Southwest CEO maps out a recovery after holiday meltdown: 'We have work to do' - CNBC

The airline has hired consulting firm Oliver Wyman to review its processes, interview staff and union members, lay out what went wrong, and determine how to avoid it in the future.

Less than a year into the airline's top job, in the aftermath of travel chaos he hadn't seen in his more than three decades at Southwest, Jordan is now tasked with making things right with passengers and employees.

The carrier has also handed out 25,000 Rapid Rewards points each, which the company estimates at a roughly $300 value, to about 2 million people who had flights booked over the chaotic holiday period, Jordan said.

Most airlines had largely recovered from the bad weather by Christmas Day, but Southwest's problems worsened when crews had to call in to get new assignments or hotel rooms, causing a backup.

Codi Smith, a 28-year-old artist who lives in Los Angeles, paid $578.60 for a Delta flight back to LA from his mother's house in St. Louis after Southwest canceled part of his return trip after Christmas.

Cameron Brainard, a voiceover artist and country music radio host, said he paid more than $1,000 to get back to New York from Nashville, Tennessee, including a rental car from Louisville, Kentucky.