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MIAMI (CBSMiami) — Thousands of American Airlines flights set to depart during the holiday season have no pilot scheduled to fly the aircraft, the Allied Pilots Association announced Wednesday.

The union called it a “scheduling failure.”

“On Friday, management disclosed a failure within the pilot schedule bidding system. As a result, thousands of flights currently do not have pilots assigned to fly them during the upcoming critical holiday period,” the union stated.

A computer glitch in the computer system American Airlines pilots use to bid for time-off based on seniority  failed to limit requests for the Christmas holiday travel season, the union representing the pilots tells CBS News.  As a result, a much larger than normal number of American’s pilots have been scheduled for vacation between 12/17 and 12/31.  The Allied Pilots Association estimates, currently, more than 15,000 American Airlines flights are at risk of being canceled because they do not have a full crew compliment.

The news upset some passengers at Miami International Airport who were planning to travel during the holiday season.

“Of course this is bad right because during the holiday season we need to have the pilots flying and it’s the time of the year that we most need them,” said Luciana Coutinho.

Likening the situation to the Grinch Who Stole Christmas, APA Communications Director Gregg Overmann said, “if not fixed it will inconvenience a lot of passengers. It’s just not something you want to see happen. That’s a big number, that’s multiple days’ worth of flying.”

“We’re going to have to get creative to require a partnership to figure out how we get those more than 15,000 flights manned with captains and first officers,” said APA spokesperson Capt. Dennis Tajer. “It’s a heavy lift.”

American Airlines (Source: CBS)

American sent a letter to employees offering time and half pay for working certain flights, but the union says the conditions of the overtime pay violate its labor contract.  The union has filed a grievance.

“It’s a big problem and we want to see it fixed but we haven’t been approached by American management with a plan that works for them and works for us,” said Overmann.

In a statement requested by CBSMiami, a spokesperson for American Airlines Miami hub wrote:  “We are working diligently to address the issue and expect to avoid cancellations this holiday season. 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.”

Industry analysts say now is not the time for holiday travelers to panic.

“Is there a risk some flights will be canceled? Yes,” said airline industry expert Henry Hartvedlt. “But I don’t think the real number will be close to 15,000.”

American Airlines is the largest U.S. carrier.