Integrating Past, Present, and Future Approaches - Spatial Mathematics: Theory and Practice through Mapping - page 231

using nearest address” and choose the following address locator: “10.0 US
Streets Geocode Service (ArcGIS Online).” Change the impedance to “length.”
On the same Options screen, mark the “Add route to map as” option as your
choice of a graphic or a shapefile, with the symbology set to a red line.
Still on the Find Route tool, under the Stops tab, this time, instead of using
the arrow to add dots, use the “Add Stop” tool. Enter the following addresses,
one at a time, and after adding each, right click and “add as stop in route”: 276
North St., Boston, MA 02113; 1500 2nd Street, Birmingham, AL 35214; 3801 Old
Greenwood Road, Fort Smith, AR 72903; and, 1402 Grant Ave, Boise, ID 83706.
Once these points are loaded as stops, select Find Route. Describe the results.
Remember that you chose, in this problem, to minimize the length. How did
this choice affect the number of US and state highways that your truck will
travel on versus interstate highways? Minimizing the length should allow for
some US and state highways to be used, and not only interstate highways,
since the goal here is to minimize the total distance the truck has to travel.
Next, experiment with the routing options. How does adding one stop, chang-
ing the order of stops, adding a barrier, or adding a time window affect the
length and time of the resulting route? Any of these items should alter the
total length and time. Repeat the process above, and this time, select the
quickest route rather than the shortest route by changing the impedance from
“length” to “time.” Is there any difference? Why? There should be a differ-
ence because in analogy with the local example of New York City, the short-
est route in distance is not necessarily the same as the fastest route in time.
The map does show a difference, but it is only visible by zooming into larger
scales. The route that is shortest in time occasionally sends your truck over
different highways than it does for the route that is shortest in length. Around
New York City, for example, your truck driver would actually save time to
travel around New York City (the red road) instead of the traveling the short-
est length route, which would go straight through New York City (the dark
red road) ( Figure 10.13 ) .
To empirically discover the difference between shortest versus quickest route,
save the routes as geodatabase feature classes or shapefiles. Then, edit the
resulting tables in those geodatabase feature classes or shapefiles, populat-
ing the distance and time fields with the data that the routing tool combined
into a description field. Summarizing these fields yielded 5999 miles and 98
hours for the shortest route, versus 6016 miles and 93.9 hours for the quickest
route. Both routes could indeed be done in a week; the quickest route adds
17 miles but cuts over 4 hours of travel time. What factors might delay the
total time required for your shipment? These factors could include rest stops
for your driver, since you cannot expect any single driver to drive nearly 100
hours without sleep or breaks. Other factors causing delays could be traffic,
stopping for toll booths, road construction, and so on. Through creating and
comparing routes, activities such as this illustrate the spatial and mathemati-
cal thinking that is critical in the investigation of real-world problems.