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        "```{index} disjunctive programming\n",
        "```\n",
        "```{index} single: application; electric vehicles\n",
        "```\n",
        "```{index} single: solver; highs\n",
        "```\n",
        "```{index} single: AMPL; Set\n",
        "```\n",
        "```{index} pandas dataframe\n",
        "```\n",
        "# Recharging strategy for an electric vehicle\n",
        "\n",
        "Whether it is to visit family, take a sightseeing tour or call on business associates, planning a road trip is a familiar and routine task. Here we consider a road trip on a pre-determined route for which need to plan rest and recharging stops. This example demonstrates use of AMPL disjunctions to model the decisions on where to stop."
      ]
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          "text": [
            "Using default Community Edition License for Colab. Get yours at: https://ampl.com/ce\n",
            "Licensed to AMPL Community Edition License for the AMPL Model Colaboratory (https://ampl.com/colab).\n"
          ]
        }
      ],
      "source": [
        "# install dependencies and select solver\n",
        "%pip install -q amplpy pandas numpy matplotlib\n",
        "\n",
        "SOLVER = \"highs\"\n",
        "\n",
        "from amplpy import AMPL, ampl_notebook\n",
        "\n",
        "ampl = ampl_notebook(\n",
        "    modules=[\"highs\"],  # modules to install\n",
        "    license_uuid=\"default\",  # license to use\n",
        ")  # instantiate AMPL object and register magics"
      ]
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      "source": [
        "## Problem Statement\n",
        "\n",
        "Given the current location $x$, battery charge $c$, and planning horizon $D$, the task is to plan a series of recharging and rest stops. Data is provided for the location and the charging rate available at each charging stations. The objective is to drive from location $x$ to location $x + D$ in as little time as possible subject to the following constraints:\n",
        "\n",
        "* To allow for unforeseen events, the state of charge should never drop below 20% of the maximum capacity.\n",
        "* The the maximum charge is $c_{max} = 80$ kWh.\n",
        "* For comfort, no more than 4 hours should pass between stops, and that a rest stop should last at least $t^{rest}$.\n",
        "* Any stop includes a $t^{lost} = 10$ minutes of \"lost time\".\n",
        "\n",
        "For this first model we make several simplifying assumptions that can be relaxed as a later time.\n",
        "\n",
        "* Travel is at a constant speed $v = 100$ km per hour and a constant discharge rate $R = 0.24$ kWh/km\n",
        "* The batteries recharge at a constant rate determined by the charging station.\n",
        "* Only consider stops at the recharging stations."
      ]
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      "source": [
        "## Modeling\n",
        "\n",
        "The problem statement identifies four state variables.\n",
        "\n",
        "* $c$ the current battery charge\n",
        "* $r$ the elapsed time since the last rest stop\n",
        "* $t$ elapsed time since the start of the trip\n",
        "* $x$ the current location\n",
        "\n",
        "The charging stations are located at positions $d_i$ for $i\\in I$ with capacity $C_i$. The arrival time at charging station $i$ is given by\n",
        "\n",
        "$$\n",
        "\\begin{align*}\n",
        "c_i^{arr} & = c_{i-1}^{dep} - R (d_i - d_{i-1}) \\\\\n",
        "r_i^{arr} & = r_{i-1}^{dep} + \\frac{d_i - d_{i-1}}{v} \\\\\n",
        "t_i^{arr} & = t_{i-1}^{dep} + \\frac{d_i - d_{i-1}}{v} \\\\\n",
        "\\end{align*}\n",
        "$$\n",
        "\n",
        "where the script $t_{i-1}^{dep}$ refers to departure from the prior location. At each charging location there is a decision to make of whether to stop, rest, and recharge. If the decision is positive, then\n",
        "\n",
        "$$\n",
        "\\begin{align*}\n",
        "c_i^{dep} & \\leq c^{max} \\\\\n",
        "r_i^{dep} & = 0 \\\\\n",
        "t_i^{dep} & \\geq t_{i}^{arr} + t_{lost} + \\frac{c_i^{dep} - c_i^{arr}}{C_i} \\\\\n",
        "t_i^{dep} & \\geq t_{i}^{arr} + t_{rest}\n",
        "\\end{align*}\n",
        "$$\n",
        "\n",
        "which account for the battery charge, the lost time and time required for battery charging, and allows for a minimum rest time. On the other hand, if a decision is make to skip the charging and rest opportunity,\n",
        "\n",
        "$$\n",
        "\\begin{align*}\n",
        "c_i^{dep} & = c_i^{arr} \\\\\n",
        "r_i^{dep} & = r_i^{arr} \\\\\n",
        "t_i^{dep} & = t_i^{arr}\n",
        "\\end{align*}\n",
        "$$\n",
        "\n",
        "The latter sets of constraints have an exclusive-or relationship. That is, either one or the other of the constraint sets hold, but not both.  \n",
        "\n",
        "$$\n",
        "\\begin{align*}\n",
        "\\min \\quad & t_{n+1}^{arr} \\\\\n",
        "\\text{s.t.} \\quad\n",
        "    & r_i^{arr}  \\leq r^{max} & \\forall \\, i \\in I \\\\\n",
        "    & c_i^{arr}  \\geq c^{min} & \\forall \\,i \\in I \\\\\n",
        "    & c_i^{arr}  = c_{i-1}^{dep} - R (d_i - d_{i-1}) & \\forall \\,i \\in I \\\\\n",
        "    & r_i^{arr}  = r_{i-1}^{dep} + \\frac{d_i - d_{i-1}}{v} & \\forall \\,i \\in I \\\\\n",
        "    & t_i^{arr}  = t_{i-1}^{dep} + \\frac{d_i - d_{i-1}}{v} & \\forall \\,i \\in I \\\\\n",
        "& \\begin{bmatrix}\n",
        "    c_i^{dep} & \\leq & c^{max} \\\\\n",
        "    r_i^{dep} & = & 0 \\\\\n",
        "    t_i^{dep} & \\geq & t_{i}^{arr} + t_{lost} + \\frac{c_i^{dep} - c_i^{arr}}{C_i} \\\\\n",
        "    t_i^{dep} & \\geq & t_{i}^{arr} + t_{rest}\n",
        "\\end{bmatrix}\n",
        "\\veebar\n",
        "\\begin{bmatrix}\n",
        "    c_i^{dep} = c_i^{arr} \\\\\n",
        "    r_i^{dep} = r_i^{arr} \\\\\n",
        "    t_i^{dep} = t_i^{arr}\n",
        "\\end{bmatrix} & \\forall \\, i \\in I.\n",
        "\\end{align*}\n",
        "$$\n"
      ]
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      "source": [
        "## Charging Station Information"
      ]
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              "    name location   kw\n",
              "0   S_00    191.6  150\n",
              "1   S_01    310.6  100\n",
              "2   S_02    516.0   50\n",
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              "5   S_05    869.7  100\n",
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              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-d4b13714-820f-4973-8c79-4b0e308fed6f button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "\n",
              "  <div id=\"id_b6d091be-2b54-4e82-9a46-ccbcc8df90a9\">\n",
              "    <style>\n",
              "      .colab-df-generate {\n",
              "        background-color: #E8F0FE;\n",
              "        border: none;\n",
              "        border-radius: 50%;\n",
              "        cursor: pointer;\n",
              "        display: none;\n",
              "        fill: #1967D2;\n",
              "        height: 32px;\n",
              "        padding: 0 0 0 0;\n",
              "        width: 32px;\n",
              "      }\n",
              "\n",
              "      .colab-df-generate:hover {\n",
              "        background-color: #E2EBFA;\n",
              "        box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "        fill: #174EA6;\n",
              "      }\n",
              "\n",
              "      [theme=dark] .colab-df-generate {\n",
              "        background-color: #3B4455;\n",
              "        fill: #D2E3FC;\n",
              "      }\n",
              "\n",
              "      [theme=dark] .colab-df-generate:hover {\n",
              "        background-color: #434B5C;\n",
              "        box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "        filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "        fill: #FFFFFF;\n",
              "      }\n",
              "    </style>\n",
              "    <button class=\"colab-df-generate\" onclick=\"generateWithVariable('stations')\"\n",
              "            title=\"Generate code using this dataframe.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M7,19H8.4L18.45,9,17,7.55,7,17.6ZM5,21V16.75L18.45,3.32a2,2,0,0,1,2.83,0l1.4,1.43a1.91,1.91,0,0,1,.58,1.4,1.91,1.91,0,0,1-.58,1.4L9.25,21ZM18.45,9,17,7.55Zm-12,3A5.31,5.31,0,0,0,4.9,8.1,5.31,5.31,0,0,0,1,6.5,5.31,5.31,0,0,0,4.9,4.9,5.31,5.31,0,0,0,6.5,1,5.31,5.31,0,0,0,8.1,4.9,5.31,5.31,0,0,0,12,6.5,5.46,5.46,0,0,0,6.5,12Z\"/>\n",
              "  </svg>\n",
              "    </button>\n",
              "    <script>\n",
              "      (() => {\n",
              "      const buttonEl =\n",
              "        document.querySelector('#id_b6d091be-2b54-4e82-9a46-ccbcc8df90a9 button.colab-df-generate');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      buttonEl.onclick = () => {\n",
              "        google.colab.notebook.generateWithVariable('stations');\n",
              "      }\n",
              "      })();\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "stations",
              "summary": "{\n  \"name\": \"stations\",\n  \"rows\": 20,\n  \"fields\": [\n    {\n      \"column\": \"name\",\n      \"properties\": {\n        \"dtype\": \"string\",\n        \"num_unique_values\": 20,\n        \"samples\": [\n          \"S_00\",\n          \"S_17\",\n          \"S_15\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"location\",\n      \"properties\": {\n        \"dtype\": \"date\",\n        \"min\": 191.6,\n        \"max\": 2896.2,\n        \"num_unique_values\": 20,\n        \"samples\": [\n          191.6,\n          2590.0,\n          2337.5\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"kw\",\n      \"properties\": {\n        \"dtype\": \"date\",\n        \"min\": \"50\",\n        \"max\": \"250\",\n        \"num_unique_values\": 4,\n        \"samples\": [\n          \"100\",\n          \"250\",\n          \"150\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {}
        }
      ],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import pandas as pd\n",
        "\n",
        "# specify number of charging stations\n",
        "n_charging_stations = 20\n",
        "\n",
        "# randomly distribute charging stations along a fixed route\n",
        "np.random.seed(1842)\n",
        "d = np.round(np.cumsum(np.random.triangular(20, 150, 223, n_charging_stations)), 1)\n",
        "\n",
        "# randomly assign changing capacities\n",
        "c = np.random.choice([50, 100, 150, 250], n_charging_stations, p=[0.2, 0.4, 0.3, 0.1])\n",
        "\n",
        "# assign names to the charging stations\n",
        "s = [f\"S_{i:02d}\" for i in range(n_charging_stations)]\n",
        "\n",
        "stations = pd.DataFrame([s, d, c]).T\n",
        "stations.columns = [\"name\", \"location\", \"kw\"]\n",
        "display(stations)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "8d537988-9151-4339-b48b-1e111469c45a",
      "metadata": {
        "id": "8d537988-9151-4339-b48b-1e111469c45a"
      },
      "source": [
        "## Route Information"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "id": "3be8a0da-811d-49cf-ab77-b42011fb7fc0",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 333
        },
        "id": "3be8a0da-811d-49cf-ab77-b42011fb7fc0",
        "outputId": "20d3eca9-34a0-44d1-de4a-e3891a4fe3fb"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x300 with 1 Axes>"
            ],
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          },
          "metadata": {}
        }
      ],
      "source": [
        "# current location (km) and charge (kw)\n",
        "x = 0\n",
        "\n",
        "# planning horizon\n",
        "D = 2000\n",
        "\n",
        "# visualize\n",
        "fig, ax = plt.subplots(1, 1, figsize=(15, 3))\n",
        "\n",
        "\n",
        "def plot_stations(stations, x, D, ax=ax):\n",
        "    for station in stations.index:\n",
        "        xs = stations.loc[station, \"location\"]\n",
        "        ys = stations.loc[station, \"kw\"]\n",
        "        ax.plot([xs, xs], [0, ys], \"b\", lw=10, solid_capstyle=\"butt\")\n",
        "        ax.text(xs, 0 - 30, stations.loc[station, \"name\"], ha=\"center\")\n",
        "\n",
        "    ax.plot([x, x + D], [0, 0], \"r\", lw=5, solid_capstyle=\"butt\", label=\"plan horizon\")\n",
        "    ax.plot([x, x + D], [0, 0], \"r.\", ms=20)\n",
        "\n",
        "    ax.axhline(0)\n",
        "    ax.set_ylim(-50, 300)\n",
        "    ax.set_xlabel(\"Distance\")\n",
        "    ax.set_ylabel(\"kw\")\n",
        "    ax.set_title(\"charging stations\")\n",
        "    ax.legend()\n",
        "\n",
        "\n",
        "plot_stations(stations, x, D)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "91ebd206-ca91-436c-86f9-71f89bb1f34d",
      "metadata": {
        "id": "91ebd206-ca91-436c-86f9-71f89bb1f34d"
      },
      "source": [
        "## Car Information"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "id": "2d6dad34-d50b-4acf-bb44-2fbf3e044086",
      "metadata": {
        "id": "2d6dad34-d50b-4acf-bb44-2fbf3e044086"
      },
      "outputs": [],
      "source": [
        "# charge limits (kw)\n",
        "c_max = 150\n",
        "c_min = 0.2 * c_max\n",
        "c = c_max\n",
        "\n",
        "# velocity km/hr and discharge rate kwh/km\n",
        "v = 100.0\n",
        "R = 0.24\n",
        "\n",
        "# lost time\n",
        "t_lost = 10 / 60\n",
        "t_rest = 10 / 60\n",
        "\n",
        "# rest time\n",
        "r_max = 3"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "c797f5b1-c0a2-498c-9f94-2beaa947d961",
      "metadata": {
        "id": "c797f5b1-c0a2-498c-9f94-2beaa947d961"
      },
      "source": [
        "## AMPL Model"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "id": "5cabe50f",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5cabe50f",
        "outputId": "4b56c963-e193-4a1c-ed18-8a1efab05eec"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Overwriting ev_plan.mod\n"
          ]
        }
      ],
      "source": [
        "%%writefile ev_plan.mod\n",
        "\n",
        "param n;\n",
        "\n",
        "# locations and road segments between location x and x + D\n",
        "set STATIONS;  # 1..n\n",
        "set LOCATIONS; # 0, 1..n, D\n",
        "set SEGMENTS;  # 1..n + 1\n",
        "\n",
        "param C{STATIONS};\n",
        "param D;\n",
        "param c_min;\n",
        "param c_max;\n",
        "param v;\n",
        "param R;\n",
        "\n",
        "param r_max;\n",
        "param location{LOCATIONS};\n",
        "param dist{SEGMENTS};\n",
        "param t_lost;\n",
        "\n",
        "# distance traveled\n",
        "var x{LOCATIONS} >= 0, <= 10000;\n",
        "\n",
        "# arrival and departure charge at each charging station\n",
        "var c_arr{LOCATIONS} >= c_min, <= c_max;\n",
        "var c_dep{LOCATIONS} >= c_min, <= c_max;\n",
        "\n",
        "# arrival and departure times from each charging station\n",
        "var t_arr{LOCATIONS} >= 0, <= 100;\n",
        "var t_dep{LOCATIONS} >= 0, <= 100;\n",
        "\n",
        "# arrival and departure rest from each charging station\n",
        "var r_arr{LOCATIONS} >= 0, <= r_max;\n",
        "var r_dep{LOCATIONS} >= 0, <= r_max;\n",
        "\n",
        "minimize min_time: t_arr[n + 1];\n",
        "\n",
        "s.t. drive_time {i in SEGMENTS}: t_arr[i] == t_dep[i-1] + dist[i]/v;\n",
        "s.t. rest_time {i in SEGMENTS}: r_arr[i] == r_dep[i-1] + dist[i]/v;\n",
        "s.t. drive_distance {i in SEGMENTS}: x[i] == x[i-1] + dist[i];\n",
        "s.t. discharge {i in SEGMENTS}: c_arr[i] == c_dep[i-1] - R * dist[i];\n",
        "\n",
        "s.t. recharge {i in STATIONS}:\n",
        "    # list of constraints that apply if there is no stop at station i\n",
        "    ((c_dep[i] == c_arr[i] and t_dep[i] == t_arr[i] and r_dep[i] == r_arr[i])\n",
        "    or\n",
        "    # list of constraints that apply if there is a stop at station i\n",
        "    (t_dep[i] == t_lost + t_arr[i] + (c_dep[i] - c_arr[i])/C[i] and\n",
        "        c_dep[i] >= c_arr[i] and r_dep[i] == 0))\n",
        "    and not\n",
        "    ((c_dep[i] == c_arr[i] and t_dep[i] == t_arr[i] and r_dep[i] == r_arr[i])\n",
        "    and\n",
        "    (t_dep[i] == t_lost + t_arr[i] + (c_dep[i] - c_arr[i])/C[i] and\n",
        "        c_dep[i] >= c_arr[i] and r_dep[i] == 0));"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "id": "d061b189-5ccd-4949-a1b9-f736533e8389",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 635
        },
        "id": "d061b189-5ccd-4949-a1b9-f736533e8389",
        "outputId": "b82e7f3d-b3df-4f1f-ae20-70bbe33df543"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "HiGHS 1.10.0: \b\b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.10.0: optimal solution; objective 24.142507\n",
            "9961 simplex iterations\n",
            "116 branching nodes\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "       location      t_arr      t_dep     c_arr     c_dep     t_stop\n",
              "index                                                               \n",
              "0           0.0   0.000000   0.000000   30.0000  150.0000   0.000000\n",
              "1         191.6   1.916000   2.389227  104.0160  150.0000   0.473227\n",
              "2         310.6   3.579227   4.031493  121.4400  150.0000   0.452267\n",
              "3         516.0   6.085493   6.252162  100.7040  100.7041   0.166669\n",
              "4         683.6   7.928162   7.928162   60.4801   60.4801   0.000000\n",
              "5         769.9   8.791162   9.241507   39.7681   53.9520   0.450345\n",
              "6         869.7  10.239507  10.740733   30.0000   63.4560   0.501227\n",
              "7        1009.1  12.134733  12.848119   30.0000  112.0079   0.713386\n",
              "8        1164.7  14.404119  14.404119   74.6639   74.6639  -0.000000\n",
              "9        1230.8  15.065119  15.231787   58.7999   58.8000   0.166668\n",
              "10       1350.8  16.431787  17.078454   30.0000  150.0000   0.646667\n",
              "11       1508.4  18.654454  18.654454  112.1760  112.1760   0.000000\n",
              "12       1639.8  19.968454  20.135120   80.6400   80.6400   0.166667\n",
              "13       1809.4  21.831120  22.236507   39.9360   75.7440   0.405387\n",
              "14       1947.3  23.615507  23.615507   42.6480   42.6480   0.000000\n",
              "15       2000.0  24.142507   0.000000   30.0000   30.0000 -24.142507"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-bd271a51-1986-49e6-b06c-631e223d4acd\" class=\"colab-df-container\">\n",
              "    <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>location</th>\n",
              "      <th>t_arr</th>\n",
              "      <th>t_dep</th>\n",
              "      <th>c_arr</th>\n",
              "      <th>c_dep</th>\n",
              "      <th>t_stop</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>index</th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>30.0000</td>\n",
              "      <td>150.0000</td>\n",
              "      <td>0.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>191.6</td>\n",
              "      <td>1.916000</td>\n",
              "      <td>2.389227</td>\n",
              "      <td>104.0160</td>\n",
              "      <td>150.0000</td>\n",
              "      <td>0.473227</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>310.6</td>\n",
              "      <td>3.579227</td>\n",
              "      <td>4.031493</td>\n",
              "      <td>121.4400</td>\n",
              "      <td>150.0000</td>\n",
              "      <td>0.452267</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>516.0</td>\n",
              "      <td>6.085493</td>\n",
              "      <td>6.252162</td>\n",
              "      <td>100.7040</td>\n",
              "      <td>100.7041</td>\n",
              "      <td>0.166669</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>683.6</td>\n",
              "      <td>7.928162</td>\n",
              "      <td>7.928162</td>\n",
              "      <td>60.4801</td>\n",
              "      <td>60.4801</td>\n",
              "      <td>0.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>769.9</td>\n",
              "      <td>8.791162</td>\n",
              "      <td>9.241507</td>\n",
              "      <td>39.7681</td>\n",
              "      <td>53.9520</td>\n",
              "      <td>0.450345</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>869.7</td>\n",
              "      <td>10.239507</td>\n",
              "      <td>10.740733</td>\n",
              "      <td>30.0000</td>\n",
              "      <td>63.4560</td>\n",
              "      <td>0.501227</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>1009.1</td>\n",
              "      <td>12.134733</td>\n",
              "      <td>12.848119</td>\n",
              "      <td>30.0000</td>\n",
              "      <td>112.0079</td>\n",
              "      <td>0.713386</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>1164.7</td>\n",
              "      <td>14.404119</td>\n",
              "      <td>14.404119</td>\n",
              "      <td>74.6639</td>\n",
              "      <td>74.6639</td>\n",
              "      <td>-0.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>1230.8</td>\n",
              "      <td>15.065119</td>\n",
              "      <td>15.231787</td>\n",
              "      <td>58.7999</td>\n",
              "      <td>58.8000</td>\n",
              "      <td>0.166668</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>1350.8</td>\n",
              "      <td>16.431787</td>\n",
              "      <td>17.078454</td>\n",
              "      <td>30.0000</td>\n",
              "      <td>150.0000</td>\n",
              "      <td>0.646667</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>1508.4</td>\n",
              "      <td>18.654454</td>\n",
              "      <td>18.654454</td>\n",
              "      <td>112.1760</td>\n",
              "      <td>112.1760</td>\n",
              "      <td>0.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>1639.8</td>\n",
              "      <td>19.968454</td>\n",
              "      <td>20.135120</td>\n",
              "      <td>80.6400</td>\n",
              "      <td>80.6400</td>\n",
              "      <td>0.166667</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>1809.4</td>\n",
              "      <td>21.831120</td>\n",
              "      <td>22.236507</td>\n",
              "      <td>39.9360</td>\n",
              "      <td>75.7440</td>\n",
              "      <td>0.405387</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>1947.3</td>\n",
              "      <td>23.615507</td>\n",
              "      <td>23.615507</td>\n",
              "      <td>42.6480</td>\n",
              "      <td>42.6480</td>\n",
              "      <td>0.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>2000.0</td>\n",
              "      <td>24.142507</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>30.0000</td>\n",
              "      <td>30.0000</td>\n",
              "      <td>-24.142507</td>\n",
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              "summary": "{\n  \"name\": \"results\",\n  \"rows\": 16,\n  \"fields\": [\n    {\n      \"column\": \"index\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 4,\n        \"min\": 0,\n        \"max\": 15,\n        \"num_unique_values\": 16,\n        \"samples\": [\n          0,\n          1,\n          5\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"location\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 626.8555245229957,\n        \"min\": 0.0,\n        \"max\": 2000.0,\n        \"num_unique_values\": 16,\n        \"samples\": [\n          0.0,\n          191.6,\n          769.9\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"t_arr\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 7.715598867381851,\n        \"min\": 0.0,\n        \"max\": 24.14250700000007,\n        \"num_unique_values\": 16,\n        \"samples\": [\n          0.0,\n          1.916,\n          8.791162000000007\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"t_dep\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 7.712878680235608,\n        \"min\": 0.0,\n        \"max\": 23.61550700000006,\n        \"num_unique_values\": 15,\n        \"samples\": [\n          15.23178700000004,\n          18.65445366666673,\n          0.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"c_arr\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 32.97191876010049,\n        \"min\": 30.0,\n        \"max\": 121.44,\n        \"num_unique_values\": 12,\n        \"samples\": [\n          39.93599999999996,\n          80.63999999999999,\n          30.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"c_dep\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 41.36660570270018,\n        \"min\": 30.0,\n        \"max\": 150.0,\n        \"num_unique_values\": 13,\n        \"samples\": [\n          42.64800000000001,\n          80.63999999999999,\n          150.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"t_stop\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 6.109653297216072,\n        \"min\": -24.142507,\n        \"max\": 0.713386,\n        \"num_unique_values\": 12,\n        \"samples\": [\n          0.405387,\n          0.166667,\n          0.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
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          "metadata": {}
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      ],
      "source": [
        "def ev_plan(stations, x, D):\n",
        "    # data preprocessing\n",
        "\n",
        "    # find stations between x and x + D\n",
        "    on_route = stations[(stations[\"location\"] >= x) & (stations[\"location\"] <= x + D)]\n",
        "\n",
        "    # adjust the index to match the model directly\n",
        "    on_route.index += 1\n",
        "\n",
        "    n = len(on_route)\n",
        "\n",
        "    # get the values of the location parameter\n",
        "    location = on_route[\"location\"].to_dict()\n",
        "    location[0] = x\n",
        "    location[n + 1] = x + D\n",
        "\n",
        "    # get the values for the dist parameter\n",
        "    dist = {}\n",
        "    for s in range(1, n + 2):\n",
        "        dist[s] = location[s] - location[s - 1]\n",
        "\n",
        "    # define the indexing sets\n",
        "    # note the +1 at the end because Python ranges are not inclusive at the endpoint\n",
        "    STATIONS = list(range(1, n + 1))  # 1 to n\n",
        "    LOCATIONS = list(range(n + 2))  # 0 to n + 1\n",
        "    SEGMENTS = list(range(1, n + 2))  # 1 to n + 1\n",
        "\n",
        "    # instantiate AMPL and load model\n",
        "    m = AMPL()\n",
        "    m.read(\"ev_plan.mod\")\n",
        "\n",
        "    m.set[\"STATIONS\"] = STATIONS\n",
        "    m.set[\"LOCATIONS\"] = LOCATIONS\n",
        "    m.set[\"SEGMENTS\"] = SEGMENTS\n",
        "\n",
        "    # load data\n",
        "    m.param[\"C\"] = on_route[\"kw\"]\n",
        "    m.param[\"location\"] = location\n",
        "    m.param[\"D\"] = D\n",
        "    m.param[\"n\"] = n\n",
        "    m.param[\"c_min\"] = c_min\n",
        "    m.param[\"c_max\"] = c_max\n",
        "    m.param[\"r_max\"] = r_max\n",
        "    m.param[\"t_lost\"] = t_lost\n",
        "    m.param[\"v\"] = v\n",
        "    m.param[\"R\"] = R\n",
        "    m.param[\"dist\"] = dist\n",
        "\n",
        "    # initial conditions\n",
        "    m.var[\"x\"][0].fix(x)\n",
        "    m.var[\"t_dep\"][0].fix(0.0)\n",
        "    m.var[\"r_dep\"][0].fix(0.0)\n",
        "    m.var[\"c_dep\"][0].fix(c)\n",
        "\n",
        "    # set solver and solve\n",
        "    m.solve(solver=SOLVER)\n",
        "    assert m.solve_result == \"solved\", m.solve_result\n",
        "\n",
        "    return m\n",
        "\n",
        "\n",
        "def get_results(model):\n",
        "    x = [(int(k), v) for k, v in model.var[\"x\"].to_list()]\n",
        "    t_arr = [v for k, v in model.var[\"t_arr\"].to_list()]\n",
        "    t_dep = [v for k, v in model.var[\"t_dep\"].to_list()]\n",
        "    c_arr = [v for k, v in model.var[\"c_arr\"].to_list()]\n",
        "    c_dep = [v for k, v in model.var[\"c_dep\"].to_list()]\n",
        "\n",
        "    results = pd.DataFrame(x, columns=[\"index\", \"location\"]).set_index(\"index\")\n",
        "    results[\"t_arr\"] = t_arr\n",
        "    results[\"t_dep\"] = t_dep\n",
        "    results[\"c_arr\"] = c_arr\n",
        "    results[\"c_dep\"] = c_dep\n",
        "    results[\"t_stop\"] = results[\"t_dep\"] - results[\"t_arr\"]\n",
        "    results[\"t_stop\"] = results[\"t_stop\"].round(6)\n",
        "\n",
        "    return results\n",
        "\n",
        "\n",
        "m = ev_plan(stations, 0, 2000)\n",
        "results = get_results(m)\n",
        "display(results)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "id": "6191e5d4-ac20-4b0c-b774-990d780f0295",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 751
        },
        "id": "6191e5d4-ac20-4b0c-b774-990d780f0295",
        "outputId": "65adaf41-a809-4d90-c0a5-097eebef48e6"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "HiGHS 1.10.0: \b\b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.10.0: optimal solution; objective 24.142507\n",
            "9961 simplex iterations\n",
            "116 branching nodes\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x800 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# visualize\n",
        "\n",
        "\n",
        "def visualize(m):\n",
        "    D = m.param[\"D\"].value()\n",
        "\n",
        "    results = get_results(m)\n",
        "\n",
        "    results[\"t_stop\"] = results[\"t_dep\"] - results[\"t_arr\"]\n",
        "\n",
        "    fig, ax = plt.subplots(2, 1, figsize=(15, 8), sharex=True)\n",
        "\n",
        "    # plot stations\n",
        "    for station in stations.index:\n",
        "        xs = stations.loc[station, \"location\"]\n",
        "        ys = stations.loc[station, \"kw\"]\n",
        "        ax[0].plot([xs, xs], [0, ys], \"b\", lw=10, solid_capstyle=\"butt\")\n",
        "        ax[0].text(xs, 0 - 30, stations.loc[station, \"name\"], ha=\"center\")\n",
        "\n",
        "    # plot planning horizon\n",
        "    ax[0].plot(\n",
        "        [x, x + D], [0, 0], \"r\", lw=5, solid_capstyle=\"butt\", label=\"plan horizon\"\n",
        "    )\n",
        "    ax[0].plot([x, x + D], [0, 0], \"r.\", ms=20)\n",
        "\n",
        "    # annotations\n",
        "    ax[0].axhline(0)\n",
        "    ax[0].set_ylim(-50, 300)\n",
        "    ax[0].set_ylabel(\"kw\")\n",
        "    ax[0].set_title(\"charging stations\")\n",
        "    ax[0].legend()\n",
        "\n",
        "    SEGMENTS = m.set[\"SEGMENTS\"].to_list()\n",
        "\n",
        "    # plot battery charge\n",
        "    for i in SEGMENTS:\n",
        "        xv = [results.loc[i - 1, \"location\"], results.loc[i, \"location\"]]\n",
        "        cv = [results.loc[i - 1, \"c_dep\"], results.loc[i, \"c_arr\"]]\n",
        "        ax[1].plot(xv, cv, \"g\")\n",
        "\n",
        "    STATIONS = m.set[\"STATIONS\"].to_list()\n",
        "\n",
        "    # plot charge at stations\n",
        "    for i in STATIONS:\n",
        "        xv = [results.loc[i, \"location\"]] * 2\n",
        "        cv = [results.loc[i, \"c_arr\"], results.loc[i, \"c_dep\"]]\n",
        "        ax[1].plot(xv, cv, \"g\")\n",
        "\n",
        "    # mark stop locations\n",
        "    for i in STATIONS:\n",
        "        if results.loc[i, \"t_stop\"] > 0:\n",
        "            ax[1].axvline(results.loc[i, \"location\"], color=\"r\", ls=\"--\")\n",
        "\n",
        "    # show constraints on battery charge\n",
        "    ax[1].axhline(c_max, c=\"g\")\n",
        "    ax[1].axhline(c_min, c=\"g\")\n",
        "    ax[1].set_ylim(0, 1.1 * c_max)\n",
        "    ax[1].set_ylabel(\"Charge (kw)\")\n",
        "\n",
        "\n",
        "visualize(ev_plan(stations, 0, 2000))"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "479452ec-be4e-46e4-baa8-4f1e9de69968",
      "metadata": {
        "id": "479452ec-be4e-46e4-baa8-4f1e9de69968"
      },
      "source": [
        "## Suggested Exercises\n",
        "\n",
        "1. Does increasing the battery capacity $c^{max}$ significantly reduce the time required to travel 2000 km? Explain what you observe.\n",
        "\n",
        "2. \"The best-laid schemes of mice and men go oft awry\" (Robert Burns, \"To a Mouse\"). Modify this model so that it can be used to update a plans in response to real-time measurements. How does the charging strategy change as a function of planning horizon $D$?"
      ]
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