{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Facility location assignment\n",
    "\n",
    "Instructor: Frans de Ruiter\n",
    "\n",
    "For assignment and data, see https://www.fransderuiter.com/JADS/\n",
    "\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from pyomo.environ import *\n",
    "import matplotlib.pyplot as plt # optional for plotting\n",
    "from matplotlib import cm # optional for plotting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Read data\n",
    "Here we load the distance table between the cities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_path = \"https://www.fransderuiter.com/JADS/Facilitylocation/FacilityLocation.xlsx\"\n",
    "# Create pandas table\n",
    "distances = pd.read_excel(data_path, sheet_name=0, header=0, skiprows=2, index_col=1)\n",
    "\n",
    "# Show table\n",
    "distances.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some data processing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "#remove 1st column ('unnamed', because there is a comment in first column it was added in the database)\n",
    "distances = distances.drop(distances.columns[0],1)\n",
    "\n",
    "# Show table with removed column\n",
    "distances.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "## Show index names\n",
    "cities = distances.columns\n",
    "print(cities)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Fixed cost for opening a DC (same for each city)\n",
    "fixed_cost = 150000\n",
    "\n",
    "# demand equals 100 for each city\n",
    "demand_per_city = 100\n",
    "\n",
    "# Supply capacity of each city is 4000\n",
    "M = 4000\n",
    "\n",
    "# Create pandas dataframe with supply\n",
    "city_params_dict = {'supply': M*np.ones(cities.size, int), \n",
    "                    'demand': demand_per_city*np.ones(cities.size, int), \n",
    "                    'fixed cost': fixed_cost*np.ones(cities.size, int)}\n",
    "city_params = pd.DataFrame(data=city_params_dict, index = cities)\n",
    "city_params.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# extract the fixed costs for a city (in this case \"Athens\") as follows:\n",
    "i_1 = 'Athens'\n",
    "city_params.loc[i_1,'fixed cost']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# extract the fixed costs for a city (in this case \"Athens\" to \"Amsterdam\") as follows:\n",
    "i_1 = 'Athens'\n",
    "j_1 = 'Amsterdam'\n",
    "distances[i_1][j_1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# TODO\n",
    "# write your optimization model in the cell here by replacing the XXXX in the cells\n",
    "\n",
    "# Create model\n",
    "m = ConcreteModel()\n",
    "\n",
    "# Variables\n",
    "m.locations = Var(cities, within=Binary)\n",
    "m.shipments = Var(cities, cities, within = NonNegativeReals)\n",
    "\n",
    "# Objective\n",
    "m.value = Objective(\n",
    "    expr=sum( XXXX for i in cities)\n",
    "    + sum( XXXX for i in cities for j in cities)\n",
    "    , sense=minimize)\n",
    "    \n",
    "# Constraints on supplying only when facility is open\n",
    "m.supply_restriction = ConstraintList()\n",
    "for i in cities:\n",
    "    m.supply_restriction.add( XXXX )\n",
    "\n",
    "# Constraints on demand fulfillment\n",
    "m.demand_fulfillment = ConstraintList()\n",
    "for j in cities:\n",
    "    m.demand_fulfillment.add( XXXX )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solve the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Optimize\n",
    "solver = SolverFactory('cbc') # Take the cbc solver, glpk is very slow\n",
    "status = solver.solve(m,tee=False,) # Set tee to True to see log of the solver\n",
    "\n",
    "# Print the status of the solved mixed integer linear model once it is done\n",
    "print(\"Status = %s \\n\" % status.solver.termination_condition)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Show the solution\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Show some visualization via tables and/or plots to present your solution.\n",
    "#TODO (optional): add more visualization, print your solution etc\n",
    "\n",
    "# Make a vector with all the shipments\n",
    "totalshipments = [sum(value(m.shipments[i,j]) for j in cities) for i in cities]\n",
    "\n",
    "plt.figure(figsize=(3,10))\n",
    "\n",
    "# make a horizontal bar plots\n",
    "plt.barh(range(cities.size),totalshipments, color=\"blue\",align=\"center\") \n",
    "\n",
    "# Use city names on the vertical axis\n",
    "plt.yticks(range(cities.size),cities,rotation=0)\n",
    "\n",
    "# Set title and show plot\n",
    "plt.title('Total shipments per DC',fontsize=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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