Group_Assign1/Linear_ProgramGanttCPM.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Checking AWS Enviornment\n",
    "Note: I had to spool an ubuntu instance because pulp wasnt working locally"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Instance Type: <HTML>\n",
      "  <HEAD>\n",
      "     Access Denied\n",
      "  </HEAD>\n",
      "<BODY>\n",
      "\n",
      "<h1>Access Denied</h1>\n",
      "\n",
      "<p>\n",
      "Access to arbitrary websites is not available from free accounts;\n",
      "you can only access sites that are on our\n",
      "<a href=\"http://www.pythonanywhere.com/whitelist\">whitelist</a>.\n",
      "If you want to suggest something to add to our whitelist\n",
      "drop us a line at nbusercare@pythonanywhere.com.  It will have\n",
      "to have an official public API.\n",
      "</p>\n",
      "\n",
      "\n",
      "<p>\n",
      "Alternatively, you can sign up for a paid account at\n",
      "<a href=\"http://www.pythonanywhere.com/account/\">http://www.pythonanywhere.com/account/</a>\n",
      "</p>\n",
      "<p>\n",
      "If you have already got a paid account and you're still getting this messge,\n",
      "you may need to reload your web app (from the \"Web\" tab) or restart\n",
      "your consoles.  If that doesn't help, drop us a line at nbusercare@pythonanywhere.com.\n",
      "</p>\n",
      "\n",
      "</BODY>\n",
      "\n",
      "RAM: 31641 MiB\n",
      "Processor Info: Intel(R) Xeon(R) Platinum 8259CL CPU @ 2.50GHz\n"
     ]
    }
   ],
   "source": [
    "import requests\n",
    "import os\n",
    "import io\n",
    "\n",
    "\n",
    "def get_instance_type():\n",
    "    \"\"\"Get the EC2 instance type.\"\"\"\n",
    "    response = requests.get(\"http://169.254.169.254/latest/meta-data/instance-type\")\n",
    "    return response.text\n",
    "\n",
    "def get_ram_details():\n",
    "    \"\"\"Get RAM details using a system command.\"\"\"\n",
    "    total_mib = os.popen(\"free -m | awk 'NR==2{print $2}'\").read().strip()\n",
    "    return f\"{total_mib} MiB\"\n",
    "\n",
    "def get_processor_info():\n",
    "    \"\"\"Get processor information.\"\"\"\n",
    "    processor_info = os.popen(\"grep 'model name' /proc/cpuinfo | uniq\").read().strip()\n",
    "    return processor_info.split(\":\")[1].strip()\n",
    "\n",
    "instance_type = get_instance_type()\n",
    "ram_details = get_ram_details()\n",
    "processor_info = get_processor_info()\n",
    "\n",
    "print(f\"Instance Type: {instance_type}\")\n",
    "print(f\"RAM: {ram_details}\")\n",
    "print(f\"Processor Info: {processor_info}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Loading Provided Dataset. \n",
    "Note: This is cleaned up data from Lawler_Jensen_ProjectPlan 10_18.xlsx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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>taskID</th>\n",
       "      <th>task</th>\n",
       "      <th>predecessorTaskIDs</th>\n",
       "      <th>bestCaseHours</th>\n",
       "      <th>expectedHours</th>\n",
       "      <th>worstCaseHours</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>A</td>\n",
       "      <td>Describe product</td>\n",
       "      <td></td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>B</td>\n",
       "      <td>Develop marketing strategy</td>\n",
       "      <td></td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>C</td>\n",
       "      <td>Design brochure</td>\n",
       "      <td>A</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>D1</td>\n",
       "      <td>Requirements analysis</td>\n",
       "      <td>A</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>D2</td>\n",
       "      <td>Software design</td>\n",
       "      <td>D1</td>\n",
       "      <td>10</td>\n",
       "      <td>16</td>\n",
       "      <td>24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>D3</td>\n",
       "      <td>System design</td>\n",
       "      <td>D1</td>\n",
       "      <td>10</td>\n",
       "      <td>16</td>\n",
       "      <td>24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>D4</td>\n",
       "      <td>Coding</td>\n",
       "      <td>D2, D3</td>\n",
       "      <td>10</td>\n",
       "      <td>16</td>\n",
       "      <td>24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>D5</td>\n",
       "      <td>Write documentation</td>\n",
       "      <td>D4</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>D6</td>\n",
       "      <td>Unit testing</td>\n",
       "      <td>D4</td>\n",
       "      <td>16</td>\n",
       "      <td>24</td>\n",
       "      <td>32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>D7</td>\n",
       "      <td>System testing</td>\n",
       "      <td>D6</td>\n",
       "      <td>16</td>\n",
       "      <td>24</td>\n",
       "      <td>32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>D8</td>\n",
       "      <td>Package deliverables</td>\n",
       "      <td>D5, D7</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>E</td>\n",
       "      <td>Survey potential market</td>\n",
       "      <td>B, C</td>\n",
       "      <td>6</td>\n",
       "      <td>10</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>F</td>\n",
       "      <td>Develop pricing plan</td>\n",
       "      <td>D8, E</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>G</td>\n",
       "      <td>Develop implementation  plan</td>\n",
       "      <td>A, D8</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>H</td>\n",
       "      <td>Write client proposal</td>\n",
       "      <td>F, G</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   taskID                          task predecessorTaskIDs  bestCaseHours  \\\n",
       "0       A              Describe product                                 1   \n",
       "1       B    Develop marketing strategy                                 1   \n",
       "2       C               Design brochure                  A              2   \n",
       "3      D1         Requirements analysis                  A              2   \n",
       "4      D2               Software design                 D1             10   \n",
       "5      D3                 System design                 D1             10   \n",
       "6      D4                        Coding             D2, D3             10   \n",
       "7      D5           Write documentation                 D4              2   \n",
       "8      D6                  Unit testing                 D4             16   \n",
       "9      D7                System testing                 D6             16   \n",
       "10     D8          Package deliverables             D5, D7              2   \n",
       "11      E       Survey potential market               B, C              6   \n",
       "12      F          Develop pricing plan              D8, E              1   \n",
       "13      G  Develop implementation  plan              A, D8              1   \n",
       "14      H         Write client proposal               F, G              2   \n",
       "\n",
       "    expectedHours  worstCaseHours  \n",
       "0               2               3  \n",
       "1               2               4  \n",
       "2               4               6  \n",
       "3               4               8  \n",
       "4              16              24  \n",
       "5              16              24  \n",
       "6              16              24  \n",
       "7               4               8  \n",
       "8              24              32  \n",
       "9              24              32  \n",
       "10              4               6  \n",
       "11             10              16  \n",
       "12              2               4  \n",
       "13              2               4  \n",
       "14              4               8  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import pulp\n",
    "\n",
    "df = pd.read_excel(\"data.xlsx\")\n",
    "df['predecessorTaskIDs'].fillna(\"\", inplace=True)\n",
    "df = df[['taskID', 'task', 'predecessorTaskIDs', 'bestCaseHours', 'expectedHours', 'worstCaseHours']]\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Defining Linear Programming Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def solve_project_plan(df, case=\"expected\"):\n",
    "    # LP Model\n",
    "    lp_problem = pulp.LpProblem(\"Project_Planning\", pulp.LpMinimize)\n",
    "    \n",
    "    # Decision vars\n",
    "    start_times = pulp.LpVariable.dicts(\"start_time\", df[\"taskID\"], 0, None)\n",
    "    \n",
    "    # Objective function\n",
    "    project_end = pulp.LpVariable(\"project_end\", 0, None)\n",
    "    lp_problem += project_end, \"Minimize_Project_Duration\"\n",
    "    \n",
    "    # adding constraints\n",
    "    for index, row in df.iterrows():\n",
    "        task = row[\"taskID\"]\n",
    "        \n",
    "        # duration of cases\n",
    "        if case == \"best\":\n",
    "            duration = row[\"bestCaseHours\"]\n",
    "        elif case == \"worst\":\n",
    "            duration = row[\"worstCaseHours\"]\n",
    "        else:\n",
    "            duration = row[\"expectedHours\"]\n",
    "        \n",
    "        predecessors = [pred.strip() for pred in row[\"predecessorTaskIDs\"].split(\",\") if pred.strip()]\n",
    "        \n",
    "        # task duration constraint\n",
    "        lp_problem += start_times[task] + duration <= project_end\n",
    "        \n",
    "        # task dependencies constraints\n",
    "        for predecessor in predecessors:\n",
    "            lp_problem += start_times[task] >= start_times[predecessor] + duration\n",
    "\n",
    "    # Solver\n",
    "    lp_problem.solve()\n",
    "    \n",
    "    # output prep\n",
    "    results = {\n",
    "        \"status\": pulp.LpStatus[lp_problem.status],\n",
    "        \"optimal_duration\": project_end.varValue,\n",
    "        \"task_start_times\": {task: var.varValue for task, var in start_times.items()}\n",
    "    }\n",
    "    \n",
    "    return results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Running Linear Solver and Saving Results\n",
    "Note: The output below is saved to results_lp_output.txt <br>\n",
    "Note: The output dataframe is saved to results_lp.csv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Welcome to the CBC MILP Solver \n",
      "Version: 2.10.3 \n",
      "Build Date: Dec 15 2019 \n",
      "\n",
      "command line - /home/daf03834-2cd7-40ad-bc31-d3b51e4b5c9f/.local/lib/python3.9/site-packages/pulp/solverdir/cbc/linux/64/cbc /tmp/cbb0021adb204c3aac53571aab3f47a6-pulp.mps timeMode elapsed branch printingOptions all solution /tmp/cbb0021adb204c3aac53571aab3f47a6-pulp.sol (default strategy 1)\n",
      "At line 2 NAME          MODEL\n",
      "At line 3 ROWS\n",
      "At line 39 COLUMNS\n",
      "At line 109 RHS\n",
      "At line 144 BOUNDS\n",
      "At line 145 ENDATA\n",
      "Problem MODEL has 34 rows, 16 columns and 68 elements\n",
      "Coin0008I MODEL read with 0 errors\n",
      "Option for timeMode changed from cpu to elapsed\n",
      "Presolve 0 (-34) rows, 0 (-16) columns and 0 (-68) elements\n",
      "Empty problem - 0 rows, 0 columns and 0 elements\n",
      "Optimal - objective value 70\n",
      "After Postsolve, objective 70, infeasibilities - dual 0 (0), primal 0 (0)\n",
      "Optimal objective 70 - 0 iterations time 0.002, Presolve 0.00\n",
      "Option for printingOptions changed from normal to all\n",
      "Total time (CPU seconds):       0.00   (Wallclock seconds):       0.03\n",
      "\n",
      "Welcome to the CBC MILP Solver \n",
      "Version: 2.10.3 \n",
      "Build Date: Dec 15 2019 \n",
      "\n",
      "command line - /home/daf03834-2cd7-40ad-bc31-d3b51e4b5c9f/.local/lib/python3.9/site-packages/pulp/solverdir/cbc/linux/64/cbc /tmp/0790a6b773c04c9bb07e6ccef8334bb8-pulp.mps timeMode elapsed branch printingOptions all solution /tmp/0790a6b773c04c9bb07e6ccef8334bb8-pulp.sol (default strategy 1)\n",
      "At line 2 NAME          MODEL\n",
      "At line 3 ROWS\n",
      "At line 39 COLUMNS\n",
      "At line 109 RHS\n",
      "At line 144 BOUNDS\n",
      "At line 145 ENDATA\n",
      "Problem MODEL has 34 rows, 16 columns and 68 elements\n",
      "Coin0008I MODEL read with 0 errors\n",
      "Option for timeMode changed from cpu to elapsed\n",
      "Presolve 0 (-34) rows, 0 (-16) columns and 0 (-68) elements\n",
      "Empty problem - 0 rows, 0 columns and 0 elements\n",
      "Optimal - objective value 108\n",
      "After Postsolve, objective 108, infeasibilities - dual 0 (0), primal 0 (0)\n",
      "Optimal objective 108 - 0 iterations time 0.002, Presolve 0.00\n",
      "Option for printingOptions changed from normal to all\n",
      "Total time (CPU seconds):       0.00   (Wallclock seconds):       0.01\n",
      "\n",
      "Welcome to the CBC MILP Solver \n",
      "Version: 2.10.3 \n",
      "Build Date: Dec 15 2019 \n",
      "\n",
      "command line - /home/daf03834-2cd7-40ad-bc31-d3b51e4b5c9f/.local/lib/python3.9/site-packages/pulp/solverdir/cbc/linux/64/cbc /tmp/6eccf95c690042e5a46a444355b4444e-pulp.mps timeMode elapsed branch printingOptions all solution /tmp/6eccf95c690042e5a46a444355b4444e-pulp.sol (default strategy 1)\n",
      "At line 2 NAME          MODEL\n",
      "At line 3 ROWS\n",
      "At line 39 COLUMNS\n",
      "At line 109 RHS\n",
      "At line 144 BOUNDS\n",
      "At line 145 ENDATA\n",
      "Problem MODEL has 34 rows, 16 columns and 68 elements\n",
      "Coin0008I MODEL read with 0 errors\n",
      "Option for timeMode changed from cpu to elapsed\n",
      "Presolve 0 (-34) rows, 0 (-16) columns and 0 (-68) elements\n",
      "Empty problem - 0 rows, 0 columns and 0 elements\n",
      "Optimal - objective value 152\n",
      "After Postsolve, objective 152, infeasibilities - dual 0 (0), primal 0 (0)\n",
      "Optimal objective 152 - 0 iterations time 0.002, Presolve 0.00\n",
      "Option for printingOptions changed from normal to all\n",
      "Total time (CPU seconds):       0.00   (Wallclock seconds):       0.01\n",
      "\n"
     ]
    }
   ],
   "source": [
    "simple_results_df = pd.DataFrame(columns=[\"Case\", \"Optimal_Duration\", *df[\"taskID\"].tolist()])\n",
    "output_buffer = io.StringIO()\n",
    "\n",
    "cases = [\"best\", \"expected\", \"worst\"]\n",
    "for case in cases:\n",
    "    result = solve_project_plan(df, case)\n",
    "    \n",
    "    print_str = f\"Results for {case} case:\\n\"\n",
    "    print_str += f\"Optimal project duration: {result['optimal_duration']} hours\\n\"\n",
    "    print_str += \"Start times for tasks:\\n\"\n",
    "    for task, start_time in result[\"task_start_times\"].items():\n",
    "        print_str += f\"Task {task}: {start_time} hours\\n\"\n",
    "    print_str += \"\\n\"\n",
    "    \n",
    "    row_data = [case, result[\"optimal_duration\"]] + list(result[\"task_start_times\"].values())\n",
    "    simple_results_df.loc[len(simple_results_df)] = row_data\n",
    "    \n",
    "    output_buffer.write(print_str)\n",
    "\n",
    "with open(\"results_lp_output.txt\", \"w\") as f:\n",
    "    f.write(output_buffer.getvalue())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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>Case</th>\n",
       "      <th>Optimal_Duration</th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "      <th>C</th>\n",
       "      <th>D1</th>\n",
       "      <th>D2</th>\n",
       "      <th>D3</th>\n",
       "      <th>D4</th>\n",
       "      <th>D5</th>\n",
       "      <th>D6</th>\n",
       "      <th>D7</th>\n",
       "      <th>D8</th>\n",
       "      <th>E</th>\n",
       "      <th>F</th>\n",
       "      <th>G</th>\n",
       "      <th>H</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>best</td>\n",
       "      <td>70.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>22.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>38.0</td>\n",
       "      <td>54.0</td>\n",
       "      <td>56.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>57.0</td>\n",
       "      <td>57.0</td>\n",
       "      <td>68.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>expected</td>\n",
       "      <td>108.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>36.0</td>\n",
       "      <td>40.0</td>\n",
       "      <td>60.0</td>\n",
       "      <td>84.0</td>\n",
       "      <td>88.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>90.0</td>\n",
       "      <td>90.0</td>\n",
       "      <td>104.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>worst</td>\n",
       "      <td>152.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>32.0</td>\n",
       "      <td>32.0</td>\n",
       "      <td>56.0</td>\n",
       "      <td>64.0</td>\n",
       "      <td>88.0</td>\n",
       "      <td>120.0</td>\n",
       "      <td>126.0</td>\n",
       "      <td>22.0</td>\n",
       "      <td>130.0</td>\n",
       "      <td>130.0</td>\n",
       "      <td>144.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Case  Optimal_Duration    A    B    C   D1    D2    D3    D4    D5  \\\n",
       "0      best              70.0  0.0  0.0  2.0  2.0  12.0  12.0  22.0  24.0   \n",
       "1  expected             108.0  0.0  0.0  4.0  4.0  20.0  20.0  36.0  40.0   \n",
       "2     worst             152.0  0.0  0.0  6.0  8.0  32.0  32.0  56.0  64.0   \n",
       "\n",
       "     D6     D7     D8     E      F      G      H  \n",
       "0  38.0   54.0   56.0   8.0   57.0   57.0   68.0  \n",
       "1  60.0   84.0   88.0  14.0   90.0   90.0  104.0  \n",
       "2  88.0  120.0  126.0  22.0  130.0  130.0  144.0  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simple_results_df.to_csv(\"results_lp.csv\")\n",
    "simple_results_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Critical Path and Gantt Chart for Best Case Solution\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Welcome to the CBC MILP Solver \n",
      "Version: 2.10.3 \n",
      "Build Date: Dec 15 2019 \n",
      "\n",
      "command line - /home/daf03834-2cd7-40ad-bc31-d3b51e4b5c9f/.local/lib/python3.9/site-packages/pulp/solverdir/cbc/linux/64/cbc /tmp/c012c4fe5ce94cd1b762ed5f318cba41-pulp.mps timeMode elapsed branch printingOptions all solution /tmp/c012c4fe5ce94cd1b762ed5f318cba41-pulp.sol (default strategy 1)\n",
      "At line 2 NAME          MODEL\n",
      "At line 3 ROWS\n",
      "At line 39 COLUMNS\n",
      "At line 109 RHS\n",
      "At line 144 BOUNDS\n",
      "At line 145 ENDATA\n",
      "Problem MODEL has 34 rows, 16 columns and 68 elements\n",
      "Coin0008I MODEL read with 0 errors\n",
      "Option for timeMode changed from cpu to elapsed\n",
      "Presolve 0 (-34) rows, 0 (-16) columns and 0 (-68) elements\n",
      "Empty problem - 0 rows, 0 columns and 0 elements\n",
      "Optimal - objective value 70\n",
      "After Postsolve, objective 70, infeasibilities - dual 0 (0), primal 0 (0)\n",
      "Optimal objective 70 - 0 iterations time 0.002, Presolve 0.00\n",
      "Option for printingOptions changed from normal to all\n",
      "Total time (CPU seconds):       0.00   (Wallclock seconds):       0.01\n",
      "\n",
      "Critical Path for best case: ['D7', 'H']\n",
      "Welcome to the CBC MILP Solver \n",
      "Version: 2.10.3 \n",
      "Build Date: Dec 15 2019 \n",
      "\n",
      "command line - /home/daf03834-2cd7-40ad-bc31-d3b51e4b5c9f/.local/lib/python3.9/site-packages/pulp/solverdir/cbc/linux/64/cbc /tmp/6fd08d0535e04cd2a0c96ab0b86265da-pulp.mps timeMode elapsed branch printingOptions all solution /tmp/6fd08d0535e04cd2a0c96ab0b86265da-pulp.sol (default strategy 1)\n",
      "At line 2 NAME          MODEL\n",
      "At line 3 ROWS\n",
      "At line 39 COLUMNS\n",
      "At line 109 RHS\n",
      "At line 144 BOUNDS\n",
      "At line 145 ENDATA\n",
      "Problem MODEL has 34 rows, 16 columns and 68 elements\n",
      "Coin0008I MODEL read with 0 errors\n",
      "Option for timeMode changed from cpu to elapsed\n",
      "Presolve 0 (-34) rows, 0 (-16) columns and 0 (-68) elements\n",
      "Empty problem - 0 rows, 0 columns and 0 elements\n",
      "Optimal - objective value 70\n",
      "After Postsolve, objective 70, infeasibilities - dual 0 (0), primal 0 (0)\n",
      "Optimal objective 70 - 0 iterations time 0.002, Presolve 0.00\n",
      "Option for printingOptions changed from normal to all\n",
      "Total time (CPU seconds):       0.00   (Wallclock seconds):       0.00\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import io\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Define a function to identify the critical path based on start times\n",
    "def identify_critical_path(df, results, case=\"best\"):\n",
    "    optimal_duration = results[\"optimal_duration\"]\n",
    "    task_start_times = results[\"task_start_times\"]\n",
    "    \n",
    "    critical_path = []\n",
    "\n",
    "    for index, row in df.iterrows():\n",
    "        task = row[\"taskID\"]\n",
    "        duration = None\n",
    "\n",
    "        # Determine the duration based on the scenario\n",
    "        if results[\"status\"] == \"Optimal\":\n",
    "            if case == \"best\":\n",
    "                duration = row[\"bestCaseHours\"]\n",
    "            elif case == \"worst\":\n",
    "                duration = row[\"worstCaseHours\"]\n",
    "            else:\n",
    "                duration = row[\"expectedHours\"]\n",
    "\n",
    "        # Calculate the task end time\n",
    "        task_end_time = task_start_times[task] + duration\n",
    "\n",
    "        # If the task ends at the project's optimal duration, it's on the critical path\n",
    "        if task_end_time == optimal_duration:\n",
    "            critical_path.append(task)\n",
    "\n",
    "    return critical_path\n",
    "\n",
    "# Identify and print the critical path for the \"best\" case\n",
    "case = \"best\"\n",
    "result = solve_project_plan(df, case)\n",
    "critical_path = identify_critical_path(df, result, case)\n",
    "\n",
    "print(f\"Critical Path for {case} case: {critical_path}\")\n",
    "case = \"best\"\n",
    "\n",
    "\n",
    "# Define a function to create a Gantt chart\n",
    "def create_gantt_chart(df, results, case=\"best\"):\n",
    "    task_start_times = results[\"task_start_times\"]\n",
    "    task_durations = {}\n",
    "    \n",
    "    for index, row in df.iterrows():\n",
    "        task = row[\"taskID\"]\n",
    "        if case == \"best\":\n",
    "            task_durations[task] = row[\"bestCaseHours\"]\n",
    "        else:\n",
    "            task_durations[task] = row[\"expectedHours\"]\n",
    "\n",
    "    tasks = list(task_start_times.keys())\n",
    "    start_times = [task_start_times[task] for task in tasks]\n",
    "    durations = [task_durations[task] for task in tasks]\n",
    "\n",
    "    fig, ax = plt.subplots(figsize=(10, 4))\n",
    "    \n",
    "    for i, task in enumerate(tasks):\n",
    "        ax.broken_barh([(start_times[i], durations[i])], (i - 0.4, 0.8), facecolors='green')\n",
    "        ax.text(start_times[i] + durations[i] / 2, i, task, ha='center', va='center', color='white')\n",
    "\n",
    "    ax.set_yticks(range(len(tasks)))\n",
    "    ax.set_yticklabels(tasks)\n",
    "    ax.set_xlabel('Time (hours)')\n",
    "    ax.set_title(f'Gantt Chart for {case} Case')\n",
    "\n",
    "    plt.show()\n",
    "\n",
    "result = solve_project_plan(df, case)\n",
    "create_gantt_chart(df, result, case)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "# Critical Path and Gantt Chart for Expected Solution\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Welcome to the CBC MILP Solver \n",
      "Version: 2.10.3 \n",
      "Build Date: Dec 15 2019 \n",
      "\n",
      "command line - /home/daf03834-2cd7-40ad-bc31-d3b51e4b5c9f/.local/lib/python3.9/site-packages/pulp/solverdir/cbc/linux/64/cbc /tmp/62c5f95685b0458e89dabeb0737d866b-pulp.mps timeMode elapsed branch printingOptions all solution /tmp/62c5f95685b0458e89dabeb0737d866b-pulp.sol (default strategy 1)\n",
      "At line 2 NAME          MODEL\n",
      "At line 3 ROWS\n",
      "At line 39 COLUMNS\n",
      "At line 109 RHS\n",
      "At line 144 BOUNDS\n",
      "At line 145 ENDATA\n",
      "Problem MODEL has 34 rows, 16 columns and 68 elements\n",
      "Coin0008I MODEL read with 0 errors\n",
      "Option for timeMode changed from cpu to elapsed\n",
      "Presolve 0 (-34) rows, 0 (-16) columns and 0 (-68) elements\n",
      "Empty problem - 0 rows, 0 columns and 0 elements\n",
      "Optimal - objective value 108\n",
      "After Postsolve, objective 108, infeasibilities - dual 0 (0), primal 0 (0)\n",
      "Optimal objective 108 - 0 iterations time 0.002, Presolve 0.00\n",
      "Option for printingOptions changed from normal to all\n",
      "Total time (CPU seconds):       0.00   (Wallclock seconds):       0.01\n",
      "\n",
      "Critical Path for expected case: []\n",
      "Welcome to the CBC MILP Solver \n",
      "Version: 2.10.3 \n",
      "Build Date: Dec 15 2019 \n",
      "\n",
      "command line - /home/daf03834-2cd7-40ad-bc31-d3b51e4b5c9f/.local/lib/python3.9/site-packages/pulp/solverdir/cbc/linux/64/cbc /tmp/7d8c40c7fabb4bf3beaeccacfaa6ecc6-pulp.mps timeMode elapsed branch printingOptions all solution /tmp/7d8c40c7fabb4bf3beaeccacfaa6ecc6-pulp.sol (default strategy 1)\n",
      "At line 2 NAME          MODEL\n",
      "At line 3 ROWS\n",
      "At line 39 COLUMNS\n",
      "At line 109 RHS\n",
      "At line 144 BOUNDS\n",
      "At line 145 ENDATA\n",
      "Problem MODEL has 34 rows, 16 columns and 68 elements\n",
      "Coin0008I MODEL read with 0 errors\n",
      "Option for timeMode changed from cpu to elapsed\n",
      "Presolve 0 (-34) rows, 0 (-16) columns and 0 (-68) elements\n",
      "Empty problem - 0 rows, 0 columns and 0 elements\n",
      "Optimal - objective value 108\n",
      "After Postsolve, objective 108, infeasibilities - dual 0 (0), primal 0 (0)\n",
      "Optimal objective 108 - 0 iterations time 0.002, Presolve 0.00\n",
      "Option for printingOptions changed from normal to all\n",
      "Total time (CPU seconds):       0.00   (Wallclock seconds):       0.01\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def identify_critical_path(df, results, case=\"expected\"):\n",
    "    optimal_duration = results[\"optimal_duration\"]\n",
    "    task_start_times = results[\"task_start_times\"]\n",
    "    \n",
    "    critical_path = []\n",
    "\n",
    "    for index, row in df.iterrows():\n",
    "        task = row[\"taskID\"]\n",
    "        duration = None\n",
    "\n",
    "        # Determine the duration based on the scenario\n",
    "        if results[\"status\"] == \"Optimal\":\n",
    "            if case == \"expected\":\n",
    "                duration = row[\"bestCaseHours\"]\n",
    "            elif case == \"worst\":\n",
    "                duration = row[\"worstCaseHours\"]\n",
    "            else:\n",
    "                duration = row[\"expectedHours\"]\n",
    "\n",
    "        # Calculate the task end time\n",
    "        task_end_time = task_start_times[task] + duration\n",
    "\n",
    "        # If the task ends at the project's optimal duration, it's on the critical path\n",
    "        if task_end_time == optimal_duration:\n",
    "            critical_path.append(task)\n",
    "\n",
    "    return critical_path\n",
    "\n",
    "# Identify and print the critical path for the \"best\" case\n",
    "case = \"expected\"\n",
    "result = solve_project_plan(df, case)\n",
    "critical_path = identify_critical_path(df, result, case)\n",
    "\n",
    "print(f\"Critical Path for {case} case: {critical_path}\")\n",
    "case = \"expected\"\n",
    "\n",
    "\n",
    "# Define a function to create a Gantt chart\n",
    "def create_gantt_chart(df, results, case=\"expected\"):\n",
    "    task_start_times = results[\"task_start_times\"]\n",
    "    task_durations = {}\n",
    "    \n",
    "    for index, row in df.iterrows():\n",
    "        task = row[\"taskID\"]\n",
    "        if case == \"expected\":\n",
    "            task_durations[task] = row[\"bestCaseHours\"]\n",
    "        else:\n",
    "            task_durations[task] = row[\"expectedHours\"]\n",
    "\n",
    "    tasks = list(task_start_times.keys())\n",
    "    start_times = [task_start_times[task] for task in tasks]\n",
    "    durations = [task_durations[task] for task in tasks]\n",
    "\n",
    "    fig, ax = plt.subplots(figsize=(10, 4))\n",
    "    \n",
    "    for i, task in enumerate(tasks):\n",
    "        ax.broken_barh([(start_times[i], durations[i])], (i - 0.4, 0.8), facecolors='blue')\n",
    "        ax.text(start_times[i] + durations[i] / 2, i, task, ha='center', va='center', color='white')\n",
    "\n",
    "    ax.set_yticks(range(len(tasks)))\n",
    "    ax.set_yticklabels(tasks)\n",
    "    ax.set_xlabel('Time (hours)')\n",
    "    ax.set_title(f'Gantt Chart for {case} Case')\n",
    "\n",
    "    plt.show()\n",
    "\n",
    "result = solve_project_plan(df, case)\n",
    "create_gantt_chart(df, result, case)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Critical Path and Gantt Chart for Worst Case Solution\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Welcome to the CBC MILP Solver \n",
      "Version: 2.10.3 \n",
      "Build Date: Dec 15 2019 \n",
      "\n",
      "command line - /home/daf03834-2cd7-40ad-bc31-d3b51e4b5c9f/.local/lib/python3.9/site-packages/pulp/solverdir/cbc/linux/64/cbc /tmp/1d6f0be67a04464aa9874b5ba01c99f1-pulp.mps timeMode elapsed branch printingOptions all solution /tmp/1d6f0be67a04464aa9874b5ba01c99f1-pulp.sol (default strategy 1)\n",
      "At line 2 NAME          MODEL\n",
      "At line 3 ROWS\n",
      "At line 39 COLUMNS\n",
      "At line 109 RHS\n",
      "At line 144 BOUNDS\n",
      "At line 145 ENDATA\n",
      "Problem MODEL has 34 rows, 16 columns and 68 elements\n",
      "Coin0008I MODEL read with 0 errors\n",
      "Option for timeMode changed from cpu to elapsed\n",
      "Presolve 0 (-34) rows, 0 (-16) columns and 0 (-68) elements\n",
      "Empty problem - 0 rows, 0 columns and 0 elements\n",
      "Optimal - objective value 152\n",
      "After Postsolve, objective 152, infeasibilities - dual 0 (0), primal 0 (0)\n",
      "Optimal objective 152 - 0 iterations time 0.002, Presolve 0.00\n",
      "Option for printingOptions changed from normal to all\n",
      "Total time (CPU seconds):       0.00   (Wallclock seconds):       0.01\n",
      "\n",
      "Critical Path for worst case: ['D7', 'H']\n",
      "Welcome to the CBC MILP Solver \n",
      "Version: 2.10.3 \n",
      "Build Date: Dec 15 2019 \n",
      "\n",
      "command line - /home/daf03834-2cd7-40ad-bc31-d3b51e4b5c9f/.local/lib/python3.9/site-packages/pulp/solverdir/cbc/linux/64/cbc /tmp/d1c5c9839ee24f889654d0ad3b7a72cf-pulp.mps timeMode elapsed branch printingOptions all solution /tmp/d1c5c9839ee24f889654d0ad3b7a72cf-pulp.sol (default strategy 1)\n",
      "At line 2 NAME          MODEL\n",
      "At line 3 ROWS\n",
      "At line 39 COLUMNS\n",
      "At line 109 RHS\n",
      "At line 144 BOUNDS\n",
      "At line 145 ENDATA\n",
      "Problem MODEL has 34 rows, 16 columns and 68 elements\n",
      "Coin0008I MODEL read with 0 errors\n",
      "Option for timeMode changed from cpu to elapsed\n",
      "Presolve 0 (-34) rows, 0 (-16) columns and 0 (-68) elements\n",
      "Empty problem - 0 rows, 0 columns and 0 elements\n",
      "Optimal - objective value 152\n",
      "After Postsolve, objective 152, infeasibilities - dual 0 (0), primal 0 (0)\n",
      "Optimal objective 152 - 0 iterations time 0.002, Presolve 0.00\n",
      "Option for printingOptions changed from normal to all\n",
      "Total time (CPU seconds):       0.00   (Wallclock seconds):       0.01\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def identify_critical_path(df, results, case=\"worst\"):\n",
    "    optimal_duration = results[\"optimal_duration\"]\n",
    "    task_start_times = results[\"task_start_times\"]\n",
    "    \n",
    "    critical_path = []\n",
    "\n",
    "    for index, row in df.iterrows():\n",
    "        task = row[\"taskID\"]\n",
    "        duration = None\n",
    "\n",
    "        # Determine the duration based on the scenario\n",
    "        if results[\"status\"] == \"Optimal\":\n",
    "            if case == \"expected\":\n",
    "                duration = row[\"bestCaseHours\"]\n",
    "            elif case == \"worst\":\n",
    "                duration = row[\"worstCaseHours\"]\n",
    "            else:\n",
    "                duration = row[\"expectedHours\"]\n",
    "\n",
    "        # Calculate the task end time\n",
    "        task_end_time = task_start_times[task] + duration\n",
    "\n",
    "        # If the task ends at the project's optimal duration, it's on the critical path\n",
    "        if task_end_time == optimal_duration:\n",
    "            critical_path.append(task)\n",
    "\n",
    "    return critical_path\n",
    "\n",
    "# Identify and print the critical path for the \"best\" case\n",
    "case = \"worst\"\n",
    "result = solve_project_plan(df, case)\n",
    "critical_path = identify_critical_path(df, result, case)\n",
    "\n",
    "print(f\"Critical Path for {case} case: {critical_path}\")\n",
    "case = \"worst\"\n",
    "\n",
    "\n",
    "# Define a function to create a Gantt chart\n",
    "def create_gantt_chart(df, results, case=\"worst\"):\n",
    "    task_start_times = results[\"task_start_times\"]\n",
    "    task_durations = {}\n",
    "    \n",
    "    for index, row in df.iterrows():\n",
    "        task = row[\"taskID\"]\n",
    "        if case == \"worst\":\n",
    "            task_durations[task] = row[\"worstCaseHours\"]\n",
    "        else:\n",
    "            task_durations[task] = row[\"expectedHours\"]\n",
    "\n",
    "    tasks = list(task_start_times.keys())\n",
    "    start_times = [task_start_times[task] for task in tasks]\n",
    "    durations = [task_durations[task] for task in tasks]\n",
    "\n",
    "    fig, ax = plt.subplots(figsize=(10, 4))\n",
    "    \n",
    "    for i, task in enumerate(tasks):\n",
    "        ax.broken_barh([(start_times[i], durations[i])], (i - 0.4, 0.8), facecolors='crimson')\n",
    "        ax.text(start_times[i] + durations[i] / 2, i, task, ha='center', va='center', color='white')\n",
    "\n",
    "    ax.set_yticks(range(len(tasks)))\n",
    "    ax.set_yticklabels(tasks)\n",
    "    ax.set_xlabel('Time (hours)')\n",
    "    ax.set_title(f'Gantt Chart for {case} Case')\n",
    "\n",
    "    plt.show()\n",
    "\n",
    "result = solve_project_plan(df, case)\n",
    "create_gantt_chart(df, result, case)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "anaconda-2022.05-py39",
   "language": "python",
   "name": "conda-env-anaconda-2022.05-py39-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}