Follow CBSMIAMI.COM: Facebook | Twitter

MIAMI (CBSMiami/CNN) – More than three weeks before Christmas, American Airlines faces a holiday meltdown but the company is working to make sure flights take off on time.

READ MORE: ‘I Have Goose Bumps’: Zoo Miami's Ron Magil On 'Rita' Laying 2nd Egg On Live Bald Eagle Cam

A computer glitch is blamed for giving too many pilots vacation time between December 17 and the 31st, and the scheduling mistake could leave thousands of flights without a captain, co-pilot or both.

American says reserve pilots will be able to fly most of the flights, and it’s offering premium pay for pilots to work certain routes.

In Miami, AA spokeswoman Alexis Aran Coello released an updated statement Thursday:

READ MORE: Boca Raton Man Faces Charges In Fatal Crash That Killed Homestead Mom, Daughter On Thanksgiving Eve

“Out of the 200,000 flights American will operate in December, only a few hundred are currently unassigned to pilots. 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. It’s another example of why we are thankful to have such an incredible team. In addition, we have more reserve pilots on hand in December than normal months and they provide us with the ability to fly many of the trips that are currently uncovered. We have not canceled any scheduled flights in December and will continue to work to ensure both our pilots and our customers are cared for.”

“We have reserve pilots to help cover flying in December, and we are paying pilots who pick up certain open trips 150 percent of their hourly rate — as much as we are allowed to pay them per the contract. We will work with the APA to take care of our pilots and ensure we get our customers to where they need to go over the holidays,” American Airlines spokesman Matt Miller said in a statement.

But the pilots’ union is urging crews not to take these assignments because they might violate the union contract.

“While the overtime is legal, the way they’re doling out is not in compliance with our contract,” said Capt. Dennis Tajer, spokesman for the APA in an interview with CNN. “The contract is important, but the most important of this is ensuring our passengers are taken care of…but this is going to require a partnership to solve it, regardless of what the rules are.”Miller said American’s leadership spoke to the APA Wednesday afternoon to hammer out a resolution to the staffing shortage.

MORE NEWS: Kyle Lowry Scores 19 Points, Heat Beat Bulls 107-104

(©2017 CBS Broadcasting Inc. All Rights Reserved. Cable News Network, Inc., a Time Warner Company, contributed to this report.)