Postman is a simulation problem, but one with a few traps.

The basic approach is to simply deliver as many letters as
possible to the furthest houses first; you must make at
least that many trips at that distance, so this is optimal.
If you instead try to deliver to the closest houses first,
you may end up with a suboptimal solution; consider the case

   House   Distance  Letters
     1        10      500
     2        20     1000

with a postman capacity of 1000.  If we do the close house first,
then the postman will deliver 500 letters to house 1, and then
500 to house 2---but will need to make a second trip to house 2,
for a total time of 2 round trips at distance 20 which is 80
time units.

If instead he takes a round trip to house 2 first, he'll deliver
all 1000 letters to house 2 in one round trip and finish up with
one final trip to house 1 carrying only 500 letters for a total
of 60.

The problem is the number of letters and the distances can be
large (although the count of houses is small).  If you simulate
each individual trip, you will run out of time, because the
total number of letters could be as high as 10^10.  So you want
to figure out how many round trips to a given house are required
and, with a tiny bit of math, figure out how many letters
will be left over to drop off along the route of the last round
trip to the next closer house (and possibly additional houses).

The second trap is a common one---the result may not fit in a
32-bit int so you need to use doubles or 64-bit ints.