BASEL, Switzerland — Nick Hayek, the chief executive of the Swatch Group, is facing a problem many of his corporate counterparts might envy: he’s doing too much business.

Swatch, the world’s largest watchmaker, is rushing to add factory capacity so that it can make enough watches to meet demand. It wants to add as many as 2,000 employees this year — about 1,500 of them at home in Switzerland. But it is struggling to find enough qualified people.

“Managing our stock is at the moment not an issue for us because demand is so big that we unfortunately don’t even have the time to build up any stock,” Mr. Hayek said last month at Baselworld, the watch industry’s biggest fair. “I hate that feeling of missing sales because of a shortage in products.”

Swatch’s production and hiring problems reflect the overall health of a sector that has rebounded from the world financial crisis. Demand for watches has soared in Asia — a region that accounted for more than half of Swiss watch exports last year — with makers of mechanical watches capturing an increasingly large slice of the market. Exports of mechanical timepieces rose 32 percent in unit terms last year, compared with an 18 percent increase for less expensive quartz watches.