nurse_scheduling_2shifts_1week.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Nurse scheduling problem \n",
    "\n",
    "## Implementing linear programming  algorithm to solve the NP-hard nurse scheduling problem. \n",
    "\n",
    "\n",
    "### Some basic constraints and assumptions:\n",
    "\n",
    "* Each day is divided into 2 separate shifts of 12 hours (day/night).\n",
    "\n",
    "* There are a number of required nurses for each of them. \n",
    "\n",
    "* A nurse is off on a specific day if no shift is assigned or if the nurse has requested a PTO on that specific day. \n",
    "\n",
    "* The planning length is 4 weeks (28 days). \n",
    "    \n",
    "    * In this notebook, used 1 week instead for the purpose of convenience and easy visualization.\n",
    "\n",
    "* Each nurse should work either 12, 24 or 36 hours hours per week.\n",
    "\n",
    "\n",
    "### I personally add few more constraints:\n",
    "\n",
    "* No nurse will work on both shifts in the single day.\n",
    "\n",
    "* A nurse who works on a nigth shift will take the next day off.\n",
    "\n",
    "* Max numbers of night shift for each nurse is at most ONE."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import scipy as sp\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "from pandas.tools.plotting import table\n",
    "import os, sys, json\n",
    "from pulp import *\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model:\n",
    "\n",
    "* Essential idea is to introduce a binary variable ***x_ns*** in order to linearize the model\n",
    "\n",
    "* Constraints and objective function can be represented as equality and inequality equations.\n",
    "\n",
    "\\begin{align}\n",
    "    x_{ns}= \n",
    "        \\begin{cases}\n",
    "            0, &\\text{nurse n will not work on shift s}\\ \\\\\n",
    "            1, &\\text{nurse n will work on shift s}\\\n",
    "        \\end{cases}\n",
    "\\end{align}\n",
    "\n",
    "* s: each shift\n",
    "\n",
    "* n: each nurse\n",
    "\n",
    "* r: list storing the required nurses in each day.\n",
    "\n",
    "\n",
    "\\begin{align}\n",
    "    \\text{r} = [\\text{number of nurses required in specific shift s}] \\\\\n",
    "    \\text{r[even index]} = [\\text{number of nurses required in day shifts}] \\\\\n",
    "    \\text{r[odd index]} = [\\text{number of nurses required in night shifts}] \n",
    "\\end{align}\n",
    "\n",
    "* PTO = Dictionary which stores the information of the off-work shifts(nurses requested PTO or other reasons)\n",
    "\n",
    "\\begin{align}\n",
    "    \\text{PTO} = \\{n : [\\text{list of off-work shifts for nurse n}]\\}\n",
    "\\end{align}\n",
    "\n",
    "\n",
    "* daily_shift: [0, 1] in this case(day = 0 /night = 1).\n",
    "\n",
    "* working_shift = [1,2,3]: nurse works either 12, 24, 36 hours per week.\n",
    "\n",
    "* planning_length: in this notebook, planning_length = 1. \n",
    "\n",
    "* Objective: minimize the numbers of scheduled nurses by satisfying all constraints. \n",
    "\n",
    "* Later on, preference of specific shifts/nurse and other constraints can be customized. \n",
    "\n",
    "* Implementing linear programming with pulp python package to find the solution of this constrained optimization problem. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initializing the parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The number of nurses required for each shift is:\n",
      "[5 3 5 3 5 3 5 3 5 3 5 3 5 3]\n",
      "\n",
      "In matrix form:\n",
      "   M Tu  W Th  F Sa Su\n",
      "0  5  5  5  5  5  5  5\n",
      "1  3  3  3  3  3  3  3\n",
      "\n",
      "Total number of nurses are: 22\n",
      "\n",
      "The nurses are: \n",
      "['nurse0', 'nurse1', 'nurse2', 'nurse3', 'nurse4', 'nurse5', 'nurse6', 'nurse7', 'nurse8', 'nurse9', 'nurse10', 'nurse11', 'nurse12', 'nurse13', 'nurse14', 'nurse15', 'nurse16', 'nurse17', 'nurse18', 'nurse19', 'nurse20', 'nurse21']\n"
     ]
    }
   ],
   "source": [
    "# nurse works either 12, 24, 36 hours per week.\n",
    "working_shift = [1, 2, 3] \n",
    "\n",
    "# maximum shifts that nurse will work\n",
    "max_shifts = 3\n",
    "\n",
    "# planning_length\n",
    "planning_length = 1 \n",
    "\n",
    "# Numbers of shift per day:\n",
    "daily_shift = [0, 1]\n",
    "\n",
    "# Label the days from Monday to Sunday. \n",
    "d = ['M', 'Tu', 'W', 'Th', 'F','Sa','Su']\n",
    "\n",
    "# Create the require_nurses dataframe\n",
    "# day_nurse: Number of nurses required in day shift.\n",
    "# night_nurse: Number of nurses required in night shift.\n",
    "col = range(0, 7*planning_length)\n",
    "\n",
    "require_nurses = pd.DataFrame(data = None, columns=d, index = daily_shift)\n",
    "\n",
    "for j in col:\n",
    "    # Small number is better for visualization.\n",
    "    day_nurse, night_nurse = 5, 3\n",
    "    require_nurses.iloc[0][j] = day_nurse\n",
    "    require_nurses.iloc[1][j] = night_nurse\n",
    "\n",
    "# List of number of nurses required in specific shift s\n",
    "\n",
    "# r[even index]: required nurses in day shift\n",
    "# r[odd index]: required nurses in night shift\n",
    "r = require_nurses.values.swapaxes(0,1).ravel()\n",
    "\n",
    "print \"The number of nurses required for each shift is:\" \n",
    "print r\n",
    "\n",
    "print \"\\nIn matrix form:\" \n",
    "print require_nurses.head()\n",
    "\n",
    "\n",
    "# Total number of the nurses, at least more than sum(r)/3. Here use sum(r)/2.5\n",
    "total = int(sum(r)/2.5)\n",
    "print \"\\nTotal number of nurses are: {}\".format(total)\n",
    "\n",
    "# Create nurses_id tag\n",
    "nurses_id = ['nurse'+str(i) for i in range(total)]\n",
    "print \"\\nThe nurses are: \"\n",
    "print nurses_id"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Nurse is off on specific shifts: PTO dictionary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{u'10': [3], u'15': [2], u'0': [1], u'3': [12, 10], u'2': [0], u'5': [1], u'4': [7, 13]}\n"
     ]
    }
   ],
   "source": [
    "# nurse has requested a PTO on that specific day or whatever reasons. \n",
    "\n",
    "with open('utils/off_shift.json', 'r') as fp:\n",
    "    off_shift = json.load(fp)\n",
    "    \n",
    "print off_shift"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Shifts and nurses lists"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The shifts are: \n",
      "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]\n",
      "\n",
      "The names of corresponding shifts are: \n",
      "['M_d', 'M_n', 'Tu_d', 'Tu_n', 'W_d', 'W_n', 'Th_d', 'Th_n', 'F_d', 'F_n', 'Sa_d', 'Sa_n', 'Su_d', 'Su_n']\n",
      "\n",
      "The nurses are: \n",
      "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21]\n"
     ]
    }
   ],
   "source": [
    "'''\n",
    "shifts: label each shift. For example: Monday day shift is 0, Monday night shift is 1, Tuesday day shift is 2, etc.\n",
    "nurses: label each nurse. Simply use integers to represent.\n",
    "'''\n",
    "\n",
    "shifts = range(2*7*planning_length)\n",
    "nurses = range(total)\n",
    "\n",
    "## Create shift names based on index:\n",
    "shift_name = []\n",
    "for s in shifts:\n",
    "    # find the day shift or night shift\n",
    "    n_or_day = 'n' if s%2 else 'd' \n",
    "    shift_name.append(d[s/2] + '_' + n_or_day)\n",
    "    \n",
    "print \"The shifts are: \" \n",
    "print shifts\n",
    "\n",
    "print \"\\nThe names of corresponding shifts are: \"\n",
    "print shift_name\n",
    "\n",
    "print \"\\nThe nurses are: \"\n",
    "print nurses"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Build constraint models:\n",
    "\n",
    "* var = pulp.LpVariable(name, lowbound, upbound, cat=\"Binary\")\n",
    "\n",
    "* pb = pulp.LpProblem(name_str, sense = 'LpMaximize' or LpMinimize)\n",
    "\n",
    "\n",
    "* problem.solve(pulp.solvers.GLPK(msg=0))\n",
    "\n",
    "* check status: pulp.LpStatus(pb.status)\n",
    "\n",
    "* pulp.value(pb.objective)\n",
    "\n",
    "* Optimal solution: var.varValue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def LpProb():\n",
    "\n",
    "    '''\n",
    "    Use pulp to solve the constrained problem using linear programming(LP) algorithm. \n",
    "    1. Start the instance of a LpProblem: pulp.LpProblem(name_str, sense = 'LpMaxmize' or 'LpMinimize')\n",
    "    2. Create LpVariables. Binary category in this case\n",
    "    3. Add constraints in either equality or inequality conditions.\n",
    "    4. Building objective using LpObjective. \n",
    "    5. Use Solver to solve the problem, display the status and optimized values.\n",
    "    '''\n",
    "\n",
    "    # The prob variable is created to contain the problem data   \n",
    "    prob = LpProblem(\"Nurse scheduling\",LpMinimize)\n",
    "    \n",
    "    # Creating the variables. \n",
    "    var = {\n",
    "     (n, s): pulp.LpVariable(\n",
    "        \"schdule_{0}_{1}\".format(n, s), cat = \"Binary\")\n",
    "        for n in nurses for s in shifts\n",
    "    }\n",
    "\n",
    "    \n",
    "    # add constraints: \n",
    "    # Nurses do not work in two consecutive shifts\n",
    "    # If nurse works for a night shift, he/she will take a next day off\n",
    "\n",
    "    for n in nurses:\n",
    "        for s in shifts:\n",
    "            if s%2 == 0:\n",
    "                prob.addConstraint(\n",
    "                var[(n,s)] + var[(n, s+1)] <= 1  # for day shift\n",
    "               )\n",
    "            elif s%2 == 1 and s < shifts[-1]:\n",
    "                # night shift. Do not forget to add condition that the last\n",
    "                # shift in the scheduling does not count.\n",
    "                prob.addConstraint(\n",
    "                var[(n, s)] + var[(n, s+1)]+var[(n, s+2)] <= 1\n",
    "                )\n",
    "\n",
    "    # add constraints:\n",
    "    # Request PTO or take a specific day off:\n",
    "    for n in nurses:\n",
    "        if str(n) in off_shift:\n",
    "            for s in off_shift[str(n)]:\n",
    "                prob.addConstraint(\n",
    "                var[(n, s)] == 0\n",
    "                )\n",
    "\n",
    "    # add constraints:\n",
    "    # Working shift is either 1, 2 or 3\n",
    "    # Here the first calculation is based on \n",
    "    for n in nurses:\n",
    "        prob.addConstraint(\n",
    "        sum(var[(n,s)] for s in shifts) <= 3    \n",
    "        )\n",
    "        prob.addConstraint(\n",
    "        sum(var[(n,s)] for s in shifts) >= 1\n",
    "        )\n",
    "\n",
    "    # add constraints\n",
    "    # Max numbers of night shift is one for each nurse\n",
    "\n",
    "    for n in nurses:\n",
    "        prob.addConstraint(\n",
    "        sum(var[(n, s)] for s in shifts if s%2) <= 1\n",
    "        )\n",
    "    # add constraints\n",
    "    # for each shift, the numbers of working nurses should be greater than\n",
    "    # the required numbers of nurses\n",
    "    for s in shifts:\n",
    "        try:\n",
    "            prob.addConstraint(\n",
    "            sum(var[(n,s)] for n in nurses) >= r[s]\n",
    "            )\n",
    "        except:\n",
    "            print \"len(shifts) should be equal to len(require_nurses)\"\n",
    "            sys.exit(-1)   \n",
    "\n",
    "            \n",
    "    # add objective: minimize the numbers of total nurses required\n",
    "    # nurse_working = []\n",
    "    # for s in shifts:\n",
    "    #     nurse_shift = sum(var[(n, s)] for n in nurses)\n",
    "    #     nurse_working.append(\n",
    "    #     pulp.LpVariable(\"nurses_%d\"%(s,), cat = 'Integer', lowBound = 0)\n",
    "    #     )\n",
    "    prob.objective = sum(var[(n,s)] for n in nurses for s in shifts)    \n",
    "    \n",
    "    return var, prob"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimal\n"
     ]
    }
   ],
   "source": [
    "## Run the solver\n",
    "\n",
    "var, prob = LpProb()\n",
    "prob.solve()\n",
    "print LpStatus[prob.status]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Check Constraints"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Check the off_shift constraint: True\n"
     ]
    }
   ],
   "source": [
    "def check_off_shift():\n",
    "    # return True if the constraints have been satisfied otherwise return False\n",
    "\n",
    "    for n in nurses:\n",
    "        if str(n) in off_shift:\n",
    "            for s in off_shift[str(n)]:\n",
    "                if value(var[(n,s)]) == 1:\n",
    "                    print n, s\n",
    "                    return False\n",
    "\n",
    "    for n in nurses:\n",
    "        for s in shifts:\n",
    "            if s%2 == 0:\n",
    "                if value(var[(n,s)]) + value(var[(n, s+1)]) > 1:\n",
    "                    return False  # for day shift\n",
    "            elif s%2 == 1 and s < shifts[-1]:\n",
    "                if value(var[(n,s)]) + value(var[(n,s+1)]) + value(var[(n, s+2)]) > 1:\n",
    "                    return False\n",
    "\n",
    "    for n in nurses:\n",
    "        tmp = sum(value(var[(n,s)]) for s in shifts) \n",
    "        if tmp > 3 or tmp < 1:\n",
    "            return False\n",
    "\n",
    "    for n in nurses:\n",
    "        if sum(value(var[(n, s)]) for s in shifts if s%2) > 1:\n",
    "            return False\n",
    "\n",
    "    for s in shifts:\n",
    "        try:\n",
    "            if sum(value(var[(n,s)]) for n in nurses) < r[s]:\n",
    "                return False\n",
    "        except:\n",
    "            print \"len(shifts) should be equal to len(require_nurses)\"\n",
    "            sys.exit(-1)   \n",
    "\n",
    "    return True\n",
    "\n",
    "\n",
    "\n",
    "print \"Check the off_shift constraint: {}\".format(check_off_shift())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Find the schedule for all nurses"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def nurse_scheduling(var = var):\n",
    "\n",
    "    schedule = pd.DataFrame(data=None, index = nurses_id, columns = shift_name)\n",
    "    \n",
    "    for k, v in var.items():\n",
    "        n, s = k[0], k[1]\n",
    "        schedule.iloc[n][s] = int(value(v)) # pulp.value()\n",
    "        \n",
    "    return schedule"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>M_d</th>\n",
       "      <th>M_n</th>\n",
       "      <th>Tu_d</th>\n",
       "      <th>Tu_n</th>\n",
       "      <th>W_d</th>\n",
       "      <th>W_n</th>\n",
       "      <th>Th_d</th>\n",
       "      <th>Th_n</th>\n",
       "      <th>F_d</th>\n",
       "      <th>F_n</th>\n",
       "      <th>Sa_d</th>\n",
       "      <th>Sa_n</th>\n",
       "      <th>Su_d</th>\n",
       "      <th>Su_n</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>nurse0</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>nurse1</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>nurse2</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>nurse3</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>nurse4</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       M_d M_n Tu_d Tu_n W_d W_n Th_d Th_n F_d F_n Sa_d Sa_n Su_d Su_n\n",
       "nurse0   1   0    1    0   0   0    0    0   0   1    0    0    0    0\n",
       "nurse1   0   1    0    0   0   0    1    0   1   0    0    0    0    0\n",
       "nurse2   0   1    0    0   1   0    1    0   0   0    0    0    0    0\n",
       "nurse3   0   0    1    0   0   0    0    0   0   0    0    0    0    1\n",
       "nurse4   0   0    0    0   0   0    1    0   1   0    0    0    1    0"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "schedule = nurse_scheduling()\n",
    "\n",
    "schedule.head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Find out the schedule for each nurse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Input the nurse id\n",
    "\n",
    "def schedule_which_nurse(nurseWho, table = var):\n",
    "    \n",
    "    '''\n",
    "    nurseWho: nurse id\n",
    "    table: Either the schedule dataframe or the linear programming solution\n",
    "    inputType: if 'lp': use linear programming solution\n",
    "               else: the dataframe\n",
    "    '''\n",
    "    # Get the data for scheduling nurse n:\n",
    "    sch = []\n",
    "       \n",
    "    for s in shifts:\n",
    "        sch.append(\n",
    "            int(value(table[(nurseWho, s)]))\n",
    "            )\n",
    "    \n",
    "    sch = np.array(sch).reshape(len(sch)/2, 2).swapaxes(0, 1)\n",
    "    \n",
    "    df_sch = pd.DataFrame(sch, index = ['day', 'night'], columns = d)\n",
    "    \n",
    "    return df_sch\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The schedule for the nurse0 is:\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>M</th>\n",
       "      <th>Tu</th>\n",
       "      <th>W</th>\n",
       "      <th>Th</th>\n",
       "      <th>F</th>\n",
       "      <th>Sa</th>\n",
       "      <th>Su</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>day</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>night</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       M  Tu  W  Th  F  Sa  Su\n",
       "day    1   1  0   0  0   0   0\n",
       "night  0   0  0   0  1   0   0"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nurse0 = schedule_which_nurse(0)\n",
    "\n",
    "print \"The schedule for the nurse0 is:\"\n",
    "\n",
    "nurse0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualize the schedule"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_table(df, figSize = (4,2), saveFig = False, figTitle = 'nurse_scheduling'):\n",
    "     \n",
    "    colors = df.applymap(lambda x: 'lightgray' if x== 0 else 'lightcoral') \n",
    "\n",
    "    fig = plt.figure(figsize=figSize)\n",
    "\n",
    "    ax = plt.subplot(2, 1, 1, frame_on = True)  # no visible frame\n",
    "    #ax.xaxis.set_visible(False)  # hide the x axis\n",
    "    #ax.yaxis.set_visible(False)\n",
    "    ax.axis('off')\n",
    "\n",
    "    tb1 = table(ax,df,\n",
    "                loc='center',\n",
    "                cellLoc='center',\n",
    "                cellColours=colors.as_matrix(),\n",
    "                fontsize=14\n",
    "          )\n",
    "\n",
    "    if saveFig == True:\n",
    "        if not os.path.isdir('figs/notebook/'):\n",
    "            os.mkdir('figs/notebook/')\n",
    "        plt.savefig('figs/notebook/'+ figTitle +'.png', bbox_inches='tight', dpi = 150)\n",
    "\n",
    "    # refresh the plot\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The schedule of all nurses: \n"
     ]
    },
    {
     "data": {
      "image/png": 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T7PYRnVo2pultNU+gqqqKv/u7v+PMmTP4+Pjw8ssv861vfQuz2TNVm5ub2bFj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\nP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U/bzEs/C8xJUpthG2Hz5s0jKCgIm83G9OnTe3R6Sg8PDxISEgC4f/8+ra2tnX/ckSNH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\nL9KNMKWUUkoppZTqRf8HkReBSxxUgQQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1445b2de10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The required nurses are: \n",
      "[5 3 5 3 5 3 5 3 5 3 5 3 5 3]\n"
     ]
    }
   ],
   "source": [
    "print \"The schedule of all nurses: \"\n",
    "plot_table(schedule, figSize = (10, 4), saveFig = True)\n",
    "\n",
    "print \"The required nurses are: \"\n",
    "print r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The schedule of nurses0\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1447780a10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The schedule of nurses1\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1445a75cd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The schedule of nurses2\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1445a75950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The schedule of nurses3\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f14476cbb50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The schedule of nurses4\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1447584390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The schedule of nurses5\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f14475063d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The schedule of nurses6\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1447794050>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The schedule of nurses7\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1447794250>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The schedule of nurses8\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1447d4a150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The schedule of nurses9\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1447cf9950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for n in nurses[:10]:\n",
    "    print 'The schedule of nurses' + str(n)\n",
    "    n0 = schedule_which_nurse(n)\n",
    "    plot_table(n0, saveFig = True, figTitle = 'nurse' + str(n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The schedule of nurses11\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1447c9bb10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The schedule of nurses12\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1447db4fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The schedule of nurses13\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1447ce92d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The schedule of nurses14\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1445bbb1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The schedule of nurses15\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f14474a2cd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The schedule of nurses16\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f14474a26d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The schedule of nurses17\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1447fd6dd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The schedule of nurses18\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f14474abe90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The schedule of nurses19\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1447ef1dd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for n in nurses[11:20]:\n",
    "    print 'The schedule of nurses' + str(n)\n",
    "    n0 = schedule_which_nurse(n)\n",
    "    plot_table(n0, saveFig = True, figTitle = 'nurse' + str(n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [conda root]",
   "language": "python",
   "name": "conda-root-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}