Clustering Algorithm for Paper Boys

Question

I need help selecting or creating a clustering algorithm according to certain criteria.

Imagine you are managing newspaper delivery persons.

• You have a set

Answer 1

This is a very quick and dirty method of discovering where your "clusters" lie. This was inspired by the game "Minesweeper."

Divide your entire delivery space up into a grid of squares. Note - it will take some tweaking of the size of the grid before this will work nicely. My intuition tells me that a square size roughly the size of a physical neighbourhood block will be a good starting point.

Loop through each square and store the number of delivery locations (houses) within each block. Use a second loop (or some clever method on the first pass) to store the number of delivery points for each neighbouring block.

Now you can operate on this grid in a similar way to photo manipulation software. You can detect the edges of clusters by finding blocks where some neighbouring blocks have no delivery points in them.

Finally you need a system that combines number of deliveries made as well as total distance travelled to create and assign routes. There may be some isolated clusters with just a few deliveries to be made, and one or two super clusters with many homes very close to each other, requiring multiple delivery people in the same cluster. Every home must be visited, so that is your first constraint.

Derive a maximum allowable distance to be travelled by any one delivery person on a single run. Next do the same for the number of deliveries made per person.

The first ever run of the routing algorithm would assign a single delivery person, send them to any random cluster with not all deliveries completed, let them deliver until they hit their delivery limit or they have delivered to all the homes in the cluster. If they have hit the delivery limit, end the route by sending them back to home base. If they could safely travel to the nearest cluster and then home without hitting their max travel distance, do so and repeat as above.

Once the route is finished for the current delivery person, check if there are homes that have not yet had a delivery. If so, assign another delivery person, and repeat the above algorithm.

This will generate initial routes. I would store all the info - the location and dimensions of each square, the number of homes within a square and all of its direct neighbours, the cluster to which each square belongs, the delivery people and their routes - I would store all of these in a database.

I'll leave the recalc procedure up to you - but having all the current routes, clusters, etc in a database will enable you to keep all historic routes, and also try various scenarios to see how to best to adapt to changes creating the least possible changes to existing routes.