NEW YORK — Just a year after its centennial celebrations, the Girl Scouts of the USA is grappling with an array of interconnected problems.

It faces declining membership and revenues, a shortage of volunteers, rifts between leadership and grassroots members, and a pension plan with a $347 million deficit.

Compounding the problems are tensions at the Girl Scouts headquarters in New York, where several senior executives have quit or been ousted in the past two year. Last week, some of the roughly 300 employees there were invited to take early retirement, and layoffs are expected in August to offset the revenue losses.

Yet Girl Scout leaders insist they are on the right track, while acknowledging that sweeping changes over the past 10 years have been difficult for many in the Scouts' extended family.