Get ready for the great luxury shutdown. No, that's not shops locking their doors to cope with the hoards scrambling for the latest handbag. It's brands cutting their store numbers to cope with a slump in demand.

Hugo Boss said on Friday that it would close 20 of its 443 freestanding stores around the world over the next 18 months. The reductions to its portfolio in Asia, Europe and the U.S. are on top of the 20 locations it's already shutting in China.

It's particularly exposed to the headwinds facing high-end apparel. It's an entry-level luxury brand, and the workers it appeals to are vulnerable to the economic aftershocks from Brexit and are likely to be worrying about their job prospects. That's hardly conducive to spending hundreds of dollars on an aspirational suit. Boss also generates about about two-thirds of its revenue from Europe, where tourism has been hit by safety fears.

But it's not alone in suffering from the luxury industry's woes. Weakening demand in key markets is hurting high-end brands across the board. And that means Boss won't be the only group to close stores.

The environment is already showing some softness, with a number of brands either cutting store count over the first half of the year or leaving it unchanged, according to Exane BNP Paribas data.

Earlier this year, Prada and Richemont said they were reviewing their store bases. That might mean negotiating better rents, or downsizing stores. But some closures are inevitable.

Boss expects to incur 57 million euros ($63.5 million) of one-time costs, primarily reflecting costs of cutting the number of its shops. Others exiting expensive leases will likely face similar charges.

But Boss expects the closures to have a positive impact on its profits from next year. It was rewarded on Friday by a share price increase of as much as 7 percent. That might encourage other groups to be equally bold.