American Airlines is working to resolve a scheduling fault that gave time off to too many pilots in December, leaving some flights without enough crew during the holiday rush.

The glitch is causing staffing shortages on thousands of flights next month, the Allied Pilots Association, the union representing the carrier’s aviators, said in a message to its members. 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,” he said.

American 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 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, said Dennis Tajer, an APA spokesman.

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

American pared share gains on the news, climbing 1.5 percent to $49.96 at 7:15 a.m. today after earlier gaining as much as 3.9 percent. The stock advanced 5.4 percent this year through Tuesday, compared with a decline of less than 1 percent for a Standard & Poor’s index of the five biggest U.S. airlines.

The glitch caused the scheduling system to show that Fort Worth, Texas-based American had ample staffing coverage for some planned flights when it actually didn’t, Miller said. American has made adjustments to the system and expects it to operate smoothly from now on.

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.