Designing Recycling Routes

Western Disposal Sevices has begun implementing new routes for the pickup of recyclable materials in Boulder. (See the article entitled (Name of article) From the Boulder Daily Camera, July 99, 1996.) These routes will be determined by a computer which will attempt to find the most efficient way for the trucks to visit various locations around city. Among the considerations being built into the model are: avoiding U-turns and places where the trucks have to back up, eliminating left turns across heavy oncoming traffic, finding the best way to deal with one way streets, and minimizing the total distance the trucks must travel.

Consider the following simplification of Western Disposal'âs challenge:

You must design a route which will make pickups at all of the recycling bins in a small portion of town. Your goal in designing the route is to determine the shortest route which will pass every bin. Assume that you must start at the company garage and, when all of the bins have been emptied, return back to the garage to empty the truck.

Find the shortest route which stops at each of the three recycling locations (A, B, and C) in following situation. The numbers along the edges represent the distance (in miles) from one location to the other. Remember, you must start and end at the garage, and pass each pickup location once.

Now, try to find a similar route for the following set of locations and distances. Note that you may need to find a best guess for the best route. Keep a record of how you decided on your route, and the route you found.