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Santa keeps his elves under horrid, appalling conditions. Working everyday of the year for little pay in the freezing cold of the North Pole. But just how many elves does he need?
How many elves would it take to build enough toys for 2+ billion boys and girls across the world?
You have to make some assumptions, so I'll answer more generally and you can plug in other numbers if you think my assumptions are off.
The number of elves required is given by
$$ C T \over D H R $$
Where
C = Number of children in the world
T = Number of toys for each child
D = Annual days of work for elves
H = Hours in an elf workday
R = Toymaking rate in toys per hour
If you assume 2 billion children, 1 toy each, 364 workdays (Christmas day through the following December 23rd - then packing the sleigh on Christmas Eve), 16 hour days (Elven sweatshop!), and each elf can make 4 toys per hour, you need around 85,851 elves. That's quite a workshop.
This is only the set of elves required to make the toys. They'll need support staff too. Making food for 85k+ elves, cleaning and maintenance, procuring all of the materials for toy-making, quality control, and other functions could easily add another 50+% to the base number.
I'll go the other way and say, hardly none. We definitely need more Santa Clauses.
Raw materials are delivered by some human logistics company to a fake address in northern Norway or Canada. No elves here.
It's still 2016 and some years ago Industry 4.0 / IoT was introduced. So, no manual work to be done here, except for maintenance and setup.
If we produce one present every ten seconds, a single machine would produce 3144000 items per year. (Source: Output of a factory line in my company)
In order to fulfill our plan to produce 2 Billion toys, we need roughly 800 of these machines.
Elven Equipment Engineers may be able to handle 10 machines per two engineers. 1600 Elves here.
Add 10 per cent management makes 1760 elves.
Quality control. We have optical sensors, high tech manufacturing, and a really neat end of line test, so we don't really need that much personal here too, mainly maintenance. Since the team is working together since the dawn of time, and are always up to date using latest CAD and Design technologies, a team of 100 elves might be sufficient.
1860.
Shipping dept. will be huge. But also not in headcount. It's also completely run by SAP in a combination with drones / autonomous driving carriers. Since it's a big warehouse, nothing ever must go wrong and the team here will be rather large, 200 - 250 elves. (Comparable to Amazon warehouses)
2110.
Some boilerplate, (and I like round numbers) we need 2500 elves to run a modern Santa Clause factory, thanks to really neat technology.
Compared to the some 1 Million Santa Clauses needed for distribution...
Well, it depends on the toy. If it is a video game here are a few stats that come up on Google.
Respawn Entertainment, the fall out company that formed after Infinity Ward, creators of the Call of Duty franchise, dismissed CEO Vince Zampella, retained 38 of 46 employees which resigned after Zampella was terminated. Respawn is the owner of the EA Games-published, Titanfall franchise. But this probably does not provide an accurate depiction of the number of persons or man hours needed to produce such a game.
A more specific stat comes from Leslie Benzies, president of Rockstar North Studio, a branch of Rockstar Games Studios responsible for the Grand Theft Auto series. He gave a number of 1000 people across multiple Rockstar Games Studios involved in the production of GTA 5 in an interview to http://www.develop-online.net.
As for other kinds of toys:
Hasbro, makers of American culture ( as well as many, many games we all know from our childhoods ) does not seem like the kind of place that subjects its "elves" to such harsh conditions. Deemed one of the best companies to work for in 2012, this site reports a total of about 5700 employees, over 3100 of them in the United States. http://www.toyassociation.org/ reports total sales of \$19.48 billion in the United States in 2015. Hasbro figures reached \$4.45 billion in 2015, making it top 22% of the U.S. market.
From there we can extrapolate some roughly 25,000 elves for the U.S.
Now given that the U.S. is only about 4.4% of the global population, we can further extend the estimate to over half a million elves - which seems reasonable, but we must consider also that only about 32% of the world is Christian and I have no idea how many people outside of the U.S. believe in Santa Claus, so I must assume that the low figure of approximately 180,000 elves and a high figure of 568,000 elves gives an appropriate range, the former being how many are needed if only Christian children in the world receive toys at Christmas and the later if all children in the world are given presents made by elves.
Note that the OP's figure 2+ billion children is as large as the number of people in the world who are Christian. Certainly fewer than all of those people are children, so the OP's figure must also include non-christian children. Given that, the larger end of my estimate seems reasonable.
Further more, the above figures are strictly for toys. As suggested above, including video games would be an entirely different model as a single game can involve the cooperation of up to 1000 individuals and hundreds of games are released each year on various platforms and online.
The United States employs 284,000 people to make toys for the US (plus more for export). The US market is roughly a quarter of the worldwide toy market. So roughly one million people. Figure that only half the toys are for Christmas and only half of those are from Santa. So 250,000 people.
Now just adjust for the relative productivity of elves versus humans. Do elves work around the clock? That's twenty shifts per week compared to five for a human. So let's call it 62,500 elves.
I'll leave it up to you if you want to give them more of an advantage than a 160-hour work week. Extra speed? Or maybe you want them to be able to do less than humans? Adjust as necessary.
