notebooks/04.06-Unit-Commitment.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "9O_tHTY_PL_s"
   },
   "source": [
    "# Unit Commitment\n",
    "\n",
    "Keywords: semi-continuous variables, cbc usage, gdp, disjunctive programming"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "VPgCJFU_zQbm"
   },
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 544
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 23798,
     "status": "ok",
     "timestamp": 1561637754415,
     "user": {
      "displayName": "",
      "photoUrl": "",
      "userId": ""
     },
     "user_tz": 300
    },
    "id": "XVxMSjhOzQbn",
    "outputId": "bd0572bd-47d0-4fb5-9ca8-638d40085fa1"
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from IPython.display import display, HTML\n",
    "\n",
    "import shutil\n",
    "import sys\n",
    "import os.path\n",
    "\n",
    "if not shutil.which(\"pyomo\"):\n",
    "    !pip install -q pyomo\n",
    "    assert(shutil.which(\"pyomo\"))\n",
    "\n",
    "if not (shutil.which(\"cbc\") or os.path.isfile(\"cbc\")):\n",
    "    if \"google.colab\" in sys.modules:\n",
    "        !apt-get install -y -qq coinor-cbc\n",
    "    else:\n",
    "        try:\n",
    "            !conda install -c conda-forge coincbc \n",
    "        except:\n",
    "            pass\n",
    "\n",
    "assert(shutil.which(\"cbc\") or os.path.isfile(\"cbc\"))\n",
    "import pyomo.environ as pyo\n",
    "import pyomo.gdp as gdp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Y_yzzUJQDJtr"
   },
   "source": [
    "## Problem statement\n",
    "\n",
    "A set of $N$ electrical generating units are available to meet a required demand $d_t$ for time period $t \\in 1, 2, \\ldots, T$. The power generated by unit $n$ for time period $t$ is denoted $x_{n,t}$.  Each generating unit is either off, $x_{n,t} = 0$ or else operating in a range $[p_n^{min}, p_n^{max}]$. The incremental cost of operating the generator during period $t$ is $a_n x_{n,t} + b_n$. A binary variable variable $u_{n,t}$ indicates the operational state of a generating unit. \n",
    "\n",
    "The unit commitment problem is then\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\min \\sum_{n\\in N} \\sum_{t\\in T} a_n x_{n,t} + b_n u_{n,t}\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "subject to\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\sum_{n\\in N} x_{n,t} & = d_t \\qquad \\forall t \\in T \\\\\n",
    "p_{n}^{min}u_{n,t} & \\leq x_{n,t} \\qquad \\forall n \\in N, \\ \\forall t \\in T \\\\\n",
    "p_{n}^{max}u_{n,t} & \\geq x_{n,t} \\qquad \\forall n \\in N, \\ \\forall t \\in T \\\\\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "where we use the short-cut notation $T = [1, 2, \\ldots T]$ and $N = [1, 2, \\ldots, N]$.\n",
    "\n",
    "This is a minimal model. A realistic model would include additional constraints corresponding to minimum up and down times for generating units, limits on the rate at which power levels can change, maintenance periods, and so forth.\n",
    "\n",
    "* Sun, Xiaoling, Xiaojin Zheng, and Duan Li. [\"Recent advances in mathematical programming with semi-continuous variables and cardinality constraint.\"](https://link.springer.com/article/10.1007/s40305-013-0004-0) Journal of the Operations Research Society of China 1, no. 1 (2013): 55-77."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Demand"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Demand')"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# demand\n",
    "T = 20\n",
    "T = np.array([t for t in range(0, T)])\n",
    "d = np.array([100 + 100*np.random.uniform() for t in T])\n",
    "\n",
    "fig, ax = plt.subplots(1,1)\n",
    "ax.bar(T+1, d)\n",
    "ax.set_xlabel('Time Period')\n",
    "ax.set_title('Demand')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generating Units"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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rjLsL2kc3qzmtq6Po9TfIf+opOpSWEjPrYuJvuYXwhAQvBw8M2cVVPJe+i9e/2ENlbT1TBidw48T+nJLc/GUjj8QKvzGmZVRdV9su/S0U73bNmjntAejcr5nNKeXLl5P70MPUZmbS4fTTyJ0yhROuvNLLwQPDtzllLErbyXtfZ6HAzOE9uHFCfwZ1b3pIZktY4TfGNN/+b1zz4+9eCQlD4er3od+EZjdXvXkzOfMfonLNGtr160fPhX8jauJEdqWleTF0YFi3u4hFaRl8tDmH9uEhXHlaH346ri8943w/h5AVfmPMsSvPg08egC9fgcg4OPdR10pYoc0rKXU5OeQ99jgl//oXobGxdPvtfcRddhkSHu7l4P6lqqRuz2Nhagaf7yokJjKcW6YM5Jozkul8jEMyW8IKvzHGc45aWLMIVjwMdZVw2k0wYS5ExjarOWdlJQXPv0DBCy+Aw0Hn666l6w03EBrdvPMCgcpR7+S/G/azMDWDrQfKSIxpz33nDuHyMb3pGNH6ZfioRxSRS1X1zaPtM8Ycx1Rh2wew9DdQuBMGToPpD0LXgc1rzumk5F/vkffYYzhyc+k0YwYJd95Bu169vBzcv6rr6nlz7V6eSd/J3sIqBiRE8fAlJ3HBiCTahflvGKonv2ruAQ4t8o3tM8Ycj3K3uPrxdy6Hrilwxdsw8KxmN1ex5nNy5s+jZvMW2p90EkmP/YUOJ5/sxcD+V1JZx98/y+TFVZkUVNQysncsvz33BM4a0s1rQzJb4oiFX0TOBs4BkkTkiQZPReOaddMYczyrLITlD8LaFyAiCmbMh1Ouh9Dm9bvX7NpF7oJHKF+2jLAeifRYsIDoc84+ri7AOlBSzetba7j5k2VU1NYzcVA8N03oz5i+nZFmrg/sC019488G1gIzcc2lf1AZcLsvQxlj/Ki+Dr54HlL/DDVlMPo6mHQvdGjeeHJHURH5f1tI0WuvERIRQfztt9N59tWEtG/+urmBJiOvnKfTMnj3qyzqncr5w3tww/j+nNAjMM9VHLHwq+p6YL2I/FNV6wBEJA7opbZGrjHHp28/hiX3QP526DfJ1Y/f7YRmNaW1tRT+85/k/20hzvJyYi+5hPhbfklY165eDu0/X+8tZlFqBks2H6BdaAiXj+nNieG5XHrOSH9Ha5InffwfichM92u/BvJEJE1V7/BpMmNM68nbDkvuhR0fuS68uvx1SJnhWvbwGKkqZR9/TO6CBdTt3kPHceNI+NVdtE9J8UHw1qeqrPg2n0WpGXy6s4Do9mH8YtIAZp+RTNeoCFJTU/0d8ag8KfwxqloqIj8FXlTV+0XkG18HM8a0gqoiSHsIPn8GwjvAtD/BmBsgrHljyqs2bCRn/jyq1q4jYuAAej37DFHjxnk5tH846p18sPEAC1Mz2Ly/lG7REfzmnCFcfmpvovwwJLMlPEkb5l4p6zLgNz7OY4xpDfUOemR9AE9c6yr+J18Nk38LUfHNaq5u/37yHnuMkvfeJ7RLF7r/4Q/EzroYCQuugtiY6rp63lq3j2fTd7K7oJJ+8R2ZP+tELhyZRERYqL/jNYsn/1X+CCwBVqnqFyLSD/jWt7GMMT6zMxU+vIeU3M3Q50yY8WdIPKlZTTkrKsh/7jkKX3wJnE66zJlDlzk/IzQAFnFvqdLqOv7x2W5eWJlJfnkNw3vFcs/Zg5l2QveAGJLZEkct/O4Ltd5ssL0TmOXLUMYYHyjIcE2ktu2/ENubjUPnMuySe5rXj19fT8m775L7+OPU5+UTfe65JNxxO+FJST4I3rpyS6t5ftUuXv1sD+U1DsanuIZkntYvsIZktoQnV+72BJ4ExgIKrARuVdV9Ps5mjPGG6lJIXwCfLYSQcFeXzum/IH/VZ80q+hWrV5Mz/yFqtm0jcuRIuj31FJHDh/sgeOvalV/BMysyeHtdFg6nk3NP6sEN4/sxLOn4W7/Xk66eF4F/8v3auFe69031VShjjBc46+HrV2HZA1CR61oMZcrvoFP3ZjVXs2MHOQ8/TEXaCsKTkkj6y6N0mjEj6L8Ff7OvmEVpGXyw8QDhoSFcOronc8b3o0+X5q0HHAw8Kfzxqvpig+2XROQ2TxoXkUxcF3zVAw5VHS0inYE3gGQgE7jMrgswxst2r4YP5sKBb6DXqfCT1yFpVLOachQWkv/UUxS9sZiQyEgS7rqTuKuuIiQiwsuhW4+qsmpHAQvTdrBqRwGdIsK4aUJ/rhmbTEKn4+fCsiPxpPDni8iVwGvu7cuBgmM4xiRVzW+wfTewTFXnicjd7u25x9CeMeZIinbDR7+Dzf+C6J4w63kYNqtZXTrOmhqK/v538hc9jbOqirgf/Yiuv7iZsM7eXxGqtdQ7lSWbXEMyN2SVEN8pgrvPHswVp/amU/vjawropnhS+K8DngL+gquPf7V7X3NdAEx0P34ZSMUKvzEtU1MOK/8Cq58ECYGJ98IZv4R2x76oh6pS9uGH5D7yKHX79hE1YQIJv/4VEf37+yB466hx1PPOl1k8s2Inu/Ir6Nu1I3+++EQuGplE+/DgHJLZEqKqvmtcZBdQhOsXxtOq+oyIFKtqbIPXFKlqXCPvnQPMAYiPjx+1ePFin+X0pvLycqKCZCibZfW+Vs+pTrrlpNFv5ytE1BaSkzCenf2upqb90cfjN5Y1bNcuOr35Fu127qQuKYnyWbOoPWGIr9J7rLn/rlUOZfmeOpbsdlBSoyRHh3Buv3BGdQslxEfnJgLhZ7W6WCncoVzxqynrVHX0oc83NTvnQ8BOVV10yP7bge6q6sm39LGqmi0iCbimftjqaXBVfQZ4BmDQoEE6ceJET9/qV6mpqVhW7wuWrK2es7YCnrwZuvaBGa/TrfepdPPwrQ2z1u7LIu/RRyn93/8Ije9Kwp8eIOaii5DQwPg2fKz/rrll1by4KpN/fLabsmoHZw7oyo0T+jN2QBefn4z218+qo66ejC/z2LQii/0ZJYQ2Md9/U1095wHDGtn/OPANHnTPqGq2+z5XRN4FxgA5IpKoqvvdVwTnHq0dY8wRtOsI130AMb2hGdMb15eXU/D0MxS+/DKEhNDlphvpcv1PCY0KzhEtmfkVPJO+k7fW7aOu3sk5wxK5cUJ/Tux5/A3JPKg4t5JN6dlsXb2f6oo6YhIiGXvJAGJPFPhr4+9pqvCrqjob2ekUD35likhHIERVy9yPp+G6Cvh9YDYwz33/3lE/mTHmyOKSj/kt6nAQuSKdjHt/Q31hIdEzzyfh9tsJT0z0fr5WsDGrhEVpGfxvw37CQkKYNco1JLNv1+D8BXY0znonmd8UsHHFPvZuKUJChH7Du9JjTCRfhq/i4T1P8c2HR55SranCXykiA1X1B9MziMhAoMqDbN2Ad92/I8KAf6rqhyLyBbBYRK4H9vD99QHGmFZQnp5Ozvz5RO/IoN3oUXR7+mkiT2zsj/vApqp8urOAhakZpH+bT1REGD8b34/rx/YlIfr4HJJZXlTD5pVZbF6ZTUVJLVFxEZwwI549Pb7hH/nPs/6b9QAM6TyEW0++lZ/xs0bbaarw/w74QET+xPcLsYzGtezibUcL6J7a4bDL+VS1AJhytPcbY7yrevt2ch96mIqVKwnv3ZviG+Yw+Lbbgu4CLKdTWbr5AAvTdrJ+bzFdoyL49YxBXHFqH2Iij78hmepU9m4pZOOKLDI3FKCqdBsUhXPcfj7m33xd8BWUwODOg7n15FuZ2mcqfaL7ABx74VfVD0TkQuBXwC/duzcCs1R1g1c/mTHGZxz5+eQ9+RTFb75JSFQUCXPn0vmKn7Bv9eqgKvo1jnr+9VUWT6/Yyc68Cnp37sD/XTSMWSf3PC6HZFaV1bJl9X42pWdRml9NRFQo7UaW8lnsh6ypXAkFMChuELeMvIVpydO+K/aeaHIcv6puxNUPb4wJMs7qagpffoWCp5/GWVtL3JVX0PWmmwiLO2z0dEArr3Hwwa465q5eTk5pDUN7RPPk5SM5e1h3wkKPn/V6wdV9tT+jhI1pWWR8lYvToYQm1bBj1Gd8EvYezpB6UiJS+OWgXzKtzzSSY5KbdZzgnyzbGPMDqkrpf/9H7qOP4MjeT9SUKSTcdScRffv6O9oxyS+v4aVVmbzyaSal1Q7O6N+FBZcO58wBXYPqLxVP1FQ52L7mABtXZFGYXQHtnBzotY206H9R1OEAA+MG8vM+NzEteRp9Y1r+39EKvzHHkcovvyJn/jyq139DxJAh9Hjwz3Q87VR/xzomewsreTZ9J298sZfaeifTT+jOmE7FXHfhaf6O5nV5e8rYuCKL7Z8fwFHrpCImny/6fcSOrl+S3KU3P0mexbTkafSL6efV41rhN+Y4ULt3L7mPPErZhx8SlpBA4oMPEnPBzIC5AMsTm7NLeXpFBv/5Zj8hAheP7MmcCf3oHx8VFOvYeqqutp4da3P5OjWTwj1V1Ic6+LbzWjZ1X0lMzwimJ09nfvI9Xi/2DXkyH/8TjewuAdaqqo3BN8aPnNXV5D35JEWv/B3Cwuh68810uf46Qjoc+xw9/qCqrNlVyKK0DFK35dGxXSjXjU3m+jP70T3m+BqSWXSggi8+yWDHmly0JoSiyANsSl6FY0A+kwdM5Pbkp+gX67ti35An3/jbA4P5fhWuWcAm4HoRmaSqt/komzHmKCQ8nIpVq4k+7zzib7uV8G6eTtjgX06n8vGWHBamZfDVnmK6RrXjV9MHceWpfYjpcPwMyax3OFn/+U6++GQHjn3tqBcHOzuvp2R4JqNHDuVPfe+gf2zrT37nSeEfAExWVQeAiCwEluJaiMWGdRrjRxIaSvIbrwfN3Pi1Difvfe0akrkjt5xenSN54MJhXDrq+BqSuTsrm2UfrqP0mxDCayIpjSjjQMpWUk6P5xeDL2JA3AC/5vOk8CcBHXF17+B+3ENV60WkxmfJjDEeCYaiX1Hj4LXP9/D8yl3sL6lmSGI0T1w+knOOoyGZeRX5fLginZ3pRWx83YESSVHCLuJHhXPJmWMZ2CVwJinwpPA/BHwtIqmAAOOBB93z73zsw2zGmCBXUF7Dy6szefnT3ZRU1XFav878+eITmZASf1wMySysLmTp5mVsWLmPTjt60am2M1HhoXByAeOnnshJyVMC8nMetfCr6vMi8j9cM2sKcO/BWTdxXdVrjDE/sK+okmdX7OSNtXuprnMy7YRu3DixPyf3Dq6LxxpTWF3Ix7uXsXrtV4Rs7kJy4Un00C5oUjknju+MwwGTp8z0d8wmeTqcMwTIc79+gIgMUNUVvotljAlGWw+U8nTaTt5fn40AF45M4sYJ/RiQ0Mnf0VqksLqQZXuWsWz7cso3hjH4wOkMrD4LjXDQZ2wMZ541lLjurplAg2HoqSfDOecDP8I1kufgNM0KWOE3xgDwRWYhC1Mz+GRrLh3ahXLNGclcf2ZfesRG+jtasxVVF7FszzKW7lrKrh0HGHzgdE4ouJBQZxgxvcIZNak/A0d3I6xd8J2U9uQb/4XAIFW1E7nGmO84ncqyrbksSstg3e4i4jqEc/tZKcw+ow+xHdr5O16zFFcXu4r97qWs2/cV/fJGMCJvEsPLuhHaThg0NpFh45OI7xXcf8F4Uvh3AuGAFX5jDHX1Tt7/OptFaRl8m1tOUmwkf5g5lMtG9yIyCL/9FlcX88neT1iSuYQ1+9cQU57AmKLpXHPgEqQulM5JHTnxvCRSTu1Ou/bHx2QHnnyKSlyjepbRoPir6i0+S2WMCTiVtQ5e/3wvz6XvJLukmsHdO/GXHw3nvJN6EB5kQzJLakr4ZM/3xd5Zr5xSMZnr8x4gJKcjIWHCgFEJDBvfk+79ogNyZE5LeFL433ffjDFtUFFFLS9/mslLqzMprqzjlOQ4/nTRMCYNSgiqgvhdsd+9hDXZa3Cog4EhQ7mm/NdE7uhOXaUSEx/J0FlJDD69O5FRwdld5QlPhnO+3BpBjDGBJau4iufSd/L653upqqvnrCEJ3DihP6OTO/s7msdKakpYvnc5SzKX8Fn2ZzjUQc8OPZnd4RckZA6iaEctEiL0Ht6VoeOT6DkoDgkJnl9mzXXEwi8ii1X1MhHZgGsUzw+o6kk+TWaM8YvtOWUsSsvg/a9dl+vMHNGDGyf0J6VbcJzQLK0t5ZM9n7A0cymf7v8Uh9NBUlQSV/W5jpQDY8hfW0dFSS21scKY8/tywtgedIwN/Kufvampb/y3uu/Pa8kBRCQUWAtkqep5ItIZeANIBjKBy1S1qCXHMMa03LrdhSxM3cnHW3KIDA/lqtP78NNx/UgKgiGZpbWlpO5NZUnmElZnr8bhdNCjYw+uHHwlox0TqVgfTuayAnZrBb1P6Mz4y5NIPrELIUF2bsJbmlpzd7/74c9VdW7D59xj++ce/q5G3QpsAaLd23cDy1R1nojc7d72tC1jjBepKsu35bIodSefZxYS2yGc284ayOzTk4nrGNh93AeL/dLMpazKXoXD6SCxYyJXDrmSSV3Pgm2xbHo/m415JbSPCmfEWb0YOi6JmPjA/0Xma56c3J3K4YX57Eb2HUZEegLnAv8H3OHefQEw0f34ZSDVk7aMMd7jqHeyOtvBvMfT2XqgjB4x7bn//BP40Sm96NAucIcsltWW/eCbfZ2zju4du3PF4CuY2mcq8aW92bQimzVf5uJ0FJA4IIZTz+9L/5EJhIa3zW/3jRHVw7rvXU+I3AT8HOgHZDR4qhOwSlWvPGrjIm8Bf3a/5y53V0+xqsY2eE2Rqh42gYeIzAHmAMTHx49avHixxx/Kn8rLy4mKivJ3DI9YVu8L9Jw19Ur6PgcfZtaRX6UkRQnn9A3n1MQwwgL0pGaVs4q1RWvZXL+ZrVVbceAgNjSWkR1GMrLjSHpKH8p2C4U7lJoSCAmH2GSIGyC0j2n9zxRIPwOTJk1ap6qjD93fVOGPAeJwFe67GzxVpqqFRzugiJwHnKOqPxeRiRxj4W9o0KBBum3btqMdMiCkpqYyceJEf8fwiGX1vkDNWVxZyyuf7ual1ZkUVtRycu9YxnWt4tZLphASgAW/vLac1H3ub/ZZq6l11pLQIYFpfaYxPXk6J8WfRMHeCtd6tV/k4KipJ753J4aNT2LgKd0Ij/DfhWSB9DMgIo0W/qb6+EtwzcF/ubuBBFyrcUWJSJSq7jnKMccCM0XkHPf7okXkH0COiCSq6n4RSQRym/eRjDFHs7+kiufTd/HPz/dQWVvP5MEJ3DSxP6ckdyY1NTWgin5FXcV33TirslZ9V+wvG3QZ8YXxXDP9Gpx1yrdrc3nnxS/J2VVKWHgIA07pxrDxSXRLjj7qMYyLJ5O0nQ88CvTAVaT74DpZO7Sp96nqPcA97jYm4vrGf6WIPAzMBua5723dXmO8bEduOU+nZfCvr7NwKpx/UiI3TOjPkMTAKo4Hi/3SzKWszFrpKvaRCVw66FKmJ09nePxwQiSEJe8vZ/WbGWz9bD81lQ7iunfgzMsGMujU7rTvePws1dhaPDmL8yfgNOBjVR0pIpNw/xXQTPOAxSJyPbAHCJxlaYwJcl/tKWJhagZLN+fQPjyEK07tw/Vn9qVX58BZfL2iroK0vWks3e0q9jX1NcRHxnNJyiVMT57OiIQRhEgI9Q4nGevy2JSeRdY2JSR0H/1GxjNsfBI9BsYG1VXDgcaTwl+nqgUiEiIiIaq63D2c02Oqmopr9A6qWgBMOeakxphGqSpp2/NYmJrBml2FxESGc8vkAcw+I5kuUYFxYVJlXSVp+9JYmrmU9Kz074r9xQMvZnrydEYmjCREXKNuygqr2ZSexeZV+6kqraVT5/YknCSce+VYOkQH9hDTYOFJ4S8WkShc8++/KiK5gMO3sYwxnqiqrWfWwtVs3l9KYkx77jt3CJeP6U3HCP8Pyaysq2RF1gqWZi5lxb4V1NTX0DWyKxcNuIgZfWf8oNg7nUrmxnw2rchi98YCAPqc2JWh43rQe2gXVqxIs6LvRZ78dFwAVAG3A1cAMcAffRnKGOOZyHahjOnbmWvHJnPBiCTahfl3rHplXSXpWeksyVxC+r50quur6dK+CxcNuIhpydM4OeFkQkO+H3FTWVrL5lXZbE7Ppqywmg7R7Rh1djJDxiYS3cUutPKVJgu/e7qF91T1LFyrb9mEbcYEmN/PbHKchc9VOapI3+cu9lnpVDmq6NK+CxcMuIDpydMPK/aqSvb2YjauyGLn13k465WkQXGcMWsAfUd0JbSNTqPQmpos/KpaLyKVIhLjHt5pjDFUOapYmbWSJZlLWLFvBVWOKjq378zM/jOZ1mcao7qN+kGxB6iuqGPbZwfYlJ5F0YFKIjqEceLEngwd1+O79WpN6/Ckq6ca2CAiHwEVB3faQizGtC0Hi/3SzKWk7UvzqNirKrmZZWxMz2LHFzk46px06xvNlNlDGDAqISjXqz0eeFL4/+u+GWPamGpH9XfFPnVf6nfF/vx+5zMt2VXsw0IOLyN1NfVs//wAm9KzydtTRlhEKCmndWfYuCTiewfH9M7HM48WYhGRSKC3qgbHvAnGmGardlSzKmsVS3YvIW1vGpWOSuIi4jiv33lMS57G6G6jGy32AAVZ5WxakcW2NQeora6nS1JHJlyeQsqY7rSL9P9II+Pi6ZW7C4B2QF8RGQH8UVVn+jibMaaV1NTXfNdnf7DYx0bEck6/c5iePL3JYl9f5yTjq1w2rshi/46S43692uOBJ7+Cfw+M4fsLsL4Wkb4+zGSMaQV1WvfdguNp+9KoqKsgNiKWs/uezfTk6ZzS/ZQjFnuAkrwqNqVnsWX1fqrL64iJj+SMiwcw+Izje73a44Enhd+hqiWH/NZufEpPY0xAq6mvYXXWapbsXsKyvcuo3lNNTEQMM5JnMC15Gqd0P4XwkCPPfeOsd5K5oYBNK7LYs7kQCRH6Du/KsHFJ9BzcNtarPR54Uvg3ishPgFARGQjcAqz2bSxjjLfU1teyOns1SzKXsHzvcirqKoiJiGFkx5Fcc9o1nJLYdLEHKC+qcV1otTKbiuIaOsZGcMp5rvVqo+ICY1oI4zlPCv8vgd8ANcBrwBLgAV+GMsa0TG19LZ9mf/pdsS+vKye6XTTTk6czrc80xiSOYdWKVZyRdMYR21Cnsm9rERvTs9i1Ph91qmu92h+ntOn1ao8HnozqqQR+456YTVW1zPexjDHH6kjFfmqfqUxLnsapiace9Zs9QFV5LVtW72dTejaleVUN1qvtQUx84MzyaZrPk1E9pwAv4Fo+EREpAa5T1XU+zmaMOYp6Zz2rsle5iv2e5ZTVldGpXSfO6nMW0/pM47TE0wgPPXqxV1UOZJSwMT2LjHV51Ductl7tccyTrp7ngZ+rajqAiJwJvAic5MtgxpijU5T7Vt6HQx1M7j2Z6cnTPS72ALVVDrZ/foCNK7IoyKogvH0oJ4xNZOj4JLokBca6scb7PCn8ZQeLPoCqrhQR6+4xJgCEhYTx/PTnSY5O9rjYA+TtLSP7CycvvrsKR009XXtFMfGKQQw8pRvt2tuFVsc7T/4Lfy4iT+M6savAj4BUETkZQFW/9GE+Y8xRDIwb6NHrHLX17FjnutAqZ1cpEgqDTk1g2PgkEvp0sgut2hBPCv8I9/39h+w/A9cvgsneDGSM8a6iAxVsSs9m66cN1qu9dCD59TuYMm2Iv+MZP/BkVM+k1ghijPGe+nonu77OZ+OKfWRtKyYkVFzr1Y5LokeKa73a1NQMf8c0fnK0hViGAb8ChuL6dr8ZWKCqG1ohmzHmGB1cr3bLqv1UuterPfWCfgw5I5GOMXahlXE5YuEXkQtwTc72Z+ARQIBRwDsicpeqvtdUwyLSHtc6vRHu47ylqveLSGfgDSAZyAQuU9Wiln8UY9omp1PZs6mATenZ7N6QjwLJw7owdHwSvYd2IcSmUTCHaOob/x+Bqaqa2WDfehH5BHjPfWtKDTBZVctFJBxYKSIfABcDy1R1nojcDdwNzG32JzCmDXPU1vPaA59TmldFZHQ7Tp7ehxPG9bD1ak2Tmir84YcUfQBUNdNdyJukqgqUH2zLfVNci7dPdO9/Gdesn1b4jWmGsHahpIzpRpceUbZerfGYuOpzI0+IrAfOV9U9h+zvA/xbVY96AZd7sfZ1wADgr6o6V0SKVTW2wWuKVDWukffOAeYAxMfHj1q8eLHnn8qPysvLiYoKjgtfLKv3BUtOsKy+EkhZJ02atE5VRx/2hKo2egMuBLYD1wAnAsOAa4FtwIVHet8R2ooFlrvbKD7kuaKjvT8lJUWDxfLly/0dwWOW1fuCJaeqZfWVQMoKrNVGauoRu3pU9V8isgu4E9cMnQJsxHUydv2x/NZR1WIRSQVmADkikqiq+0UkEcg9lraMMca0TJPDOd0F/urmNCwi8UCdu+hHAmcB84H3gdnAPPf90U4SG2OM8SJfTsqRCLzs7ucPARar6n9E5FNgsYhcD+wBLvVhBmOMMYfwWeFX1W+AkY3sLwCm+Oq4xhhjmnbUsV8iMtaTfcYYY4KDJ4N+n/RwnzHGmCDQ1JQNp+OagTNeRO5o8FQ0EOrrYMYYY3yjqT7+dkCU+zWdGuwvBS7xZShjjDG+09Q4/jQgTUReUtXdrZjJGGOMDzXV1fOYqt4GPCUih83roKozfRnMGGOMbzTV1fN39/2C1ghijDGmdTTV1bPOfZ/WenGMMcb42lEv4HKP2f890Mf9esE163I/30YzxhjjC55cufs8cDuu6ZXrfRvHGGOMr3lS+EtU9QOfJzHGGNMqPCn8y0XkYeAdXMspAqCqX/oslTHGGJ/xpPCf6r5vuIqLApO9H8cYY4yvHbXwq+qk1ghijDGmdTR1Adcdh+xSIB9Yqaq7fJrKGGOMzzQ1O2enQ27RuLp7PhCRH7dCNmOMMT7Q1AVcf2hsv4h0Bj4GXvdVKGOMMb7jyXz8P6Cqhbgu4jLGGBOEjrnwi8hkoMgHWYwxxrSCpk7ubsB1QrehzkA2cPXRGhaRXsArQHfACTyjqo+7u4reAJKBTOAyVbVfJMYY00qaGs553iHbChSoaoWHbTuAO1X1SxHpBKwTkY+Aa4BlqjpPRO4G7gbmHmNuY4wxzdTUyd0WLb6iqvuB/e7HZSKyBUgCLgAmul/2MpCKFX5jjGk1onrYGiveP4hIMrACGAbsUdXYBs8VqWpcI++ZA8wBiI+PH7V48WKf5/SG8vJyoqKi/B3DI5bV+4IlJ1hWXwmkrJMmTVqnqqMPe0JVfXrDtW7vOuBi93bxIc8XHa2NlJQUDRbLly/3dwSPWVbvC5acqpbVVwIpK7BWG6mpxzyq51iISDjwNvCqqr7j3p0jIonu5xOBXF9mMMYY80M+K/wiIrjm8t+iqo82eOp9YLb78WzgPV9lMMYYczhPZudsrrHAVcAGEfnave9eYB6wWESuB/YAl/owgzHGmEP4rPCr6kqOfIXvFF8d1xhjTNN82sdvjDEm8FjhN8aYNsYKvzHGtDFW+I0xpo2xwm+MMW2MFX5jjGljrPAbY0wbY4XfGGPaGCv8xhjTxljhN8aYNsYKvzHGtDFW+I0xpo2xwm+MMW2MFX5jjGljrPAbY0wbY4XfGGPaGCv8xhjTxljhN8aYNsYKvzHGtDE+K/wi8oKI5IrIxgb7OovIRyLyrfs+zlfHN8YY0zhffuN/CZhxyL67gWWqOhBY5t42xhjTinxW+FV1BVB4yO4LgJfdj18GLvTV8Y0xxjROVNV3jYskA/9R1WHu7WJVjW3wfJGqNtrdIyJzgDkA8fHxoxYvXuyznN5UXl5OVFSUv2N4xLJ6X7DkBMvqK4GUddKkSetUdfRhT6iqz25AMrCxwXbxIc8XedJOSkqKBovly5f7O4LHLKv3BUtOVcvqK4GUFVirjdTU1h7VkyMiiQDu+9xWPr4xxrR5rV343wdmux/PBt5r5eMbY0yb58vhnK8BnwKDRGSfiFwPzAOmisi3wFT3tjHGmFYU5quGVfXyIzw1xVfHNMYYc3R25a4xxrQxVviNMaaNscJvjDFtjBV+Y4xpY6zwG2NMG2OF3xhj2hgr/MYY08ZY4TfGmDbGCr8xxrQxVviNMaaNscJvjDFtjBV+Y4xpY6zwG2NMG2OF3xhj2hgr/MYY08ZY4TfGmDbGCr8xxrQxVviNMaaNscJvjDFtjBV+Y4xpY/xS+EVkhohsE5EdInK3PzIYY0xb1eqFX0RCgb8CZwMnAJeLyAmtncMYY9oqf3zjHwPsUNWdqloLvA5c4IccxhjTJoX54ZhJwN4G2/uAUw99kYjMAea4N2tEZGMrZPOGrkC+v0N4yLJ6X7DkBMvqK4GUtU9jO/1R+KWRfXrYDtVngGcARGStqo72dTBvsKy+ESxZgyUnWFZfCYas/ujq2Qf0arDdE8j2Qw5jjGmT/FH4vwAGikhfEWkH/Bh43w85jDGmTWr1rh5VdYjIL4AlQCjwgqpuOsrbnvF9Mq+xrL4RLFmDJSdYVl8J+Kyielj3ujHGmOOYXblrjDFtjBV+Y4xpYwK68Af61A4i8oKI5Da8xkBEOovIRyLyrfs+zp8Z3Zl6ichyEdkiIptE5NYAztpeRD4XkfXurH8I1KwHiUioiHwlIv9xbwdkVhHJFJENIvK1iKx17wvUrLEi8paIbHX/3J4eiFlFZJD73/PgrVREbgvErA0FbOEPkqkdXgJmHLLvbmCZqg4Elrm3/c0B3KmqQ4DTgJvd/5aBmLUGmKyqw4ERwAwROY3AzHrQrcCWBtuBnHWSqo5oMM48ULM+DnyoqoOB4bj+fQMuq6puc/97jgBGAZXAuwRg1h9Q1YC8AacDSxps3wPc4+9cjeRMBjY22N4GJLofJwLb/J2xkczvAVMDPSvQAfgS15XdAZkV13Uoy4DJwH8C+WcAyAS6HrIv4LIC0cAu3INPAjnrIfmmAauCIWvAfuOn8akdkvyU5Vh0U9X9AO77BD/n+QERSQZGAmsI0KzurpOvgVzgI1UN2KzAY8CvAWeDfYGaVYGlIrLOPSUKBGbWfkAe8KK7C+05EelIYGZt6MfAa+7HAZ01kAu/R1M7GM+JSBTwNnCbqpb6O8+RqGq9uv507gmMEZFhfo7UKBE5D8hV1XX+zuKhsap6Mq7u05tFZLy/Ax1BGHAysFBVRwIVBFpXySHcF6POBN70dxZPBHLhD9apHXJEJBHAfZ/r5zwAiEg4rqL/qqq+494dkFkPUtViIBXXeZRAzDoWmCkimbhmmZ0sIv8gMLOiqtnu+1xc/dBjCMys+4B97r/0AN7C9YsgELMedDbwparmuLcDOWtAF/5gndrhfWC2+/FsXP3pfiUiAjwPbFHVRxs8FYhZ40Uk1v04EjgL2EoAZlXVe1S1p6om4/r5/ERVryQAs4pIRxHpdPAxrv7ojQRgVlU9AOwVkUHuXVOAzQRg1gYu5/tuHgjsrIF7ctd9UuQcYDuQAfzG33kayfcasB+ow/Ut5XqgC66Tfd+67zsHQM4zcXWTfQN87b6dE6BZTwK+cmfdCPzOvT/gsh6SeyLfn9wNuKy4+s3Xu2+bDv7/FIhZ3blGAGvdPwf/AuICOGsHoACIabAvILMevNmUDcYY08YEclePMcYYH7DCb4wxbYwVfmOMaWOs8BtjTBtjhd8YY9oYK/wmKIhIcsNZUN37fi8idx3lfaNF5An344kicsYRXneNiOS5Z1jcLCI/82bWY3jvDzKKyI0icnVzsxjTmFZfetGY1qSqa3GNBwfXWPtyYPURXv6Gqv5CRBKATSLyvn5/JSYiEqaqDp8GPiSjqi7y8fFMG2Tf+M1xQURSRWS+ey7/7SIyzr1/ooj8xz053Y3A7e5v9eOO1Ja6pjTIAPqIyEsi8qiILAfmi8gIEflMRL4RkXcPzrMuIqPEtYbAp8DNDXJdIyJPNdj+j4hMdD+eISJfut+3rLGMDf+qaeLYjX52Y47ECr85noSp6hjgNuD+hk+oaiawCPiLuuZPTz9SIyLSD9eVrjvcu1KAs1T1TuAVYK6qngRsaHCcF4FbVPV0T4KKSDzwLDBLXWsPXOpBxiMdu8nPbsyhrPCbYHGkS8wb7j84+dw6XOskHKsfuaeDfg24QVUL3fvfVNV6EYkBYlU1zb3/ZWB8I/v/7sGxTgNWqOougAbHatSRjt3gJS397KYNsT5+EywKcM3X0lBnXAt2HFTjvq+neT/bb6jqLxrZX3GU9wlH/sXk4IdfsNp78J7maOlnN22IfeM3QUFVy4H9IjIFXGvF4pqueeUxNFMGdGpBhhKgqEEf+lVAmrqmjy4RkTPd+69o8LZMYISIhIhIL1xTIQN8CkwQkb7w3ec5YsYjHbu5n8W0bfbNwASTq4G/isgj7u0/qGrGMbz/38BbInIB8Mum+vmbMBtYJCIdgJ3Ate791wIviEglsKTB61fh+qtkA67ZRr8EUNU89ypY74hICK752qcemtHDYxtzTGx2TmOMaWOsq8cYY9oYK/zGGNPGWOE3xpg2xgq/Mca0MVb4jTGmjbHCb4wxbYwVfmOMaWP+H7zqtP1IGOpdAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# generating units\n",
    "N = 5\n",
    "pmax = 2*max(d)/N\n",
    "pmin = 0.6*pmax\n",
    "\n",
    "N = np.array([n for n in range(0, N)])\n",
    "a = np.array([0.5 + 0.2*np.random.randn() for n in N])\n",
    "b = np.array([10*np.random.uniform() for n in N])\n",
    "\n",
    "p = np.linspace(pmin, pmax)\n",
    "\n",
    "fig, ax = plt.subplots(1,1)\n",
    "for n in N:\n",
    "    ax.plot(p, a[n]*p + b[n])\n",
    "ax.set_xlim(0, pmax)\n",
    "ax.set_ylim(0, max(a*pmax + b))\n",
    "ax.set_xlabel('Unit Production')\n",
    "ax.set_ylabel('Unit Operating Cost')\n",
    "ax.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pyomo model 1: Conventional implementation for emi-continuous variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# ==========================================================\n",
      "# = Solver Results                                         =\n",
      "# ==========================================================\n",
      "# ----------------------------------------------------------\n",
      "#   Problem Information\n",
      "# ----------------------------------------------------------\n",
      "Problem: \n",
      "- Name: unknown\n",
      "  Lower bound: 2078.39330587\n",
      "  Upper bound: 2078.39330587\n",
      "  Number of objectives: 1\n",
      "  Number of constraints: 200\n",
      "  Number of variables: 180\n",
      "  Number of binary variables: 100\n",
      "  Number of integer variables: 100\n",
      "  Number of nonzeros: 180\n",
      "  Sense: minimize\n",
      "# ----------------------------------------------------------\n",
      "#   Solver Information\n",
      "# ----------------------------------------------------------\n",
      "Solver: \n",
      "- Status: ok\n",
      "  User time: -1.0\n",
      "  System time: 0.21\n",
      "  Wallclock time: 0.23\n",
      "  Termination condition: optimal\n",
      "  Termination message: Model was solved to optimality (subject to tolerances), and an optimal solution is available.\n",
      "  Statistics: \n",
      "    Branch and bound: \n",
      "      Number of bounded subproblems: 0\n",
      "      Number of created subproblems: 0\n",
      "    Black box: \n",
      "      Number of iterations: 85\n",
      "  Error rc: 0\n",
      "  Time: 0.2525980472564697\n",
      "# ----------------------------------------------------------\n",
      "#   Solution Information\n",
      "# ----------------------------------------------------------\n",
      "Solution: \n",
      "- number of solutions: 0\n",
      "  number of solutions displayed: 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x504 with 5 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def unit_commitment():\n",
    "    m = pyo.ConcreteModel()\n",
    "\n",
    "    m.N = pyo.Set(initialize=N)\n",
    "    m.T = pyo.Set(initialize=T)\n",
    "\n",
    "    m.x = pyo.Var(m.N, m.T, bounds = (0, pmax))\n",
    "    m.u = pyo.Var(m.N, m.T, domain=pyo.Binary)\n",
    "    \n",
    "    # objective\n",
    "    m.cost = pyo.Objective(expr = sum(m.x[n,t]*a[n] + m.u[n,t]*b[n] for t in m.T for n in m.N), sense=pyo.minimize)\n",
    "    \n",
    "    # demand\n",
    "    m.demand = pyo.Constraint(m.T, rule=lambda m, t: sum(m.x[n,t] for n in N) == d[t])\n",
    "    \n",
    "    # semi-continuous\n",
    "    m.lb = pyo.Constraint(m.N, m.T, rule=lambda m, n, t: pmin*m.u[n,t] <= m.x[n,t])\n",
    "    m.ub = pyo.Constraint(m.N, m.T, rule=lambda m, n, t: pmax*m.u[n,t] >= m.x[n,t])\n",
    "    return m\n",
    "   \n",
    "m = unit_commitment()\n",
    "pyo.SolverFactory('cbc').solve(m).write()\n",
    "\n",
    "fig, ax = plt.subplots(max(N)+1, 1, figsize=(8, 1.5*max(N)+1))\n",
    "for n in N:\n",
    "    ax[n].bar(T+1, [m.x[n,t]() for t in T])\n",
    "    ax[n].set_xlim(0, max(T)+2)\n",
    "    ax[n].set_ylim(0, 1.1*pmax)\n",
    "    ax[n].plot(ax[n].get_xlim(), np.array([pmax, pmax]), 'r--')\n",
    "    ax[n].plot(ax[n].get_xlim(), np.array([pmin, pmin]), 'r--')\n",
    "    ax[n].set_title('Unit ' + str(n+1))\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pyomo model 2: GDP implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[0,0].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[1,0].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[2,0].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[3,0].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[4,0].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[0,1].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[1,1].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[2,1].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[3,1].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[4,1].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[0,2].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[1,2].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[2,2].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[3,2].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[4,2].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[0,3].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[1,3].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[2,3].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[3,3].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[4,3].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[0,4].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[1,4].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[2,4].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[3,4].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[4,4].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[0,5].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[1,5].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[2,5].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[3,5].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[4,5].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[0,6].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[1,6].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[2,6].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[3,6].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[4,6].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[0,7].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[1,7].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[2,7].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[3,7].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[4,7].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[0,8].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[1,8].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[2,8].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[3,8].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[4,8].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[0,9].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[1,9].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[2,9].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[3,9].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[4,9].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[0,10].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[1,10].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[2,10].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[3,10].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[4,10].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[0,11].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[1,11].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[2,11].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[3,11].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[4,11].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[0,12].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[1,12].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[2,12].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[3,12].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[4,12].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[0,13].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[1,13].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[2,13].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[3,13].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[4,13].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[0,14].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[1,14].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[2,14].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[3,14].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[4,14].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[0,15].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[1,15].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[2,15].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[3,15].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[4,15].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[0,16].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[1,16].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[2,16].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[3,16].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[4,16].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[0,17].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[1,17].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[2,17].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[3,17].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[4,17].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[0,18].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[1,18].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[2,18].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[3,18].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[4,18].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[0,19].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[1,19].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[2,19].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[3,19].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "WARNING: DEPRECATED: Implicit conversion of the Boolean indicator_var\n",
      "    'sc2[4,19].indicator_var' to a binary variable is deprecated and will be\n",
      "    removed.  Either express constraints on indicator_var using\n",
      "    LogicalConstraints or work with the associated binary variable from\n",
      "    indicator_var.get_associated_binary()  (deprecated in 6.0) (called from /v\n",
      "    ar/folders/cm/z3t28j296f98jdp1vqyplkz00000gn/T/ipykernel_32621/270333742.p\n",
      "    y:18)\n",
      "# ==========================================================\n",
      "# = Solver Results                                         =\n",
      "# ==========================================================\n",
      "# ----------------------------------------------------------\n",
      "#   Problem Information\n",
      "# ----------------------------------------------------------\n",
      "Problem: \n",
      "- Name: unknown\n",
      "  Lower bound: 1789.58530805\n",
      "  Upper bound: 1789.58530805\n",
      "  Number of objectives: 1\n",
      "  Number of constraints: 20\n",
      "  Number of variables: 100\n",
      "  Number of binary variables: 200\n",
      "  Number of integer variables: 200\n",
      "  Number of nonzeros: 100\n",
      "  Sense: minimize\n",
      "# ----------------------------------------------------------\n",
      "#   Solver Information\n",
      "# ----------------------------------------------------------\n",
      "Solver: \n",
      "- Status: ok\n",
      "  User time: -1.0\n",
      "  System time: 0.24\n",
      "  Wallclock time: 0.25\n",
      "  Termination condition: optimal\n",
      "  Termination message: Model was solved to optimality (subject to tolerances), and an optimal solution is available.\n",
      "  Statistics: \n",
      "    Branch and bound: \n",
      "      Number of bounded subproblems: 0\n",
      "      Number of created subproblems: 0\n",
      "    Black box: \n",
      "      Number of iterations: 0\n",
      "  Error rc: 0\n",
      "  Time: 0.28235697746276855\n",
      "# ----------------------------------------------------------\n",
      "#   Solution Information\n",
      "# ----------------------------------------------------------\n",
      "Solution: \n",
      "- number of solutions: 0\n",
      "  number of solutions displayed: 0\n"
     ]
    }
   ],
   "source": [
    "def unit_commitment_gdp():\n",
    "    m = pyo.ConcreteModel()\n",
    "\n",
    "    m.N = pyo.Set(initialize=N)\n",
    "    m.T = pyo.Set(initialize=T)\n",
    "\n",
    "    m.x = pyo.Var(m.N, m.T, bounds = (0, pmax))\n",
    "    \n",
    "    # demand\n",
    "    m.demand = pyo.Constraint(m.T, rule=lambda m, t: sum(m.x[n,t] for n in N) == d[t])\n",
    "    \n",
    "    # representing the semicontinous variables as disjuctions\n",
    "    m.sc1 = gdp.Disjunct(m.N, m.T, rule=lambda d, n, t: d.model().x[n,t] == 0)\n",
    "    m.sc2 = gdp.Disjunct(m.N, m.T, rule=lambda d, n, t: d.model().x[n,t] >= pmin)\n",
    "    m.sc = gdp.Disjunction(m.N, m.T, rule=lambda m, n, t: [m.sc1[n,t], m.sc2[n,t]])\n",
    "    \n",
    "    # objective. Note use of the disjunct indicator variable\n",
    "    m.cost = pyo.Objective(expr = sum(m.x[n,t]*a[n] + m.sc2[n,t].indicator_var*b[n] for t in m.T for n in m.N), sense=pyo.minimize)\n",
    "\n",
    "    # alternative formulation. But how to access the indicator variable?\n",
    "    #m.semicontinuous = gdp.Disjunction(m.N, m.T, rule=lambda m, n, t: [m.x[n,t]==0, m.x[n,t] >= pmin])\n",
    "    pyo.TransformationFactory('gdp.hull').apply_to(m)\n",
    "    return m\n",
    "   \n",
    "m_gdp = unit_commitment_gdp()\n",
    "pyo.SolverFactory('cbc').solve(m_gdp).write()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### There is a problem here!\n",
    "\n",
    "Why are the results different?  Somehow it appears values of the indicator variables are being ignored."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n =  0  t =  0   True False  46.85\n",
      "n =  0  t =  1   True False   0.00\n",
      "n =  0  t =  2   True False  46.85\n",
      "n =  0  t =  3   True False  46.85\n",
      "n =  0  t =  4   True False  46.85\n",
      "n =  0  t =  5   True False   0.00\n",
      "n =  0  t =  6   True False  46.85\n",
      "n =  0  t =  7   True False   0.00\n",
      "n =  0  t =  8   True False   0.00\n",
      "n =  0  t =  9   True False   0.00\n",
      "n =  0  t = 10   True False   0.00\n",
      "n =  0  t = 11   True False  46.85\n",
      "n =  0  t = 12   True False  46.85\n",
      "n =  0  t = 13   True False   0.00\n",
      "n =  0  t = 14   True False   0.00\n",
      "n =  0  t = 15   True False   0.00\n",
      "n =  0  t = 16   True False   0.00\n",
      "n =  0  t = 17   True False  46.85\n",
      "n =  0  t = 18   True False  46.85\n",
      "n =  0  t = 19   True False  46.85\n",
      "n =  1  t =  0   True False   0.00\n",
      "n =  1  t =  1   True False   0.00\n",
      "n =  1  t =  2   True False   0.00\n",
      "n =  1  t =  3   True False   0.00\n",
      "n =  1  t =  4   True False   0.00\n",
      "n =  1  t =  5   True False   0.00\n",
      "n =  1  t =  6   True False   0.00\n",
      "n =  1  t =  7   True False   0.00\n",
      "n =  1  t =  8   True False   0.00\n",
      "n =  1  t =  9   True False   0.00\n",
      "n =  1  t = 10   True False   0.00\n",
      "n =  1  t = 11   True False   0.00\n",
      "n =  1  t = 12   True False   0.00\n",
      "n =  1  t = 13   True False   0.00\n",
      "n =  1  t = 14   True False   0.00\n",
      "n =  1  t = 15   True False   0.00\n",
      "n =  1  t = 16   True False   0.00\n",
      "n =  1  t = 17   True False   0.00\n",
      "n =  1  t = 18   True False   0.00\n",
      "n =  1  t = 19   True False   0.00\n",
      "n =  2  t =  0   True False  69.26\n",
      "n =  2  t =  1   True False  78.08\n",
      "n =  2  t =  2   True False  72.66\n",
      "n =  2  t =  3   True False  78.08\n",
      "n =  2  t =  4   True False  78.08\n",
      "n =  2  t =  5   True False  78.08\n",
      "n =  2  t =  6   True False  78.08\n",
      "n =  2  t =  7   True False  78.08\n",
      "n =  2  t =  8   True False  78.08\n",
      "n =  2  t =  9   True False  78.08\n",
      "n =  2  t = 10   True False  56.01\n",
      "n =  2  t = 11   True False  69.44\n",
      "n =  2  t = 12   True False  78.08\n",
      "n =  2  t = 13   True False  75.63\n",
      "n =  2  t = 14   True False  78.08\n",
      "n =  2  t = 15   True False  58.14\n",
      "n =  2  t = 16   True False  78.08\n",
      "n =  2  t = 17   True False  78.08\n",
      "n =  2  t = 18   True False  70.69\n",
      "n =  2  t = 19   True False  78.08\n",
      "n =  3  t =  0   True False   0.00\n",
      "n =  3  t =  1   True False   0.00\n",
      "n =  3  t =  2   True False   0.00\n",
      "n =  3  t =  3   True False   0.00\n",
      "n =  3  t =  4   True False   0.00\n",
      "n =  3  t =  5   True False   0.00\n",
      "n =  3  t =  6   True False   0.00\n",
      "n =  3  t =  7   True False   0.00\n",
      "n =  3  t =  8   True False   0.00\n",
      "n =  3  t =  9   True False   0.00\n",
      "n =  3  t = 10   True False   0.00\n",
      "n =  3  t = 11   True False   0.00\n",
      "n =  3  t = 12   True False   0.00\n",
      "n =  3  t = 13   True False   0.00\n",
      "n =  3  t = 14   True False   0.00\n",
      "n =  3  t = 15   True False   0.00\n",
      "n =  3  t = 16   True False   0.00\n",
      "n =  3  t = 17   True False   0.00\n",
      "n =  3  t = 18   True False   0.00\n",
      "n =  3  t = 19   True False   0.00\n",
      "n =  4  t =  0   True False  46.85\n",
      "n =  4  t =  1   True False  58.87\n",
      "n =  4  t =  2   True False  46.85\n",
      "n =  4  t =  3   True False  60.14\n",
      "n =  4  t =  4   True False  59.28\n",
      "n =  4  t =  5   True False  71.02\n",
      "n =  4  t =  6   True False  62.14\n",
      "n =  4  t =  7   True False  74.93\n",
      "n =  4  t =  8   True False  66.69\n",
      "n =  4  t =  9   True False  67.96\n",
      "n =  4  t = 10   True False  46.85\n",
      "n =  4  t = 11   True False  46.85\n",
      "n =  4  t = 12   True False  67.69\n",
      "n =  4  t = 13   True False  46.85\n",
      "n =  4  t = 14   True False  59.46\n",
      "n =  4  t = 15   True False  46.85\n",
      "n =  4  t = 16   True False  76.70\n",
      "n =  4  t = 17   True False  70.27\n",
      "n =  4  t = 18   True False  46.85\n",
      "n =  4  t = 19   True False  67.73\n"
     ]
    }
   ],
   "source": [
    "for n in N:\n",
    "    for t in T:\n",
    "        print(\"n = {0:2d}  t = {1:2d}   {2} {3}  {4:5.2f}\".format(n, t, m_gdp.sc1[n,t].indicator_var(), m_gdp.sc2[n,t].indicator_var(), m.x[n,t]()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
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   "name": "04.05-Unit-Commitment.ipynb",
   "provenance": [
    {
     "file_id": "https://github.com/jckantor/ND-Pyomo-Cookbook/blob/master/notebooks/04.03-Maintenance-Planning.ipynb",
     "timestamp": 1561638344737
    },
    {
     "file_id": "https://github.com/jckantor/ND-Pyomo-Cookbook/blob/master/notebooks/04.03-Maintenance-Planning.ipynb",
     "timestamp": 1556576712896
    }
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   "toc_visible": true,
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    "name": "ipython",
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