I don't see why you've added the mythical-creatures tag, after all, he is real! You should really know that by now...

How many households are we talking about? Afterwards, it's a Travelling Salesman Problem

There's a good amount of time saved by timezones, as the Santas have a window of time that's different for each timezone. Different groups of people also celebrate Christmas at different dates. There's 24th and 25th of december, as well as 6th and 7th of january.

Does it have to take account the limit of his stomach ? Cause after a hundred glass of cherry and a mince pie, I don't think he'll ba able to continue ...

@Asoub you are right - the magical resurrected (or whatever) corpse of a guy from the 4th century, who goes around the entire globe in one night is obviously going to have a problem with his belly...even though he also has an effectively bottomless sack of presents and manages to squeeze through chimneys with little effort.

Since the great fairy dust shortage of 2013 (leading to the tragic high velocity impact death of Rudolf when he fell out of the sky above Chelyabinsk Oblast, in February, they were running a bit late with their Russian deliveries due to the shortage) he's switched to an automated drone delivery system, still only 1 Santa, but rather a lot more Elves than before (sitting behind PC's guiding the deliveries)

@Pelinore: Automated drone delivery... So Santa is responsible for closing Gatwick Airport!!!

Yup one of his, probably why the police haven't found it yet.

You do know that the 'Santa' Mommy's kissing is Daddy, right?

@AJFaraday search your feelings, you know it to be true

Are we just considering delivery Santas or does this include the logistical and support Santas who manage their routes?

@Studoku, administration and logistics can be handled by elves. Only delivery requires a Santa.

I'm really disappointed by the answers to this question. I'd classify every single answer here a joke answer. Nobody seems to be actually trying to answer the question as posed.

A rough estimate of how many Santas there are can be approximated by the number of malls, each mall seems to have a Santa this time of year.

@nzaman This is the easy case as no segments have a negative weight. However, I don't think the travel time is a big deal as most hops are short compared to the time needed to deliver presents and eat.

There are four Santas.

If one of the requirements of the question is "a shuffling in the chimney", is it an implicit assumption that residences without chimneys large enough for a human to traverse (or any chimney at all) are not "really" visited by Santa? Or are answers required to allow for Santas achieving entry to all residences regardless of chimney presence (without breaking laws of physics)? (Thinking of having a serious go at this, if the housing / heating statistics are readily available)

@LorenPechtel: I've been on this site too long: at first reading I was wondering what time travel had to do with anything :( The reason travel time is important is because each hop has a fixed cost, which is hopping down chimneys or other access points and delivering presents and eating. Now, we can't do anything about the delivering and eating, but we can cut the access costs, as in, if you have two trees in adjacent buildings and one on the other end of the city, Santa should finish the job that's nearest, before travelling to the distant one.

@KerrAvon2055, you might find the stats on that, but it'll probably be related to secondary data like the banning of coal fires in urban areas in the UK after the great smog or the widespread use of gas central heating over open fires.

@nzaman What I'm saying is that for most trips the fixed cost is going to way dominate the variable cost and thus the variable cost isn't all that important.