scenario You are the personal assistant to a chief executive

\"scenario\"

You are the personal assistant to a chief executive of an international company. Your
boss wishes to plan a promotional tour of major cities and prominent locations in some area of the world; e.g.,
North America, Scandinavia, Mediterranean, Central Europe, South-East Asia, Middle East, North Africa,
Southern or Central Africa, South America, Central America, the Pacific, etc. Travel will be done by using
a chartered jet with pilot hired for the tour.
Your task is firstly to choose 8–10 locations from capital cities and famous tourist destinations within such
a geographical region. (This is the easy part; use a map and make appropriate selections.)
Secondly you must produce a route that starts from the largest capital city, where the jet will be rented, and
visits all the locations exactly once, before returning to that starting city. However, as primary costs for this
venture will be the amount of fuel required and the pilot’s flying time, you want to make the overall length of
the round trip to be as short as possible.
To achieve this 2nd part, you will need to create a table of the flying distances between each of your chosen
locations. Use sites on the internet to find the information you need to build up this table; e.g., as cells within
a spreadsheet. (As shown in a lecture the Wolfram Alpha website† provides a way to obtain such information.)
Other sites‡ give some information.
Interpreting these distances as weights within a complete graph having a node for each location, the choice of
round trip constitutes finding a Hamiltonian cycle within this weighted complete graph. The aim is to find
a Hamiltonian cycle that has the lowest total weight, or at least one that is close to being of lowest weight.
Since there is no efficient reliable algorithm to ensure finding the minimal weight cycle, you must do the best
you can and provide some justification for why you think the route you are proposing is at least close to being
minimal.
Present your answer in a neat, clear fashion; e.g., with the route marked out on a map, as well as a listing
of each step along the way.
You can (and should, as you want to make a good impression with your boss) include other information that
might be of interest to your boss while on such a tour. This could be information that you uncover whilst
collecting the flight distances; e.g., expected flight times, cost of jet fuel, average cost per night in a 5-star
hotel, distance from the airport to city centre, best time of year to visit this location, any active volcanos
nearby or other potentially catastrophic circumstances (whether natural or man-made) that may affect the
chosen route, etc.

Solution

North America, , Mediterranean, Central Europe, , Middle East, North Africa,South-East Asia
Southern or Central Africa, South America,Scandinavia, Central America, the Pacific