{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "4ed711c8",
   "metadata": {},
   "source": [
    "# The P-Dispersion (max-min-min) Problem\n",
    "\n",
    "*Authors:* [Erin Olson](https://github.com/erinrolson), [James Gaboardi](https://github.com/jGaboardi), [Levi J. Wolf](https://github.com/ljwolf), [Qunshan Zhao](https://github.com/qszhao)\n",
    "\n",
    "\n",
    "When locating some types of facilites a primary objective may be to limit the potential for cascading adverse effects damage should one facility be damaged. Therefore, maximally dispersed arrangement would be the most beneficial. For example, power plants are generally not near other power plants as a precaution against localized damage or disablement during a natural disaster. To address this kind of scenarios with a mixed-integer program, Kuby (1987) described the following problem: _Locate $p$ facilities so that the minimum distance between any pair of facilities is maximized._\n",
    "\n",
    "**P-Dispersion can be written as:**\n",
    "\n",
    "\\begin{equation*}\n",
    "\\textbf{Maximize } D \n",
    "\\end{equation*}\n",
    "\n",
    "___Subject to:___\n",
    "\\begin{equation*}\n",
    "\\sum_{i \\in I} Y_i = p \n",
    "\\end{equation*}\n",
    "\n",
    "\\begin{equation*}\n",
    "D \\leq d_{ij} + M (2 - Y_{i} - Y_{j}), \\quad \\forall i \\in I \\quad \\forall j > i \n",
    "\\end{equation*}\n",
    "\n",
    "\\begin{equation*}\n",
    "Y_i = \\{0,1\\}, \\quad \\forall i \\in I\n",
    "\\end{equation*}\n",
    "\n",
    "___Where:___\n",
    "\n",
    "\\begin{array}{lll}\n",
    "i,j & \\small = & \\textrm{index of potential facility sites} \\\\\n",
    "n & \\small = & \\textrm{number of potential facility sites} \\\\\n",
    "d_{ij} & \\small = & \\textrm{shortest path distance between sites } i \\textrm{ and } j \\\\\n",
    "M & \\small = & \\textrm{some large number; such that } M \\geq \\max_{ij}\\{d_{ij}\\} \\\\\n",
    "p & \\small = & \\textrm{number of facilities to be located} \\\\\n",
    "Y_i & \\small = & \\begin{cases} \n",
    "          1 \\quad \\text{if facility is located at node } i\\\\\n",
    "          0 \\quad \\text{if otherwise} \\\\\n",
    "       \\end{cases} \\end{array}\n",
    "\n",
    "_The above fomulation was adapted from Maliszewski et al (2012), the original formulation is from Kuby (1987)._ \n",
    "\n",
    "This tutorial generates synthetic facility sites near a 10x10 lattice representing a gridded urban core. Three $p$-Dispersion instances are solved while varying parameters:\n",
    "\n",
    "* `PDispersion.from_cost_matrix()` with network distance as the metric\n",
    "* `PDispersion.from_geodataframe()` with euclidean distance as the metric\n",
    "* `PDispersion.from_geodataframe()` with predefined facility locations and euclidean distance as the metric\n",
    "\n",
    "Unlike other facility location models available in `spopt.locate`, the $p$-Dispersion problem does not take demand/client locations into consideration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "67638055",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:30.469050Z",
     "start_time": "2023-01-10T18:23:30.433456Z"
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    "execution": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Last updated: 2023-12-10T14:02:34.599234-05:00\n",
      "\n",
      "Python implementation: CPython\n",
      "Python version       : 3.12.0\n",
      "IPython version      : 8.18.0\n",
      "\n",
      "Compiler    : Clang 15.0.7 \n",
      "OS          : Darwin\n",
      "Release     : 23.1.0\n",
      "Machine     : x86_64\n",
      "Processor   : i386\n",
      "CPU cores   : 8\n",
      "Architecture: 64bit\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%config InlineBackend.figure_format = \"retina\"\n",
    "%load_ext watermark\n",
    "%watermark"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "dfd6bccc",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:33.017045Z",
     "start_time": "2023-01-10T18:23:30.472931Z"
    },
    "execution": {
     "iopub.execute_input": "2023-12-10T19:02:34.617807Z",
     "iopub.status.busy": "2023-12-10T19:02:34.617458Z",
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     "shell.execute_reply.started": "2023-12-10T19:02:34.617779Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Watermark: 2.4.3\n",
      "\n",
      "spopt     : 0.5.1.dev53+g5cadae7\n",
      "spaghetti : 1.7.4\n",
      "geopandas : 0.14.1\n",
      "matplotlib: 3.8.2\n",
      "pulp      : 2.7.0\n",
      "shapely   : 2.0.2\n",
      "numpy     : 1.26.2\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import geopandas\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.patches import Patch\n",
    "import matplotlib.lines as mlines\n",
    "import numpy\n",
    "import pulp\n",
    "import shapely\n",
    "import spopt\n",
    "from spopt.locate import PDispersion, simulated_geo_points\n",
    "\n",
    "import warnings\n",
    "with warnings.catch_warnings():\n",
    "    warnings.simplefilter(\"ignore\")\n",
    "    # ignore deprecation warning - GH pysal/spaghetti#649\n",
    "    import spaghetti\n",
    "\n",
    "%watermark -w\n",
    "%watermark -iv"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e952f337",
   "metadata": {},
   "source": [
    "Since the model needs a cost matrix (distance, time, etc.) we should define some variables. First we will assign some the number of facility locations followed by the random seed in order to reproduce the results. Finally, the solver, assigned below as `pulp.COIN_CMD`, is an interface to optimization solver developed by [COIN-OR](https://github.com/coin-or/Cbc). If you want to use another optimization interface, such as Gurobi or CPLEX, see this [guide](https://coin-"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6725bc44",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:33.028779Z",
     "start_time": "2023-01-10T18:23:33.022873Z"
    },
    "execution": {
     "iopub.execute_input": "2023-12-10T19:02:36.426908Z",
     "iopub.status.busy": "2023-12-10T19:02:36.426211Z",
     "iopub.status.idle": "2023-12-10T19:02:36.430681Z",
     "shell.execute_reply": "2023-12-10T19:02:36.429865Z",
     "shell.execute_reply.started": "2023-12-10T19:02:36.426873Z"
    }
   },
   "outputs": [],
   "source": [
    "# quantity supply points\n",
    "FACILITY_COUNT = 16\n",
    "\n",
    "# number of candidate facilities in optimal solution\n",
    "P_FACILITIES = 3\n",
    "\n",
    "# random seeds for reproducibility\n",
    "FACILITY_SEED = 6\n",
    "\n",
    "# set the solver\n",
    "solver = pulp.COIN_CMD(msg=False, warmStart=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e579217",
   "metadata": {},
   "source": [
    "## Lattice 10x10\n",
    "\n",
    "Create a 10x10 lattice with 9 interior lines, both vertical and horizontal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "4371f5e5",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:33.082856Z",
     "start_time": "2023-01-10T18:23:33.034844Z"
    },
    "execution": {
     "iopub.execute_input": "2023-12-10T19:02:36.432004Z",
     "iopub.status.busy": "2023-12-10T19:02:36.431662Z",
     "iopub.status.idle": "2023-12-10T19:02:36.463798Z",
     "shell.execute_reply": "2023-12-10T19:02:36.463207Z",
     "shell.execute_reply.started": "2023-12-10T19:02:36.431983Z"
    }
   },
   "outputs": [],
   "source": [
    "with warnings.catch_warnings():\n",
    "    warnings.simplefilter(\"ignore\")\n",
    "    # ignore deprecation warning - GH pysal/libpysal#468\n",
    "    lattice = spaghetti.regular_lattice((0, 0, 10, 10), 9, exterior=True)\n",
    "ntw = spaghetti.Network(in_data=lattice)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf6e7748",
   "metadata": {},
   "source": [
    "Transform the `spaghetti` instance into a geodataframe."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d767d1ad",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:33.225733Z",
     "start_time": "2023-01-10T18:23:33.086985Z"
    },
    "execution": {
     "iopub.execute_input": "2023-12-10T19:02:36.465023Z",
     "iopub.status.busy": "2023-12-10T19:02:36.464745Z",
     "iopub.status.idle": "2023-12-10T19:02:36.541632Z",
     "shell.execute_reply": "2023-12-10T19:02:36.540619Z",
     "shell.execute_reply.started": "2023-12-10T19:02:36.465002Z"
    }
   },
   "outputs": [],
   "source": [
    "streets = spaghetti.element_as_gdf(ntw, arcs=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "1f639684",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:33.263515Z",
     "start_time": "2023-01-10T18:23:33.228853Z"
    },
    "execution": {
     "iopub.execute_input": "2023-12-10T19:02:36.543668Z",
     "iopub.status.busy": "2023-12-10T19:02:36.543159Z",
     "iopub.status.idle": "2023-12-10T19:02:36.571459Z",
     "shell.execute_reply": "2023-12-10T19:02:36.570728Z",
     "shell.execute_reply.started": "2023-12-10T19:02:36.543650Z"
    }
   },
   "outputs": [],
   "source": [
    "streets_buffered = geopandas.GeoDataFrame(\n",
    "    geopandas.GeoSeries(streets[\"geometry\"].buffer(0.5).unary_union),\n",
    "    crs=streets.crs,\n",
    "    columns=[\"geometry\"],\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ff2e134",
   "metadata": {},
   "source": [
    "Plotting the network created by `spaghetti` we can verify that it mimics a district with quarters and streets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "d4b67cb3",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:33.471286Z",
     "start_time": "2023-01-10T18:23:33.266165Z"
    },
    "execution": {
     "iopub.execute_input": "2023-12-10T19:02:36.574370Z",
     "iopub.status.busy": "2023-12-10T19:02:36.574128Z",
     "iopub.status.idle": "2023-12-10T19:02:36.738005Z",
     "shell.execute_reply": "2023-12-10T19:02:36.737126Z",
     "shell.execute_reply.started": "2023-12-10T19:02:36.574353Z"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 413,
       "width": 416
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "streets.plot();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8fcf8cfe",
   "metadata": {},
   "source": [
    "## Simulate points in a network\n",
    "\n",
    "The `simulated_geo_points` function simulates points near a network. In this case, it uses the 10x10 lattice network created using the `spaghetti` package. Below we use the function defined above and simulate the points near the lattice edges."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d5aad045",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:33.482666Z",
     "start_time": "2023-01-10T18:23:33.473980Z"
    },
    "execution": {
     "iopub.execute_input": "2023-12-10T19:02:36.739339Z",
     "iopub.status.busy": "2023-12-10T19:02:36.739006Z",
     "iopub.status.idle": "2023-12-10T19:02:36.748063Z",
     "shell.execute_reply": "2023-12-10T19:02:36.747134Z",
     "shell.execute_reply.started": "2023-12-10T19:02:36.739314Z"
    }
   },
   "outputs": [],
   "source": [
    "facility_points = simulated_geo_points(\n",
    "    streets_buffered, needed=FACILITY_COUNT, seed=FACILITY_SEED\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bfb6aa6b",
   "metadata": {},
   "source": [
    "Plotting the facility points we can see that the function generates dummy points to an area of 10x10, which is the area created by our lattice created on previous cells."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "91d8cddf",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:33.960755Z",
     "start_time": "2023-01-10T18:23:33.485494Z"
    },
    "execution": {
     "iopub.execute_input": "2023-12-10T19:02:36.749306Z",
     "iopub.status.busy": "2023-12-10T19:02:36.748992Z",
     "iopub.status.idle": "2023-12-10T19:02:37.156260Z",
     "shell.execute_reply": "2023-12-10T19:02:37.155506Z",
     "shell.execute_reply.started": "2023-12-10T19:02:36.749282Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 505,
       "width": 776
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(6, 6))\n",
    "streets.plot(ax=ax, alpha=0.8, zorder=1, label=\"streets\")\n",
    "facility_points.plot(\n",
    "    ax=ax, color=\"red\", zorder=2, label=f\"facility candidate sites ($n$={FACILITY_COUNT})\"\n",
    ")\n",
    "plt.legend(loc=\"upper left\", bbox_to_anchor=(1.05, 1));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7bb0cc9b",
   "metadata": {},
   "source": [
    "## Assign simulated points network locations\n",
    "\n",
    "The facility points do not adhere to network space. Calculating distances between them without restricting movement to the network results in a euclidean distances,'as the crow flies.' While this is acceptable for some applications, for others it is more realistic to consider network traversal (e.g. Does a mail carrier follow roads to deliver letters or fly from mailbox to mailbox?).\n",
    "\n",
    "In our first example we will consider distance along the 10x10 lattice network created above. Therefore, we must first snap the observation points to the network prior to calculating a cost matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "1d447220",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:33.997317Z",
     "start_time": "2023-01-10T18:23:33.967233Z"
    },
    "execution": {
     "iopub.execute_input": "2023-12-10T19:02:37.157744Z",
     "iopub.status.busy": "2023-12-10T19:02:37.157419Z",
     "iopub.status.idle": "2023-12-10T19:02:37.190551Z",
     "shell.execute_reply": "2023-12-10T19:02:37.189723Z",
     "shell.execute_reply.started": "2023-12-10T19:02:37.157721Z"
    }
   },
   "outputs": [],
   "source": [
    "with warnings.catch_warnings():\n",
    "    warnings.simplefilter(\"ignore\")\n",
    "    # ignore deprecation warning - GH pysal/libpysal#468\n",
    "    ntw.snapobservations(facility_points, \"facilities\", attribute=True)\n",
    "facilities_snapped = spaghetti.element_as_gdf(ntw, pp_name=\"facilities\", snapped=True)\n",
    "facilities_snapped.drop(columns=[\"id\", \"comp_label\"], inplace=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af1768f2",
   "metadata": {},
   "source": [
    "Now the plot seems more organized as the points occupy network space. The network is plotted below with the network locations of the facility points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "81fe5065",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:34.310140Z",
     "start_time": "2023-01-10T18:23:34.000540Z"
    },
    "execution": {
     "iopub.execute_input": "2023-12-10T19:02:37.192298Z",
     "iopub.status.busy": "2023-12-10T19:02:37.191853Z",
     "iopub.status.idle": "2023-12-10T19:02:37.467001Z",
     "shell.execute_reply": "2023-12-10T19:02:37.466312Z",
     "shell.execute_reply.started": "2023-12-10T19:02:37.192271Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 505,
       "width": 798
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(6, 6))\n",
    "streets.plot(ax=ax, alpha=0.8, zorder=1, label=\"streets\")\n",
    "facilities_snapped.plot(\n",
    "    ax=ax, color=\"red\", zorder=2, label=f\"facility candidate sites ($n$={FACILITY_COUNT})\"\n",
    ")\n",
    "plt.legend(loc=\"upper left\", bbox_to_anchor=(1.05, 1));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5f02e47",
   "metadata": {},
   "source": [
    "## Calculating the (network distance) cost matrix\n",
    "Calculate the inter-facility network distance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "4fbb1d6d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:34.381679Z",
     "start_time": "2023-01-10T18:23:34.312980Z"
    },
    "execution": {
     "iopub.execute_input": "2023-12-10T19:02:37.468463Z",
     "iopub.status.busy": "2023-12-10T19:02:37.468025Z",
     "iopub.status.idle": "2023-12-10T19:02:37.530938Z",
     "shell.execute_reply": "2023-12-10T19:02:37.530244Z",
     "shell.execute_reply.started": "2023-12-10T19:02:37.468440Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(16, 16)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cost_matrix = ntw.allneighbordistances(\n",
    "    sourcepattern=ntw.pointpatterns[\"facilities\"], fill_diagonal=0.\n",
    ")\n",
    "cost_matrix.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a67562b",
   "metadata": {},
   "source": [
    "The expected result here is a network distance facilities points, in our case a 2D 16x16*** array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "98bf0abb",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:34.390422Z",
     "start_time": "2023-01-10T18:23:34.384090Z"
    },
    "execution": {
     "iopub.execute_input": "2023-12-10T19:02:37.532452Z",
     "iopub.status.busy": "2023-12-10T19:02:37.531973Z",
     "iopub.status.idle": "2023-12-10T19:02:37.537359Z",
     "shell.execute_reply": "2023-12-10T19:02:37.536822Z",
     "shell.execute_reply.started": "2023-12-10T19:02:37.532430Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.        ,  3.78794131, 11.63723819,  4.99347068,  9.66917542],\n",
       "       [ 3.78794131,  0.        , 13.84929687,  7.20552937, 11.88123411],\n",
       "       [11.63723819, 13.84929687,  0.        ,  6.6437675 ,  2.66349027],\n",
       "       [ 4.99347068,  7.20552937,  6.6437675 ,  0.        ,  4.67570474],\n",
       "       [ 9.66917542, 11.88123411,  2.66349027,  4.67570474,  0.        ]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cost_matrix[:5,:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "41681306",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:34.397069Z",
     "start_time": "2023-01-10T18:23:34.392434Z"
    },
    "execution": {
     "iopub.execute_input": "2023-12-10T19:02:37.538368Z",
     "iopub.status.busy": "2023-12-10T19:02:37.538165Z",
     "iopub.status.idle": "2023-12-10T19:02:37.543154Z",
     "shell.execute_reply": "2023-12-10T19:02:37.542383Z",
     "shell.execute_reply.started": "2023-12-10T19:02:37.538350Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.        ,  3.15016768,  9.526461  ,  9.71401032,  3.00949261],\n",
       "       [ 3.15016768,  0.        , 10.67662868,  6.56384263,  4.93972891],\n",
       "       [ 9.526461  , 10.67662868,  0.        , 11.24047132,  6.51696839],\n",
       "       [ 9.71401032,  6.56384263, 11.24047132,  0.        , 11.50357155],\n",
       "       [ 3.00949261,  4.93972891,  6.51696839, 11.50357155,  0.        ]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cost_matrix[-5:,-5:]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd231297",
   "metadata": {},
   "source": [
    "With ``PDispersion.from_cost_matrix`` we model the $p$-dispersion problem to maximize the minimum inter-facility \n",
    "cost (in this case network distance in generic units, as calculated above) while siting $p$ facilites."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "43393fcb",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:34.515202Z",
     "start_time": "2023-01-10T18:23:34.399391Z"
    },
    "execution": {
     "iopub.execute_input": "2023-12-10T19:02:37.544024Z",
     "iopub.status.busy": "2023-12-10T19:02:37.543831Z",
     "iopub.status.idle": "2023-12-10T19:02:37.651919Z",
     "shell.execute_reply": "2023-12-10T19:02:37.650779Z",
     "shell.execute_reply.started": "2023-12-10T19:02:37.544007Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<spopt.locate.p_dispersion.PDispersion at 0x16423bad0>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pdispersion_from_cm = PDispersion.from_cost_matrix(\n",
    "    cost_matrix, P_FACILITIES, name=f\"p-dispersion-network-distance\"\n",
    ")\n",
    "pdispersion_from_cm = pdispersion_from_cm.solve(solver)\n",
    "pdispersion_from_cm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "f0c9b8e8",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:34.526089Z",
     "start_time": "2023-01-10T18:23:34.519658Z"
    },
    "execution": {
     "iopub.execute_input": "2023-12-10T19:02:37.653905Z",
     "iopub.status.busy": "2023-12-10T19:02:37.653354Z",
     "iopub.status.idle": "2023-12-10T19:02:37.658624Z",
     "shell.execute_reply": "2023-12-10T19:02:37.657738Z",
     "shell.execute_reply.started": "2023-12-10T19:02:37.653868Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A maximized minimum inter-facility distance between any two sited candiate facilities of 10.706 distance units is observed while siting facilities at 3 of the available 16 locations.\n"
     ]
    }
   ],
   "source": [
    "pdispersion_obj = round(pdispersion_from_cm.problem.objective.value(), 3)\n",
    "print(\n",
    "    \"A maximized minimum inter-facility distance between any two sited candiate \"\n",
    "    f\"facilities of {pdispersion_obj} distance units is observed while siting \"\n",
    "    f\"facilities at {P_FACILITIES} of the available {FACILITY_COUNT} locations.\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad67dbb2",
   "metadata": {},
   "source": [
    "Define the decision variable names used for mapping later."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "0883d494",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:34.547112Z",
     "start_time": "2023-01-10T18:23:34.529055Z"
    },
    "execution": {
     "iopub.execute_input": "2023-12-10T19:02:37.659894Z",
     "iopub.status.busy": "2023-12-10T19:02:37.659612Z",
     "iopub.status.idle": "2023-12-10T19:02:37.672599Z",
     "shell.execute_reply": "2023-12-10T19:02:37.671966Z",
     "shell.execute_reply.started": "2023-12-10T19:02:37.659874Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>geometry</th>\n",
       "      <th>dv</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>POINT (9.32146 3.15178)</td>\n",
       "      <td>y0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>POINT (8.53352 -0.04134)</td>\n",
       "      <td>y1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>POINT (0.68422 6.04557)</td>\n",
       "      <td>y2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>POINT (5.32799 4.10688)</td>\n",
       "      <td>y3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>POINT (3.18949 6.34771)</td>\n",
       "      <td>y4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>POINT (4.31956 7.59470)</td>\n",
       "      <td>y5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>POINT (5.19840 5.86744)</td>\n",
       "      <td>y6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>POINT (6.59891 10.39247)</td>\n",
       "      <td>y7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>POINT (8.51844 4.04521)</td>\n",
       "      <td>y8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>POINT (9.13894 8.56135)</td>\n",
       "      <td>y9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>POINT (0.09922 7.40501)</td>\n",
       "      <td>y10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>POINT (8.32388 7.60047)</td>\n",
       "      <td>y11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>POINT (7.30045 5.45031)</td>\n",
       "      <td>y12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>POINT (0.87307 10.03412)</td>\n",
       "      <td>y13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>POINT (3.93582 1.88646)</td>\n",
       "      <td>y14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>POINT (7.39003 10.43628)</td>\n",
       "      <td>y15</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    geometry   dv\n",
       "0    POINT (9.32146 3.15178)   y0\n",
       "1   POINT (8.53352 -0.04134)   y1\n",
       "2    POINT (0.68422 6.04557)   y2\n",
       "3    POINT (5.32799 4.10688)   y3\n",
       "4    POINT (3.18949 6.34771)   y4\n",
       "5    POINT (4.31956 7.59470)   y5\n",
       "6    POINT (5.19840 5.86744)   y6\n",
       "7   POINT (6.59891 10.39247)   y7\n",
       "8    POINT (8.51844 4.04521)   y8\n",
       "9    POINT (9.13894 8.56135)   y9\n",
       "10   POINT (0.09922 7.40501)  y10\n",
       "11   POINT (8.32388 7.60047)  y11\n",
       "12   POINT (7.30045 5.45031)  y12\n",
       "13  POINT (0.87307 10.03412)  y13\n",
       "14   POINT (3.93582 1.88646)  y14\n",
       "15  POINT (7.39003 10.43628)  y15"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "facility_points[\"dv\"] = pdispersion_from_cm.fac_vars\n",
    "facility_points[\"dv\"] = facility_points[\"dv\"].map(lambda x: x.name.replace(\"_\", \"\"))\n",
    "facilities_snapped[\"dv\"] = facility_points[\"dv\"]\n",
    "facility_points"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1f4b31a0",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-10-22T14:40:39.366530Z",
     "start_time": "2022-10-22T14:40:39.366518Z"
    }
   },
   "source": [
    "## Calculating euclidean distance from a `GeoDataFrame`\n",
    "\n",
    "With ``PDispersion.from_cost_matrix`` we model the $p$-dispersion problem to maximize the minimum inter-facility \n",
    "cost (in this case euclidean distance in generic units) while siting $p$ facilites.\n",
    "\n",
    "Next we will solve the $p$-dispersion problem considering all candidate locations for potential selection."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "3ae768c1",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:34.653494Z",
     "start_time": "2023-01-10T18:23:34.549901Z"
    },
    "execution": {
     "iopub.execute_input": "2023-12-10T19:02:37.673478Z",
     "iopub.status.busy": "2023-12-10T19:02:37.673301Z",
     "iopub.status.idle": "2023-12-10T19:02:37.766878Z",
     "shell.execute_reply": "2023-12-10T19:02:37.765734Z",
     "shell.execute_reply.started": "2023-12-10T19:02:37.673463Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<spopt.locate.p_dispersion.PDispersion at 0x167d98e00>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distance_metric = \"euclidean\"\n",
    "pdispersion_from_gdf = PDispersion.from_geodataframe(\n",
    "    facilities_snapped,\n",
    "    \"geometry\",\n",
    "    P_FACILITIES,\n",
    "    distance_metric=distance_metric,\n",
    "    name=f\"p-dispersion-{distance_metric}-distance\"\n",
    ")\n",
    "pdispersion_from_gdf = pdispersion_from_gdf.solve(solver)\n",
    "pdispersion_from_gdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "0aa3cec1",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:34.661088Z",
     "start_time": "2023-01-10T18:23:34.657115Z"
    },
    "execution": {
     "iopub.execute_input": "2023-12-10T19:02:37.769058Z",
     "iopub.status.busy": "2023-12-10T19:02:37.768464Z",
     "iopub.status.idle": "2023-12-10T19:02:37.775154Z",
     "shell.execute_reply": "2023-12-10T19:02:37.773963Z",
     "shell.execute_reply.started": "2023-12-10T19:02:37.768995Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A maximized minimum inter-facility distance between any two sited candiate facilities of 8.574 distance units is observed while siting facilities at 3 of the available 16 locations.\n"
     ]
    }
   ],
   "source": [
    "pdispersion_obj = round(pdispersion_from_gdf.problem.objective.value(), 3)\n",
    "print(\n",
    "    \"A maximized minimum inter-facility distance between any two sited candiate \"\n",
    "    f\"facilities of {pdispersion_obj} distance units is observed while siting \"\n",
    "    f\"facilities at {P_FACILITIES} of the available {FACILITY_COUNT} locations.\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d53d6bfe",
   "metadata": {},
   "source": [
    "However, in many real world applications there may already be existing facility locations with the goal being to add one or more new facilities. Here we will define facilites $y_{11}$ and $y_{12}$ as already existing (they must be present in the model solution). This will lead to a sub-optimal solution.\n",
    "\n",
    "***Important:*** The facilities in `\"predefined_loc\"` are a binary array where `1` means the associated location must appear in the solution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "7ca5aa68",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:34.679228Z",
     "start_time": "2023-01-10T18:23:34.664344Z"
    },
    "execution": {
     "iopub.execute_input": "2023-12-10T19:02:37.777034Z",
     "iopub.status.busy": "2023-12-10T19:02:37.776542Z",
     "iopub.status.idle": "2023-12-10T19:02:37.791164Z",
     "shell.execute_reply": "2023-12-10T19:02:37.789837Z",
     "shell.execute_reply.started": "2023-12-10T19:02:37.777011Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>geometry</th>\n",
       "      <th>dv</th>\n",
       "      <th>predefined_loc</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>POINT (9.32146 3.15178)</td>\n",
       "      <td>y0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>POINT (8.53352 -0.04134)</td>\n",
       "      <td>y1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>POINT (0.68422 6.04557)</td>\n",
       "      <td>y2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>POINT (5.32799 4.10688)</td>\n",
       "      <td>y3</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>POINT (3.18949 6.34771)</td>\n",
       "      <td>y4</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>POINT (4.31956 7.59470)</td>\n",
       "      <td>y5</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>POINT (5.19840 5.86744)</td>\n",
       "      <td>y6</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>POINT (6.59891 10.39247)</td>\n",
       "      <td>y7</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>POINT (8.51844 4.04521)</td>\n",
       "      <td>y8</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>POINT (9.13894 8.56135)</td>\n",
       "      <td>y9</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>POINT (0.09922 7.40501)</td>\n",
       "      <td>y10</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>POINT (8.32388 7.60047)</td>\n",
       "      <td>y11</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>POINT (7.30045 5.45031)</td>\n",
       "      <td>y12</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>POINT (0.87307 10.03412)</td>\n",
       "      <td>y13</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>POINT (3.93582 1.88646)</td>\n",
       "      <td>y14</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>POINT (7.39003 10.43628)</td>\n",
       "      <td>y15</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    geometry   dv  predefined_loc\n",
       "0    POINT (9.32146 3.15178)   y0               0\n",
       "1   POINT (8.53352 -0.04134)   y1               0\n",
       "2    POINT (0.68422 6.04557)   y2               0\n",
       "3    POINT (5.32799 4.10688)   y3               0\n",
       "4    POINT (3.18949 6.34771)   y4               0\n",
       "5    POINT (4.31956 7.59470)   y5               0\n",
       "6    POINT (5.19840 5.86744)   y6               0\n",
       "7   POINT (6.59891 10.39247)   y7               0\n",
       "8    POINT (8.51844 4.04521)   y8               0\n",
       "9    POINT (9.13894 8.56135)   y9               0\n",
       "10   POINT (0.09922 7.40501)  y10               0\n",
       "11   POINT (8.32388 7.60047)  y11               1\n",
       "12   POINT (7.30045 5.45031)  y12               1\n",
       "13  POINT (0.87307 10.03412)  y13               0\n",
       "14   POINT (3.93582 1.88646)  y14               0\n",
       "15  POINT (7.39003 10.43628)  y15               0"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "facility_points[\"predefined_loc\"] = 0\n",
    "facility_points.loc[(11, 12), \"predefined_loc\"] = 1\n",
    "facilities_snapped[\"predefined_loc\"] = facility_points[\"predefined_loc\"]\n",
    "facility_points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "a8a4e8cf",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:34.741687Z",
     "start_time": "2023-01-10T18:23:34.682497Z"
    },
    "execution": {
     "iopub.execute_input": "2023-12-10T19:02:37.793018Z",
     "iopub.status.busy": "2023-12-10T19:02:37.792362Z",
     "iopub.status.idle": "2023-12-10T19:02:37.845790Z",
     "shell.execute_reply": "2023-12-10T19:02:37.844805Z",
     "shell.execute_reply.started": "2023-12-10T19:02:37.792986Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<spopt.locate.p_dispersion.PDispersion at 0x167e3f380>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pdispersion_from_gdf_pre = PDispersion.from_geodataframe(\n",
    "    facilities_snapped,\n",
    "    \"geometry\",\n",
    "    P_FACILITIES,\n",
    "    predefined_facility_col=\"predefined_loc\",\n",
    "    distance_metric=distance_metric,\n",
    "    name=f\"p-dispersion-{distance_metric}-distance-predefined\"\n",
    ")\n",
    "pdispersion_from_gdf_pre = pdispersion_from_gdf_pre.solve(solver)\n",
    "pdispersion_from_gdf_pre"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "3f0db1d5",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:34.748694Z",
     "start_time": "2023-01-10T18:23:34.744627Z"
    },
    "execution": {
     "iopub.execute_input": "2023-12-10T19:02:37.853011Z",
     "iopub.status.busy": "2023-12-10T19:02:37.852630Z",
     "iopub.status.idle": "2023-12-10T19:02:37.856858Z",
     "shell.execute_reply": "2023-12-10T19:02:37.856229Z",
     "shell.execute_reply.started": "2023-12-10T19:02:37.852983Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A maximized minimum inter-facility distance between any two sited candiate facilities of 2.371 distance units is observed while siting facilities at 3 of the available 16 locations.\n"
     ]
    }
   ],
   "source": [
    "pdispersion_obj = round(pdispersion_from_gdf_pre.problem.objective.value(), 3)\n",
    "print(\n",
    "    \"A maximized minimum inter-facility distance between any two sited candiate \"\n",
    "    f\"facilities of {pdispersion_obj} distance units is observed while siting \"\n",
    "    f\"facilities at {P_FACILITIES} of the available {FACILITY_COUNT} locations.\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "837d517a",
   "metadata": {},
   "source": [
    "## Plotting the results\n",
    "\n",
    "The two cells below describe the plotting of the results. For each method from the `PDispersion` class (`.from_cost_matrix()`, `.from_geodataframe()`) there is a plot displaying the facility site that was selected with a colored star."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "250da306",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:34.755858Z",
     "start_time": "2023-01-10T18:23:34.750701Z"
    },
    "execution": {
     "iopub.execute_input": "2023-12-10T19:02:37.858215Z",
     "iopub.status.busy": "2023-12-10T19:02:37.857961Z",
     "iopub.status.idle": "2023-12-10T19:02:37.862901Z",
     "shell.execute_reply": "2023-12-10T19:02:37.862316Z",
     "shell.execute_reply.started": "2023-12-10T19:02:37.858197Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'y0': 'darkcyan',\n",
       " 'y1': 'mediumseagreen',\n",
       " 'y2': 'saddlebrown',\n",
       " 'y3': 'darkslategray',\n",
       " 'y4': 'lightskyblue',\n",
       " 'y5': 'thistle',\n",
       " 'y6': 'lavender',\n",
       " 'y7': 'darkgoldenrod',\n",
       " 'y8': 'peachpuff',\n",
       " 'y9': 'coral',\n",
       " 'y10': 'mediumvioletred',\n",
       " 'y11': 'blueviolet',\n",
       " 'y12': 'fuchsia',\n",
       " 'y13': 'cyan',\n",
       " 'y14': 'limegreen',\n",
       " 'y15': 'mediumorchid'}"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dv_colors_arr = [\n",
    "    \"darkcyan\",\n",
    "    \"mediumseagreen\",\n",
    "    \"saddlebrown\",\n",
    "    \"darkslategray\",\n",
    "    \"lightskyblue\",\n",
    "    \"thistle\",\n",
    "    \"lavender\",\n",
    "    \"darkgoldenrod\",\n",
    "    \"peachpuff\",\n",
    "    \"coral\",\n",
    "    \"mediumvioletred\",\n",
    "    \"blueviolet\",\n",
    "    \"fuchsia\",\n",
    "    \"cyan\",\n",
    "    \"limegreen\",\n",
    "    \"mediumorchid\",\n",
    "]\n",
    "dv_colors = {f\"y{i}\": dv_colors_arr[i] for i in range(len(dv_colors_arr))}\n",
    "dv_colors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "99b1906a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:34.770679Z",
     "start_time": "2023-01-10T18:23:34.758414Z"
    },
    "execution": {
     "iopub.execute_input": "2023-12-10T19:02:37.864334Z",
     "iopub.status.busy": "2023-12-10T19:02:37.863930Z",
     "iopub.status.idle": "2023-12-10T19:02:37.874581Z",
     "shell.execute_reply": "2023-12-10T19:02:37.873552Z",
     "shell.execute_reply.started": "2023-12-10T19:02:37.864312Z"
    }
   },
   "outputs": [],
   "source": [
    "def plot_results(model, p, facs, clis=None, ax=None):\n",
    "    \"\"\"Visualize optimal solution sets and context.\"\"\"\n",
    "    if not ax:\n",
    "        multi_plot = False\n",
    "        fig, ax = plt.subplots(figsize=(6, 6))\n",
    "        markersize, markersize_factor = 4, 4\n",
    "    else:\n",
    "        ax.axis(\"off\")\n",
    "        multi_plot = True\n",
    "        markersize, markersize_factor = 2, 2\n",
    "    \n",
    "    ax.set_title(model.name, fontsize=15)\n",
    "    facility_count = len(model.fac_vars)\n",
    "    fac_sites = {}\n",
    "    \n",
    "    plot_clis = isinstance(clis, geopandas.GeoDataFrame)\n",
    "    if plot_clis:\n",
    "        cli_points = {}\n",
    "        \n",
    "    for i, dv in enumerate(model.fac_vars):\n",
    "        if dv.varValue:\n",
    "            dv, predef = facs.loc[i, [\"dv\", \"predefined_loc\"]]\n",
    "            fac_sites[dv] = [i, predef]\n",
    "            if plot_clis:\n",
    "                geom = clis.iloc[model.fac2cli[i]][\"geometry\"]\n",
    "                cli_points[dv] = geom\n",
    "    \n",
    "    # study area and legend entries initialization\n",
    "    streets.plot(ax=ax, alpha=1, color=\"black\", zorder=1)\n",
    "    legend_elements = [mlines.Line2D([], [], color=\"black\", label=\"streets\")]\n",
    "    \n",
    "    if plot_clis:\n",
    "        # any clients that not asscociated with a facility\n",
    "        if model.name.startswith(\"mclp\"):\n",
    "            c = \"k\"\n",
    "            if model.n_cli_uncov:\n",
    "                idx = [i for i, v in enumerate(model.cli2fac) if len(v) == 0]\n",
    "                pnt_kws = dict(ax=ax, fc=c, ec=c, marker=\"s\", markersize=7, zorder=2)\n",
    "                clis.iloc[idx].plot(**pnt_kws)\n",
    "            _label = f\"Demand sites not covered ($n$={model.n_cli_uncov})\"\n",
    "            _mkws = dict(marker=\"s\", markerfacecolor=c, markeredgecolor=c, linewidth=0)\n",
    "            legend_elements.append(mlines.Line2D([], [], ms=3, label=_label, **_mkws))\n",
    "\n",
    "    # all candidate facilities\n",
    "    facs.plot(ax=ax, fc=\"brown\", marker=\"*\", markersize=80, zorder=8)\n",
    "    _label = f\"Facility sites ($n$={facility_count})\"\n",
    "    _mkws = dict(marker=\"*\", markerfacecolor=\"brown\", markeredgecolor=\"brown\")\n",
    "    legend_elements.append(mlines.Line2D([], [], ms=7, lw=0, label=_label, **_mkws))\n",
    "    \n",
    "    # client-facility symbology and legend entries\n",
    "    zorder = 4\n",
    "    for fname, (fac, predef) in fac_sites.items():\n",
    "        \n",
    "        cset = dv_colors[fname]\n",
    "        \n",
    "        if plot_clis:\n",
    "            # clients\n",
    "            geoms = cli_points[fname]\n",
    "            gdf = geopandas.GeoDataFrame(geoms)\n",
    "            gdf.plot(ax=ax, zorder=zorder, ec=\"k\", fc=cset, markersize=100 * markersize)\n",
    "            _label = f\"Demand sites covered by {fname}\"\n",
    "            _mkws = dict(markerfacecolor=cset, markeredgecolor=\"k\", ms=markersize + 7)\n",
    "            legend_elements.append(\n",
    "                mlines.Line2D([], [], marker=\"o\", lw=0, label=_label, **_mkws)\n",
    "            )\n",
    "        # facilities\n",
    "        ec = \"k\"\n",
    "        lw = 2\n",
    "        predef_label = \"predefined\"\n",
    "        if model.name.endswith(predef_label) and predef:\n",
    "            ec = \"r\"\n",
    "            lw = 3\n",
    "            fname += f\" ({predef_label})\"\n",
    "        facs.iloc[[fac]].plot(\n",
    "            ax=ax, marker=\"*\", markersize=1000, zorder=9, fc=cset, ec=ec, lw=lw\n",
    "        )\n",
    "        _mkws = dict(markerfacecolor=cset, markeredgecolor=ec, markeredgewidth=lw)\n",
    "        legend_elements.append(\n",
    "            mlines.Line2D([], [], marker=\"*\", ms=20, lw=0, label=fname, **_mkws)\n",
    "        )\n",
    "        # increment zorder up and markersize down for stacked client symbology\n",
    "        zorder += 1\n",
    "        if plot_clis:\n",
    "            markersize -= markersize_factor / p\n",
    "    \n",
    "    if not multi_plot:\n",
    "        # legend\n",
    "        kws = dict(loc=\"upper left\", bbox_to_anchor=(1.05, 0.7))\n",
    "        plt.legend(handles=legend_elements, **kws)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb124be7",
   "metadata": {},
   "source": [
    "### P-Dispersion built from cost matrix (network distance)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "05504b98",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:35.264726Z",
     "start_time": "2023-01-10T18:23:34.773148Z"
    },
    "execution": {
     "iopub.execute_input": "2023-12-10T19:02:37.877000Z",
     "iopub.status.busy": "2023-12-10T19:02:37.876518Z",
     "iopub.status.idle": "2023-12-10T19:02:38.351286Z",
     "shell.execute_reply": "2023-12-10T19:02:38.349856Z",
     "shell.execute_reply.started": "2023-12-10T19:02:37.876972Z"
    }
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 529,
       "width": 706
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_results(pdispersion_from_cm, P_FACILITIES, facility_points)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f774853",
   "metadata": {},
   "source": [
    "### P-Dispersion built from geodataframe (euclidean distance)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "39baa5ed",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:35.681008Z",
     "start_time": "2023-01-10T18:23:35.267574Z"
    },
    "execution": {
     "iopub.execute_input": "2023-12-10T19:02:38.352607Z",
     "iopub.status.busy": "2023-12-10T19:02:38.352334Z",
     "iopub.status.idle": "2023-12-10T19:02:38.814475Z",
     "shell.execute_reply": "2023-12-10T19:02:38.813676Z",
     "shell.execute_reply.started": "2023-12-10T19:02:38.352588Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 529,
       "width": 706
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_results(pdispersion_from_gdf, P_FACILITIES, facility_points)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da6e7401",
   "metadata": {},
   "source": [
    "### P-Dispersion with preselected facilities (euclidean distance)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "1a5e68dd",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:36.142414Z",
     "start_time": "2023-01-10T18:23:35.683575Z"
    },
    "execution": {
     "iopub.execute_input": "2023-12-10T19:02:38.817057Z",
     "iopub.status.busy": "2023-12-10T19:02:38.816380Z",
     "iopub.status.idle": "2023-12-10T19:02:39.232152Z",
     "shell.execute_reply": "2023-12-10T19:02:39.231468Z",
     "shell.execute_reply.started": "2023-12-10T19:02:38.817026Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 529,
       "width": 706
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_results(pdispersion_from_gdf_pre, P_FACILITIES, facility_points)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d82bea6b",
   "metadata": {},
   "source": [
    "-----------------------------------\n",
    "\n",
    "## Comparing solution from varied metrics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "47c49823",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:37.136128Z",
     "start_time": "2023-01-10T18:23:36.148889Z"
    },
    "execution": {
     "iopub.execute_input": "2023-12-10T19:02:39.233643Z",
     "iopub.status.busy": "2023-12-10T19:02:39.233325Z",
     "iopub.status.idle": "2023-12-10T19:02:40.172483Z",
     "shell.execute_reply": "2023-12-10T19:02:40.171734Z",
     "shell.execute_reply.started": "2023-12-10T19:02:39.233621Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2000x1000 with 3 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 588,
       "width": 1569
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axarr = plt.subplots(1, 3, figsize=(20, 10))\n",
    "fig.subplots_adjust(wspace=-0.01)\n",
    "for i, m in enumerate(\n",
    "    [pdispersion_from_cm, pdispersion_from_gdf, pdispersion_from_gdf_pre]\n",
    "):\n",
    "    plot_results(\n",
    "        m, P_FACILITIES, facility_points, ax=axarr[i]\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff2ce865",
   "metadata": {},
   "source": [
    "All 3 solutions to the $p$-dispersion problem vary spatially, as seen above, but they also all include facility $y_1$ since it is the most isolated location. A good demonstration of the intended results of dispersion can be seen in the first two models, `P-Dispersion-network-distance` and `P-Dispersion-euclidean-distance`, where the selected candidate facilites are arranged to form pseudo-equilateral triangles. Of course, the `P-Dispersion-euclidean-distance-predefined` model does not follow this pattern due to the stipulation that facilities $y_{11}$ and $y_{12}$ be included in the optimal solution.\n",
    "\n",
    "\n",
    "## References\n",
    "\n",
    "- [Kuby, Michael J. 1987. Programming Models for Facility Dispersion: The p-Dispersion and Maximum Dispersion Problems. Geographical Analysis, 19, 315–329.](https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1538-4632.1987.tb00133.x)\n",
    "- [Maliszewski, Paul J., Michael J. Kuby, and Mark W. Horner. 2012. A comparison of multi-objective spatial dispersion models for managing critical assets in urban areas. Computers, Environment and Urban Systems. 36 (4):331-341.](https://www.sciencedirect.com/science/article/pii/S0198971511001293?via%3Dihub)"
   ]
  }
 ],
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