Société mathématique du Canada
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  1. At certain times charities call households offering to pick-up used items for sale in their stores. They often do a particular geographical area at a time. Their problem, once they know where the pick-ups are, is to decide on the most efficient routes to make the collection. Find out how they do this and investigate improving their procedure. A similar question can be asked about snow plows clearing city streets, or garbage collection. References: Euclidean tours, chinese postman problem - information can be found in most books on graph theory but one of particular interest is [B&C].
  2. How should one locate ambulance stations, so as to best serve the needs of the community? How do major hospitals schedule the use of operating theatres? Are they doing it the best way possible so that the maximum number of operations are done each day? The reference given above may help.
  3. How does the NBA work out the basketball schedule? How would you do such a schedule bearing in mind distances between locations of games, home team advantage etc.? Could you devise a good schedule for one of your local competitions? Reference: [D,L&W].
  4. How would a factory schedule the production of bicycles? Which parts are put together first? How many people are required to work at each stage of the production? Reference: [Gra].
  5. Look for new strategies for solving the traveling salesman problem.

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