Assignment 1: Discussion—The Traveling Salesman Problem

Some problems in mathematics can be stated very simply but may involve complex solutions. One of the most famous of these is the Traveling Salesman Problem or, as it is known to mathematicians, the TSP.

The TSP is the problem of deciding the most efficient route to take between multiple cities to save time and money. This problem occupies the minds of managers from shipping companies to postal services to airlines. The routes you choose affect both your income and your expenses. Therefore, the TSP is an extremely important problem in the modern world. If you haven’t already done so, please read the section of your textbook which provides a detailed overview of the TSP and the numerous methods used to find solutions.

Now, put yourself in the role of a business manager that must make deliveries to five different cities in five different states. You may pick the five cities that you would like to use in this scenario. Prepare a multiple paragraph response of between 200-300 words addressing the following:

• State the problem you are solving making sure to mention the five delivery destinations.
• Clearly demonstrate each step you followed to reach the most efficient route between these five cities.
• Consider all of the expenses that may be incurred while making these deliveries and how choosing an efficient route helps to curtail these costs.

HERE IS AN EXAMPLE:

I’m a business manager that has to make deliveries to five different cities and my first delivery is in my hometown of Greensboro, NC.  The 1^st delivery is at 8:00 a.m., my 2^nd delivery is in Charlotte, NC at 12:00 p.m., my 3^rd delivery is in Memphis, TN the following morning at 7:00 a.m., my 4^th delivery is in Birmingham, AL at 12:00 p.m., and my last delivery is in Atlanta at 4:00 p.m.

In order to find the best possible routes, I go online and get driving directions through Mapquest.com even though I have a GPS.  I go online so that I can plan ahead so that I can make my deliveries on time.

Prior to leaving for my 1^st appointment at 8:00 a.m., I will fill up the car, which will cost approximately $45.00.  From my 1^st appointment in Greensboro, NC, I will take 85S and then 77S to Charlotte, NC, which is approximately 93 miles from Greensboro, NC and it takes approximately 1 hour and 37 minutes. I will top off at a Wendy’s and order 2 chicken sandwiches (love them!) for $2.00 since my delivery appointment isn’t until 12:00 p.m.  After my delivery in Charlotte, NC, I will take 277S to 85S to 74W.  I will then take I-40W and then TN3 South.  I will arrive in Memphis, TN at around 10:30 p.m. since it will take 10 hours after driving 620 miles and after filling up the gas tank twice which totals approximately $90.00.  I spend the night at the Days Inn Hotel in Memphis, TN at $55.00 for one night and make my 7:00 a.m. appointment.  I fill up the tank again and order 2 egg, sausage and cheese croissants at Burger King for $3.00 and leave Memphis, TN at 8:00 a.m., I take TN3 South to I-40E, then 240S then 240E.  Then I take 78E to CR-77S.  Then 65S to 59N to Birmingham, AL.  I will arrive in Birmingham at 12:00 p.m. and make the delivery. It takes approximately 4 hours and it’s 237 miles from Memphis, TN.  At 12:30 p.m., I leave Birmingham, AL and take 20E to GA-154 to Atlanta, GA.  I arrive at 3:30 p.m. and stop off at Wendy’s again to buy 2 more chicken sandwiches.  This trip takes approximately 3 hours and is 147 miles from Birmingham, AL.  I fill up the tank again and head back home.  I get on 85N and travel 478 miles, which will take approximately 8 hours.

The expenses incurred for this trip will be approximately $270.00 for gas, which includes going back home, $10.00 for food, snacks, coffee, and soda, and $55.00 for lodging.