    "\n",
    "A schedule is also represented here by a Pandas dataframe indexed by job names. The columns indicate the start, finish, and the amount by each job is past due. The following function creates the schedule corresponding to the scenario in which jobs are executed in the order given by the `jobs` dataframe."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "bb753289-ac47-4ee4-9a8f-7f72e6e362da",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>start</th>\n",
       "      <th>finish</th>\n",
       "      <th>past</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>2.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>7.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C</th>\n",
       "      <td>13.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>6.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>D</th>\n",
       "      <td>21.0</td>\n",
       "      <td>25.0</td>\n",
       "      <td>15.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>E</th>\n",
       "      <td>25.0</td>\n",
       "      <td>27.0</td>\n",
       "      <td>22.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>F</th>\n",
       "      <td>27.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>15.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>G</th>\n",
       "      <td>30.0</td>\n",
       "      <td>32.0</td>\n",
       "      <td>10.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   start  finish  past\n",
       "A    2.0     7.0   0.0\n",
       "B    7.0    13.0   0.0\n",
       "C   13.0    21.0   6.0\n",
       "D   21.0    25.0  15.0\n",
       "E   25.0    27.0  22.0\n",
       "F   27.0    30.0  15.0\n",
       "G   30.0    32.0  10.0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def schedule_jobs(jobs, seq):\n",
    "    schedule = pd.DataFrame(index=jobs.index)\n",
    "    t = 0\n",
    "    for job in seq:\n",
    "        t = max(t, jobs.loc[job][\"release\"])\n",
    "        schedule.loc[job, \"start\"] = t\n",
    "        t += jobs.loc[job, \"duration\"]\n",
    "        schedule.loc[job, \"finish\"] = t\n",
    "        schedule.loc[job, \"past\"] = max(0, t - jobs.loc[job, \"due\"])\n",
    "\n",
    "    return schedule\n",
    "\n",
    "\n",
    "schedule = schedule_jobs(jobs, jobs.index)\n",
    "schedule"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e927f02f-a044-41f2-acb0-0f97b44714ab",
   "metadata": {},
   "source": [
    "### Gantt chart\n",
    "\n",
    "A classical way of visualizing scheduling data in the form of a Gantt chart. The next cell defines a function `gantt` that plots a Gantt chart given jobs and schedule information. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ca36897b-9f2c-4973-bc61-f192e5a54f36",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using the \"job order\" strategy, the total past due is 68.0\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 1300x490 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def gantt(jobs, schedule, title=\"\"):\n",
    "    w = 0.25  # bar width\n",
    "\n",
    "    plt.rcParams.update({\"font.size\": 13})\n",
    "    fig, ax = plt.subplots(1, 1, figsize=(13, 0.7 * len(jobs.index)))\n",
    "\n",
    "    for k, job in enumerate(jobs.index):\n",
    "        r = jobs.loc[job, \"release\"]\n",
    "        d = jobs.loc[job, \"due\"]\n",
    "        s = schedule.loc[job, \"start\"]\n",
    "        f = schedule.loc[job, \"finish\"]\n",
    "\n",
    "        # Show job release-due window\n",
    "        ax.fill_between(\n",
    "            [r, d], [-k - w, -k - w], [-k + w, -k + w], lw=1, color=\"k\", alpha=0.2\n",
    "        )\n",
    "        ax.plot(\n",
    "            [r, r, d, d, r], [-k - w, -k + w, -k + w, -k - w, -k - w], lw=0.5, color=\"k\"\n",
    "        )\n",
    "\n",
    "        # Show job start-finish window\n",
    "        color = \"g\" if f <= d else \"r\"\n",
    "        ax.fill_between(\n",
    "            [s, f], [-k - w, -k - w], [-k + w, -k + w], color=color, alpha=0.6\n",
    "        )\n",
    "        ax.text(\n",
    "            (s + f) / 2.0,\n",
    "            -k,\n",
    "            \"Job \" + job,\n",
    "            color=\"white\",\n",
    "            weight=\"bold\",\n",
    "            ha=\"center\",\n",
    "            va=\"center\",\n",
    "        )\n",
    "\n",
    "        # If past due\n",
    "        if f > d:\n",
    "            ax.plot([d] * 2, [-k + w, -k + 2 * w], lw=0.5, color=\"k\")\n",
    "            ax.plot([f] * 2, [-k + w, -k + 2 * w], lw=0.5, color=\"k\")\n",
    "            ax.plot([d, f], [-k + 1.5 * w] * 2, solid_capstyle=\"butt\", lw=1, color=\"k\")\n",
    "            ax.text(\n",
    "                f + 0.5,\n",
    "                -k + 1.5 * w,\n",
    "                f\"{schedule.loc[job, 'past']} past due\",\n",
    "                va=\"center\",\n",
    "            )\n",
    "\n",
    "    total_past_due = schedule[\"past\"].sum()\n",
    "    ax.set_ylim(-len(jobs.index), 1)\n",
    "    print(f'Using the \"{title}\" strategy, the total past due is {total_past_due}')\n",
    "    ax.set_xlabel(\"Time\")\n",
    "    ax.set_ylabel(\"Jobs\")\n",
    "    ax.set_yticks([])\n",
    "    ax.spines[\"right\"].set_visible(False)\n",
    "    ax.spines[\"left\"].set_visible(False)\n",
    "    ax.spines[\"top\"].set_visible(False)\n",
    "\n",
    "    custom_lines = [\n",
    "        Line2D([0], [0], c=\"k\", lw=10, alpha=0.2),\n",
    "        Line2D([0], [0], c=\"g\", lw=10, alpha=0.6),\n",
    "        Line2D([0], [0], c=\"r\", lw=10, alpha=0.6),\n",
    "    ]\n",
    "    ax.legend(\n",
    "        custom_lines,\n",
    "        [\"Job release/due window\", \"Completed on time\", \"Completed past due\"],\n",
    "        bbox_to_anchor=(1.05, 1),\n",
    "        loc=\"upper left\",\n",
    "    )\n",
    "\n",
    "    plt.tight_layout()\n",
    "    plt.show()\n",
    "\n",
    "\n",
    "gantt(jobs, schedule, \"job order\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c92b7e68-bb11-429a-a8f0-996187b4ea60",
   "metadata": {},
   "source": [
    "## Empirical Scheduling Rules\n",
    "\n",
    "To provide a comparison to scheduling using a MILO model, we first implement three well-known and accepted empirical rules for scheduling jobs on a single machine:\n",
    "\n",
    "* First in, first out (FIFO)\n",
    "* Earliest due data (EDD)\n",
    "* Shortest processing time (SPT)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10d6d0a5-50bc-4cdc-88e7-2c1fb5c9a149",
   "metadata": {},
   "source": [
    "### First-in, first-out (FIFO)\n",
    "\n",
    "One of the most common scheduling rules is to execute jobs in the order they are released for processing, in other words \"first-in, first-out\" (FIFO). The following cell creates a Pandas dataframe  is indexed by job names. The start time, finish time, and, if past due, the amount by which the job is past due.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "57cd67ca-c1cf-458c-8fa0-55a17a57a61a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using the \"First in, First out\" strategy, the total past due is 31.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1300x490 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fifo = schedule_jobs(jobs, jobs.sort_values(by=\"release\").index)\n",
    "gantt(jobs, fifo, \"First in, First out\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "440e9aa9-54af-4694-b830-0d0cef91c9a1",
   "metadata": {},
   "source": [
    "### Earliest due date (EDD)\n",
    "\n",
    "When due dates are known, a common scheduling rule is to prioritize jobs by due date. This strategy will be familiar to any student deciding which homework assignment should to work on next."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a8181151-0d96-4479-8a53-fa8bcbc5bd17",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using the \"Earliest due date\" strategy, the total past due is 27.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1300x490 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "edd = schedule_jobs(jobs, jobs.sort_values(by=\"due\").index)\n",
    "gantt(jobs, edd, \"Earliest due date\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c0b81bd",
   "metadata": {},
   "source": [
    "### Shortest processing time (SPT)\n",
    "\n",
    "When the job durations are known, another common scheduling rule is to prioritize jobs by their (remaining) processing time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "561a2188",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using the \"Shortest Processing Time\" strategy, the total past due is 51.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1300x490 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "spt = schedule_jobs(jobs, jobs.sort_values(by=\"duration\").index)\n",
    "gantt(jobs, spt, \"Shortest Processing Time\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "372cbc7d-bf20-4171-a602-eef2f727dbdd",
   "metadata": {},
   "source": [
    "## Optimal scheduling using disjunctive programming\n",
    "\n",
    "The modeling starts by defining the problem data.\n",
    "\n",
    "<div align=\"center\">\n",
    "\n",
    "| Symbol | Description \n",
    "|:---- | :--- \n",
    "| $\\text{release}_j$ | when job $j$ is available\n",
    "| $\\text{duration}_j$ | how long job $j$ takes\n",
    "| $\\text{due}_j$ | when job $j$ is due \n",
    "\n",
    "</div>\n",
    "\n",
    "The essential decision variables are the times at which each job starts processing, but it is convenient to add auxiliary variables defining the times at which each job finishes and the amount by which each job is past due.\n",
    "\n",
    "<div align=\"center\">\n",
    "\n",
    "| Symbol | Description\n",
    "|:---- | :--- \n",
    "| $\\text{start}_j$ | when job $j$ starts\n",
    "| $\\text{finish}_j$ | when job $j$ finishes\n",
    "| $\\text{past}_j$ | how long job $j$ is past due\n",
    "\n",
    "</div>\n",
    "\n",
    "Depending on application and circumstances, various objectives can be considered. Suitable objectives include the total number of late jobs, the longest past due interval, or the sum of all past due intervals. We consider an optimization problem that minimizes the sum of past due intervals, that is\n",
    "\n",
    "$$\n",
    "\\min \\sum_j \\text{past}_j\n",
    "$$\n",
    "\n",
    "Constraints describe the required logical relationships among the decision variables. For example, a job cannot start until it is released for processing\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\text{start}_{j} & \\geq \\text{release}_{j}\\\\\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "Once started, machine processing continues until the job is finished. The finish time for each job is compared to the due time, and any past due interval is stored the $\\text{past}_j$ decision variable. \n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\text{finish}_j & = \\text{start}_j + \\text{duration}_j \\\\\n",
    "\\text{past}_{j} & \\geq \\text{finish}_j - \\text{due}_{j} \\\\\n",
    "\\text{past}_{j} & \\geq 0\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "The final set of constraints require that no pair of jobs be operating on the same machine at the same time. For this purpose, we consider each unique pair ($i$, $j$) where the constraint $i < j$ to imposed to avoid considering the same pair twice. Then for any unique pair $i$ and $j$,  either $i$ finishes before $j$ starts, or $j$ finishes before $i$ starts. This is expressed as the family of disjunctions \n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\begin{bmatrix}\n",
    "\\text{finish}_i \\leq \\text{start}_j\n",
    "\\end{bmatrix}\n",
    "& \\veebar\n",
    "\\begin{bmatrix}\n",
    "\\text{finish}_j \\leq \\text{start}_i\n",
    "\\end{bmatrix}\n",
    "& \\forall i < j\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "This model and constraints can be directly translated to Pyomo using the Disjuction component as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ef23f8cc-e5ef-406b-af8b-ddbdbac8b2f9",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>start</th>\n",
       "      <th>finish</th>\n",
       "      <th>past</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>2.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>14.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C</th>\n",
       "      <td>22.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>15.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>D</th>\n",
       "      <td>7.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>E</th>\n",
       "      <td>0.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>F</th>\n",
       "      <td>11.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>G</th>\n",
       "      <td>20.0</td>\n",
       "      <td>22.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   start  finish  past\n",
       "A    2.0     7.0   0.0\n",
       "B   14.0    20.0   0.0\n",
       "C   22.0    30.0  15.0\n",
       "D    7.0    11.0   1.0\n",
       "E    0.0     2.0   0.0\n",
       "F   11.0    14.0   0.0\n",
       "G   20.0    22.0   0.0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using the \"Minimize total past due\" strategy, the total past due is 16.0\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 1300x490 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def machine_schedule(jobs):\n",
    "    m = pyo.ConcreteModel(\"Job machine scheduling\")\n",
    "\n",
    "    # Create a set of jobs using the dataframe index and a\n",
    "    # set of orderd pairs of distinct jobs (i,j) with i < j\n",
    "    m.JOBS = pyo.Set(initialize=jobs.index)\n",
    "    m.PAIRS = pyo.Set(initialize=m.JOBS * m.JOBS, filter=lambda m, i, j: i < j)\n",
    "\n",
    "    # We set an upper bound on the time horizon to 100\n",
    "    m.maxtime = pyo.Param(initialize=100)\n",
    "    m.start = pyo.Var(m.JOBS, domain=pyo.NonNegativeReals, bounds=(0, m.maxtime))\n",
    "    m.finish = pyo.Var(m.JOBS, domain=pyo.NonNegativeReals, bounds=(0, m.maxtime))\n",
    "    m.past = pyo.Var(m.JOBS, domain=pyo.NonNegativeReals, bounds=(0, m.maxtime))\n",
    "\n",
    "    @m.Constraint(m.JOBS)\n",
    "    def job_release(m, job):\n",
    "        return m.start[job] >= jobs.loc[job, \"release\"]\n",
    "\n",
    "    @m.Constraint(m.JOBS)\n",
    "    def job_duration(m, job):\n",
    "        return m.finish[job] == m.start[job] + jobs.loc[job, \"duration\"]\n",
    "\n",
    "    @m.Constraint(m.JOBS)\n",
    "    def past_due_constraint(m, job):\n",
    "        return m.past[job] >= m.finish[job] - jobs.loc[job, \"due\"]\n",
    "\n",
    "    @m.Disjunction(m.PAIRS, xor=True)\n",
    "    def machine_deconflict(m, job_a, job_b):\n",
    "        return [m.finish[job_a] <= m.start[job_b], m.finish[job_b] <= m.start[job_a]]\n",
    "\n",
    "    @m.Objective(sense=pyo.minimize)\n",
    "    def minimize_past(m):\n",
    "        return sum(m.past[job] for job in m.JOBS)\n",
    "\n",
    "    return m\n",
    "\n",
    "\n",
    "m = machine_schedule(jobs)\n",
    "pyo.TransformationFactory(\"gdp.bigm\").apply_to(m)\n",
    "SOLVER.solve(m)\n",
    "\n",
    "optimalschedule = pd.DataFrame(\n",
    "    {\n",
    "        \"start\": m.start.extract_values(),\n",
    "        \"finish\": m.finish.extract_values(),\n",
    "        \"past\": m.past.extract_values(),\n",
    "    }\n",
    ")\n",
    "\n",
    "display(optimalschedule)\n",
    "gantt(jobs, optimalschedule, \"Minimize total past due\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fdadb6fe",
   "metadata": {},
   "source": [
    "The solution obtained solving the optimization problem outperforms that derived from any of the rules outline above. Nonetheless, heuristic techniques become essential when tackling large scheduling problems.\n",
    "\n",
    "For comparison, we also implement a standard MILO using the big-M method. The idea is to introduce a binary variable $z_{ij} \\in \\{0,1\\}$ for each disjunctive constraint above.\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\text{finish}_i & \\leq  \\text{start}_j + M z_{ij} \\\\\n",
    "\\text{finish}_j & \\leq  \\text{start}_i + M (1 - z_{ij}).\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "This creates an equivalent MILO model which leads to the same solution, but it features many more variables and is usually slower to solve."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "a70842a9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>start</th>\n",
       "      <th>finish</th>\n",
       "      <th>past</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>6.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>14.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C</th>\n",
       "      <td>22.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>15.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>D</th>\n",
       "      <td>2.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>E</th>\n",
       "      <td>0.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>F</th>\n",
       "      <td>11.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>G</th>\n",
       "      <td>20.0</td>\n",
       "      <td>22.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   start  finish  past\n",
       "A    6.0    11.0   1.0\n",
       "B   14.0    20.0   0.0\n",
       "C   22.0    30.0  15.0\n",
       "D    2.0     6.0   0.0\n",
       "E    0.0     2.0   0.0\n",
       "F   11.0    14.0   0.0\n",
       "G   20.0    22.0   0.0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using the \"Minimize total past due\" strategy, the total past due is 16.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1300x490 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def machine_scheduleMILO(jobs):\n",
    "    m = pyo.ConcreteModel(\"Job machine scheduling using MILO formulation\")\n",
    "\n",
    "    m.JOBS = pyo.Set(initialize=jobs.index)\n",
    "    m.PAIRS = pyo.Set(initialize=m.JOBS * m.JOBS, filter=lambda m, i, j: i < j)\n",
    "\n",
    "    m.maxtime = pyo.Param(initialize=100)\n",
    "    m.start = pyo.Var(m.JOBS, domain=pyo.NonNegativeReals, bounds=(0, m.maxtime))\n",
    "    m.finish = pyo.Var(m.JOBS, domain=pyo.NonNegativeReals, bounds=(0, m.maxtime))\n",
    "    m.past = pyo.Var(m.JOBS, domain=pyo.NonNegativeReals, bounds=(0, m.maxtime))\n",
    "\n",
    "    # Auxiliary binary variables to linearize the disjunction using the big-M approach\n",
    "    m.z = pyo.Var(m.PAIRS, domain=pyo.Binary)\n",
    "    m.bigM = pyo.Param(initialize=10000)\n",
    "\n",
    "    @m.Constraint(m.JOBS)\n",
    "    def job_release(m, job):\n",
    "        return m.start[job] >= jobs.loc[job, \"release\"]\n",
    "\n",
    "    @m.Constraint(m.JOBS)\n",
    "    def job_duration(m, job):\n",
    "        return m.finish[job] == m.start[job] + jobs.loc[job, \"duration\"]\n",
    "\n",
    "    @m.Constraint(m.JOBS)\n",
    "    def past_due_constraint(m, job):\n",
    "        return m.past[job] >= m.finish[job] - jobs.loc[job, \"due\"]\n",
    "\n",
    "    @m.Constraint(m.PAIRS)\n",
    "    def machine_deconflict_a(m, job_a, job_b):\n",
    "        return m.finish[job_a] <= m.start[job_b] + m.bigM * (1 - m.z[job_a, job_b])\n",
    "\n",
    "    @m.Constraint(m.PAIRS)\n",
    "    def machine_deconflict_b(m, job_a, job_b):\n",
    "        return m.finish[job_b] <= m.start[job_a] + m.bigM * m.z[job_a, job_b]\n",
    "\n",
    "    @m.Objective(sense=pyo.minimize)\n",
    "    def minimize_past(m):\n",
    "        return sum(m.past[job] for job in m.JOBS)\n",
    "\n",
    "    SOLVER.solve(m)\n",
    "\n",
    "    return m\n",
    "\n",
    "\n",
    "m = machine_scheduleMILO(jobs)\n",
    "\n",
    "optimalschedule_MILO = pd.DataFrame(\n",
    "    {\n",
    "        \"start\": m.start.extract_values(),\n",
    "        \"finish\": m.finish.extract_values(),\n",
    "        \"past\": m.past.extract_values(),\n",
    "    }\n",
    ")\n",
    "\n",
    "display(optimalschedule_MILO)\n",
    "gantt(jobs, optimalschedule_MILO, \"Minimize total past due\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}