Here's the problem - your range of numbers has only 3.6x10^9 possible values where as your sample unique string (which looks like a hex integer with 36 digits) has 16^32 possible values (i.e. many more). So when mapping your string into your integer range there will be collisions.
The mapping function itself can be pretty straightforward, I would do something such as below (also, consider using only a part of the input string for integer conversion, e.g. the first seven digits, if performance becomes critical):
def my_hash(str, min, max) range = (max - min).abs (str.to_i(16) % range) + min end my_hash(did, min_cid, max_cid) # => 2461595789
[Edit] If you are using Ruby 1.8 and your adjusted range can be represented as a Fixnum, just use the hash value of the input string object instead of parsing it as a big integer. Note that this strategy might not be safe in Ruby 1.9 (per the comment by @DataWraith) as object hash values may be randomized between invocations of the interpreter so you would not get the same hash number for the same input string when you restart your application:
def hash_range(obj, min, max) (obj.hash % (max-min).abs) + [min, max].min end hash_range(did, min_cid, max_cid) # => 3886226395
And, of course, you'll have to decide what to do about collisions. You'll likely have to persist a bucket of input strings which map to the same value and decide how to resolve the conflicts if you are looking up by the mapped value.
