WASHINGTON — Secret Service director Julia Pierson has demoted the supervisor of one of the agency’s largest divisions and reassigned nearly two dozen members of its staff, part of a broader cleanup effort in the wake of embarrassing drinking incidents on two recent presidential trips, according to three people familiar with the moves.

The agency also has ordered stricter rules on drinking for the division, known as special operations, forbidding them from drinking alcohol within 12 hours of reporting for duty and 24 hours before the president’s arrival at any trip location.

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Five employees of special operations were implicated in misconduct ahead of trips by President Obama last month to the Netherlands and Miami. The division is central to the agency’s efforts to ensure the safety of Obama and his family.