American Airlines Group Inc. is rushing to resolve a scheduling fault that gave time off to too many pilots in December — a flaw that has left more than 15,000 flights without sufficient crew during the holiday rush, according to a union for the carrier’s pilots.

The Allied Pilots Association estimated the number of affected flights, from Dec. 17 to Dec. 31, based on information provided by the carrier, said Dennis Tajer, a spokesman for the union. American spokesman Matt Miller declined to quantify the potential number of flights involved, saying the airline expects to correct the problem and avoid cancellations.

“We are working through this to make sure we take care of our pilots and get our customers to where they need to go over the holidays,” Miller said.

The computer-system problem will force American to rebuild its staffing schedule, similar to what airlines must do after major weather disruptions, said John Cox, chief executive officer of consultant Safety Operating Systems and a former commercial airline pilot. Revenue will take a hit if American has to scrub many flights. At a minimum, the carrier is likely to face higher labor costs just as investors are stepping up scrutiny of airline expenses.

“It will be a challenge, but I don’t think there will be mass cancellations,” Cox said. “There’s going to be a lot of midnight oil spent on it, but I think they’ll get the vast majority of them covered one way or another.”

UNION GRIEVANCE

American pared share gains on the news, climbing 1.3 percent to $49.86 at 1:51 p.m. in New York, easily the smallest gain on a Standard & Poor’s index of the five biggest U.S. airlines. American advanced 5.4 percent this year through Tuesday, compared with a decline of less than 1 percent for the index.

The Fort Worth, Texas-based carrier is offering pilots 150 percent of their normal hourly wage to pick up some of the flights, the top rate laid out in their contract, Miller said.

The APA, representing 15,000 American pilots, has filed a grievance, saying the proposed solution violates its labor pact. The union wants to consult with American to find a solution that will motivate pilots to give up vacation they’ve already been granted after years of working over the holidays, Tajer said.

“This is certainly not routine,” Tajer said. “This is a crisis right now, and in that crisis, they’ve gone solo.”

SYSTEM MALFUNCTION

The glitch caused the scheduling system to show that American had ample staffing coverage for some planned flights when it actually didn’t, Miller said. The carrier has made adjustments to the system and expects it to operate smoothly from now on. American, the world’s largest airline, operates about 6,700 flights a day.

Flights that are scheduled without a captain, first officer or both originate from Dallas-Fort Worth International, American’s largest hub, and airports in Boston, Miami, New York, Philadelphia, Salt Lake City and Charlotte, North Carolina, according to a company memo to the union, which was seen by Bloomberg News.