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 who 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.

Respond to at least two posts contributed by your peers and comment on the problem they demonstrated and the steps they employed to reach a solution. What would you have done the same or different? Do you agree with the solution? Can you suggest a different approach to solving the same problem?