clean up flow.ipynb headings

Author: jGaboardi

notebooks/flow.ipynb

@@ -5,22 +5,10 @@
    "id": "412b4109",
    "metadata": {},
    "source": [
-    "#### Flow Refueling Location Model (FRLM)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "1653f7c3",
-   "metadata": {},
-   "source": [
-    "*Authors:* [Zixin Feng](https://github.com/fengzixin0617), [Germano Barcelos](https://github.com/gegen07), [Levi John Wolf](https://github.com/ljwolf), [Qunshan Zhao](https://github.com/qszhao) "
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "6f51910e",
-   "metadata": {},
-   "source": [
+    "# Flow Refueling Location Model (FRLM)\n",
+    "\n",
+    "*Authors:* [Zixin Feng](https://github.com/fengzixin0617), [Germano Barcelos](https://github.com/gegen07), [Levi John Wolf](https://github.com/ljwolf), [Qunshan Zhao](https://github.com/qszhao) \n",
+    "\n",
     "The FRLM is a location-allocation model for optimally locating refueling facilities for range-limited vehicles, such as alt-fuel vehicles. For these vehicles, it may be necessary to stop at more than one facility in order to successfully refuel the entire path length. The model optimally locates $p$ refueling stations on a network so as to maximize the total flow volume refueled. The model could also work for any new network-based, range limited surface transport mode.\n",
     "\n",
     "**FRLM can be written as:**\n",
@@ -33,7 +21,6 @@
     "& x_k, v_h, y_q \\in \\{0,1\\} \\quad \\forall k, h, q \n",
     "\\\\[0.7em] \\end{array}$\n",
     "\n",
-    "\n",
     "$\\begin{array}{ll}\n",
     "q & = \\text{index of origin–destination (O–D) pairs} \\\\\n",
     "Q & = \\text{set of all O–D pairs} \\\\\n",
@@ -50,8 +37,6 @@
     "v_h & = \\text{1 if all facilities in combination } h \\text{ are open, 0 otherwise}\n",
     "\\end{array}$\n",
     "\n",
-    "\n",
-    "\n",
     "_The formulation above is adapted from Kuby and Lim (2005)._"
    ]
   },
@@ -106,7 +91,7 @@
    "id": "305573d9",
    "metadata": {},
    "source": [
-    "#### Create sample network "
+    "## Create sample network "
    ]
   },
   {
@@ -167,14 +152,7 @@
    "id": "184a969c",
    "metadata": {},
    "source": [
-    "#### Create sample flows"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "eddccfc7",
-   "metadata": {},
-   "source": [
+    "## Create sample flows\n",
     "\n",
     "Create Origin-Destination (OD) pairs to represent travel demand across a spatial network. Each tuple in the dataset follows the format `(origin_node, destination_node, flow_volume)`. The flow volumes are the total number of trips between each pair of locations."
    ]
@@ -293,7 +271,7 @@
    "id": "dd88791c",
    "metadata": {},
    "source": [
-    "### Basic FRLM model "
+    "## Basic FRLM model "
    ]
   },
   {
@@ -373,21 +351,23 @@
    "metadata": {},
    "source": [
     "- Retrieve flow/vmt coverage details, and get Dict with coverage info for each OD pair\n",
+    "\n",
     "```python\n",
     "flow_coverage = model.get_flow_coverage()\n",
     "vmt_coverage = model.get_vmt_coverage()\n",
     "```\n",
     "\n",
     " - Retrieve node coverage percentage\n",
+    "\n",
     "```python\n",
     "node_coverage_pct = model.get_node_coverage_percentage()\n",
     "```\n",
     "\n",
     " - Get all available statistics in one call\n",
+    "\n",
     "```python\n",
     "details = model.get_detailed_results()\n",
-    "```\n",
-    "\n"
+    "```"
    ]
   },
   {
@@ -662,27 +642,15 @@
     "plt.show()"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "id": "c7a45013",
-   "metadata": {},
-   "source": [
-    "The red dot indicates the selected facility location. Green lines show the OD flows that are covered by the selected facility."
-   ]
-  },
   {
    "cell_type": "markdown",
    "id": "9fa7b991",
    "metadata": {},
    "source": [
-    "### FRLM threshold extension"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "17b0b5e5",
-   "metadata": {},
-   "source": [
+    "The red dot indicates the selected facility location. Green lines show the OD flows that are covered by the selected facility.\n",
+    "\n",
+    "## FRLM threshold extension\n",
+    "\n",
     "The FRLM threshold extension is based on the original FRLM. The extended model optimally locates $p$ refueling stations on a network to maximize the sum of weighted demand of covered origin/destination zones, where 'covered' means that the zone exceeds a specified threshold percentage of their total outbound/inbound round trips that are refuelable. \n",
     "\n",
     "**FRLM threshold extension can be written as:**\n",
@@ -857,19 +825,13 @@
     "plt.show()"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "id": "56112e4f",
-   "metadata": {},
-   "source": [
-    "### Capacited FRLM"
-   ]
-  },
   {
    "cell_type": "markdown",
    "id": "f3d57627",
    "metadata": {},
    "source": [
+    "## Capacited FRLM\n",
+    "\n",
     "The original FRLM is an uncapacitated model. It assumes that the presence of a refueling station is sufficient to serve all flows passing through a node, regardless of their volume. Although it is applicable for early stages of alternative fuel vehicle adoption, it may not be applicable when the adoption of alternative fuel vehicles increase. The capacitated FRLM thus limits the number of vehicles refueled at each station.\n",
     "\n",
     "Compared to the original FRLM, the capacitated FRLM has three changes.\n",
@@ -912,7 +874,7 @@
     "b_{qh} & \\text{1 if combination } h \\text{ can refuel OD pair } q  \\text{, 0 otherwise} \\\\\n",
     "e_q & \\text{Average fraction of round trips for OD pair } q \\text{ that require refueling} \\\\\n",
     "g_{qhk} & \\text{Average number of times a vehicle traveling on path } q \\text{ and being refueled by combination} h \\text{ stops at station } k \\text{ on each round trip that requires refueling} \\\\\n",
-    "\\\\ \\end{array}$\n"
+    "\\\\ \\end{array}$"
    ]
   },
   {
@@ -1271,7 +1233,7 @@
     "\n",
     "- [Hong, S., & Kuby, M. (2016). A threshold covering flow-based location model to build a critical mass of alternative-fuel stations. Journal of Transport Geography, 56, 128-137.](https://doi.org/10.1016/j.jtrangeo.2016.08.019)\n",
     "\n",
-    "- [Kuby, M., & Lim, S. (2005). The flow-refueling location problem for alternative-fuel vehicles. Socio-Economic Planning Sciences, 39(2), 125-145.](https://doi.org/10.1016/j.seps.2004.03.001)\n"
+    "- [Kuby, M., & Lim, S. (2005). The flow-refueling location problem for alternative-fuel vehicles. Socio-Economic Planning Sciences, 39(2), 125-145.](https://doi.org/10.1016/j.seps.2004.03.001)"
    ]
   }
  ],