It really depends on many factors, such as the industry the company is in, the reason behind the brand refresh and various others.
Putting myself in the rather comfortable shoes of a CEO, I would immediately discount Option A for any company with a marketing budget less than at least $20 million, and even then writing it off would cost 5% of the budget. Basically, I wouldn't accept writing off that much stock unless the company is in the sports industry, and the stock is periodical - such as annual brochures, where writing off is expected anyway, and even then I'd wait until they were outdated.
If it's a company with a consistent rate of change as you sort of suggest, where promo stock lasts for a specific period and then changes after that anyway, then you need a really good reason not to just wait until 'change-time'.
I think Option B has far more potential, and in a large company where profit is key, it is the option that most with a vested financial interest will choose.
Now to explore the far more viable option, there are various approaches you can take with this.
An option I've seen employed in retail companies doing a brand refresh is to send new materials and install new branding on the more important/valuable sites, and send old stock to other sites that have yet to undergo the transformation. Bearing in mind that the transformation was significant though familiar enough to the old brand in colour scheme, that it would still be recognised if a customer at a new site went to an old site.
Another option that has been mentioned, is the soft launch approach, where new promotional items are released as the old stuff runs out or requires upgrading/fixing/servicing anyway.
An example of this is a company that legally endorses plumbers in the UK, called the Gas Safe Register. After undergoing a significant overhaul from the name CORGI, new van stickers and promo materials were sent out in batches throughout a number of years to the hundreds of thousands of independently contracting plumbers.
So it really depends on the amount of change from the old brand, the type of business that it is, who it serves, how it's physically arranged and the targets of the refresh.
For example, if the refresh was required because the brand is failing, then the decision should have been made prior to even starting the rebrand that all old material would go out of the window and there would be a big, attention-drawing, look-at-us-we're-new 'hard' launch event.
If the refresh is because a recent survey on customers revealed a general opinion that the brand is starting to look old, then there's no hurry. Soft launch by introducing materials when the old materials run out. It takes a while for any change to be noticed anyway.. but if you've changed everything from the font and colour scheme of the logo to the strapline etc you'd have to change it all at the same time, at least by site. So when a site runs out of letterheads and business cards, and say more than 50% of their branded materials, you should install the new logo throughout so as not to confuse customers at least locally.
Another option is to share remaining materials across sites fairly evenly, or send all old materials to sites that perform least well because of location or other factors.
So, I'll finish up with some questions you could ask to evaluate your course of action:
Is the business widespread enough to isolate separate sites?
Realistically, how fast does the change have to happen?
Is the new brand consistent/familiar enough to the old brand that they could exist side-by-side? Like is it the same purple as the old uniforms?
Why is it changing/refreshing?
What is the personality of the company? Are they fresh, slick, modern and up-to-date, living-on-the-edge like young Apple? or traditional, sturdy, well known/established, staple of public consumerism, wide customer base, not going to go out of business any time soon like Walmart?
And of course, the bottom line in business is always:
- How much will each potential course of action cost? For which you'll need an accountant..
I hope this all makes sense.