probCPM.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from criticalpath import Node\n",
    "import pymc as pm\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# data = [\n",
    "#     {\"activity\": \"A\", \"duration\": 3, \"predecessors\": []},\n",
    "#     {\"activity\": \"B\", \"duration\": 4, \"predecessors\": [\"A\"]},\n",
    "#     {\"activity\": \"C\", \"duration\": 2, \"predecessors\": [\"A\"]},\n",
    "#     {\"activity\": \"D\", \"duration\": 5, \"predecessors\": [\"A\"]},\n",
    "#     {\"activity\": \"E\", \"duration\": 3, \"predecessors\": [\"C\", \"B\"]},\n",
    "#     {\"activity\": \"F\", \"duration\": 2, \"predecessors\": [\"D\"]},\n",
    "#     {\"activity\": \"G\", \"duration\": 3, \"predecessors\": [\"E\", \"F\"]},\n",
    "#     {\"activity\": \"I\", \"duration\": 2, \"predecessors\": [\"G\"]},\n",
    "# ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14"
      ]
     },
     "execution_count": 172,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = [\n",
    "    {\"activity\": \"A\", \"true_duration\": 3, \"predecessors\": [], \n",
    "     \"true_std\": 1, \"guess\": 8, \"vagueness\": 1.5},\n",
    "    {\"activity\": \"B\", \"true_duration\": 3, \"predecessors\": [\"A\"], \n",
    "     \"true_std\": 0.5, \"guess\": 2, \"vagueness\": 1.3},\n",
    "    {\"activity\": \"C\", \"true_duration\": 4, \"predecessors\": [\"A\"], \n",
    "     \"true_std\": 1.5, \"guess\": 2, \"vagueness\": 4},\n",
    "    {\"activity\": \"D\", \"true_duration\": 6, \"predecessors\": [\"A\"], \n",
    "     \"true_std\": 2, \"guess\": 4, \"vagueness\": 2},\n",
    "    {\"activity\": \"E\", \"true_duration\": 5, \"predecessors\": [\"B\", \"C\", \"D\"], \n",
    "     \"true_std\": 3, \"guess\": 2, \"vagueness\": 1.2},\n",
    "]\n",
    "\n",
    "p = Node('project')\n",
    "\n",
    "for node in data:\n",
    "    p.add(Node(node['activity'], duration=node['true_duration']))\n",
    "\n",
    "for node in data:\n",
    "    if node['predecessors'] != []:\n",
    "        for predecessor in node['predecessors']:\n",
    "            p.link(predecessor, node['activity'])\n",
    "\n",
    "p.update_all()\n",
    "\n",
    "p.duration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[A, D, E]"
      ]
     },
     "execution_count": 173,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p.get_critical_path()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulate_normal(data:list[dict]):\n",
    "    \n",
    "    for idx, task in enumerate(data):\n",
    "        n_prev = np.random.randint(0,5)\n",
    "        prev = np.round(np.random.normal(task[\"true_duration\"], task[\"true_std\"], n_prev),2)\n",
    "        data[idx][\"prev_durations\"] = prev\n",
    "\n",
    "    return data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [],
   "source": [
    "d = simulate_normal(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [],
   "source": [
    "obs = d[0][\"prev_durations\"]\n",
    "expert_guess = 8\n",
    "vagueness = 1.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_22593/3284531684.py:1: RuntimeWarning: Mean of empty slice.\n",
      "  obs.mean()\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "nan"
      ]
     },
     "execution_count": 180,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "obs.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_posterior_mean(obs, expert_guess, vagueness):\n",
    "    with pm.Model() as task_model:\n",
    "\n",
    "        mu = pm.Normal('mu', mu=expert_guess, sigma=vagueness)\n",
    "        sigma = pm.HalfNormal('sigma', sigma=3)\n",
    "\n",
    "        y = pm.Normal('y', mu=mu, sigma=sigma, observed=obs)\n",
    "\n",
    "        trace = pm.sample()\n",
    "\n",
    "    return trace.posterior[\"mu\"].values.mean(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "get_posterior_mean(obs, expert_guess, vagueness)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 2 seconds.\n",
      "We recommend running at least 4 chains for robust computation of convergence diagnostics\n"
     ]
    }
   ],
   "source": [
    "for idx, task in enumerate(d):\n",
    "    posterior = get_posterior_mean(\n",
    "        task[\"prev_durations\"], \n",
    "        task[\"guess\"], \n",
    "        task[\"vagueness\"])\n",
    "    d[idx][\"posterior\"] = posterior"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [],
   "source": [
    "durations = []\n",
    "critial_paths = []\n",
    "\n",
    "for it in range(1000):\n",
    "    p = Node('project')\n",
    "\n",
    "    for node in d:\n",
    "        p.add(Node(node['activity'], duration=node['posterior'][it]))\n",
    "\n",
    "    for node in d:\n",
    "        if node['predecessors'] != []:\n",
    "            for predecessor in node['predecessors']:\n",
    "                p.link(predecessor, node['activity'])\n",
    "\n",
    "    p.update_all()\n",
    "\n",
    "    durations.append(p.duration)\n",
    "    critial_paths.append([str(j) for j in p.get_critical_path()])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(10, 5))\n",
    "plt.hist(durations, bins=50)\n",
    "plt.xlabel('Duration')\n",
    "plt.ylabel('Count')\n",
    "plt.title('Duration of Project')\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Critical Path Histogram')"
      ]
     },
     "execution_count": 169,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(10, 5))\n",
    "x, y = np.unique(critial_paths, return_counts=True)\n",
    "plt.bar(x, y)\n",
    "plt.xlabel('Activity')\n",
    "plt.ylabel('# of times on critical path')\n",
    "plt.title('Critical Path Histogram')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.11.4"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}