American Airlines and its union at odds over how many flights still need pilots

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American Airlines and its pilot union are having a public spat over just how many of its holiday flights don’t have a pilot assigned.

The carrier said Thursday that “only a few hundred” flights remain without a captain due to a scheduling glitch.

“Out of the 200,000 flights American will operate in December, only a few hundred are currently unassigned,” American said in a statement. “That number of open flights continues to decrease thanks to our pilots who are stepping up to the plate and picking up trips to ensure customers are taken care of.”

But the Allied Pilots Association said that’s not true in its own statement on Thursday. The union said it has access to American’s December crew assignments “in real time,” and that “thousands of flights are still listed as unassigned.”

“We remain seriously concerned about the potential for significant schedule disruption for our passengers, pilots, and fellow employees during the critical holiday travel season,” the union said.

So far, American hasn’t canceled any flights.

Related: American Airlines doesn’t have enough pilots scheduled for holiday travel

To help address the shortage, American Airlines is offering pilots who pick up certain open trips 150% of their hourly pay. But the APA, for its part, has advised pilots not to take the open flights, saying the airline’s solution violates the union contract.

The APA first announced Wednesday that a computer glitch had left thousands of December flights unassigned. The scheduling issues mostly affect the busy holiday period in the second half of December.

American says it will address any problems with its system of reserve pilots, who can help out as needed.

“We have more reserve pilots on hand in December than [in] normal months and they provide us with the ability to fly many of the trips that are currently uncovered,” American said Thursday.

Reserve pilots have on-call schedules, and are still fully qualified to man a plane and fly regularly.