CNN’s Andy Rose, Andi Babineau, Adrienne Broaddus, Dave Alsap, Nick Valencia, Devon Sayers, David Goldman, Leslie Perrot, Carlos Suarez, Karla Cripps and Ross Levitt contributed to this story.

By Gregory Wallace and Forrest Brown, CNN

The boss of Southwest Airlines has vowed he will “make good” to passengers hit by his company’s disastrous holiday meltdown as the carrier was delivering on its promise to resume better service on Friday.

“This has impacted so many people — so many customers — over the holidays,” CEO Bob Jordan said in an interview on ABC’s “Good Morning America.”

“I’m extremely sorry for that. There’s just no way almost to apologize enough.”

Jordan said reimbursements for passengers would cover travelers’ costs including “rental cars, hotel rooms, meals, booking customers on other airlines — that will all be part of what we’re covering.”

“We’re offering refunds, covering expenses — we’ll be going back out with even more after that,” he said. “Beyond safety, there is no greater focus at this point than taking care of our customers, reuniting them with their bags, getting refunds processed.”

The airline’s difficulties started with the massive, frigid winter storm, but they lingered — and even worsened — at Southwest as other major airlines recovered. Almost 15,800 flights Southwest have been canceled since December 22 in a disruption that has shaken the company to its core.

“This was just an unprecedented storm for everybody — for all airlines,” Jordan said. “The storm had an impact, but we had impacts beyond the storm that obviously impacted Southwest very differently.”

How Friday flights have been going

Jordan said the airline would fly on Friday its full schedule of around 3,900 flights. It’s working out as promised — things are much, much improved.

The flight tracking site FlightAware shows Southwest has canceled only 43 flights by 6 p.m. ET, or just 1% of its total flights.

In fact, it’s been the best day for flying since the winter storm first barreled through much of the US before Christmas. Only 153 flights total have been canceled for Friday as of 6 p.m. ET. As for delays, there were almost 4,400 in the US. Southwest accounted for roughly 755 of those, or about 19% of its flights.

As for Saturday, there wasn’t a single Southwest cancellation posted as of 6 p.m. ET Friday, and only 23 for the US.

Southwest has set up Southwest.com/traveldisruption for customers to submit refund and reimbursement requests for meals, hotel and alternate transportation; as well as to connect customers to their baggage.

Luggage aftermath

While planes are in the air again, there are still mountains of misplaced luggage scattered across the land.

Take the case of Southwest passenger Lisa Carpenter. She’s finally heading home to Phoenix after she was stranded in Chicago this week. She said she got a call from Southwest on Friday morning with news her missing luggage made it to her original destination and that FedEx would ship the bags to her home.

“My bags made it to Albany, New York, but I didn’t. I don’t know how, but they didn’t have a flight for me. I don’t know how that happened, but I didn’t get there to see my family,” Carpenter told CNN.

She also said she plans to purchase a tracking device for her luggage before traveling again, and she’s looking to fly with other carriers.

“I will be very skeptical about booking with Southwest again,” she said. “I was out here alone and had to buy new clothes.”

DOT to Southwest: Do right by passengers

Top US government officials have been disconcerted, to say the very least, about how Southwest got to this point. And they’re demanding Southwest makes things right — or face financial repercussions.

The DOT formally warned Southwest on Thursday that it will face consequences if it fails to make right by stranded and inconvenienced passengers.

Transportation Secretary Pete Buttigieg wrote in a letter to Jordan that officials will take action against the airline if it does not follow through on promises to reimburse passengers for alternative transportation costs, as well as provide meals, hotels, refunds and baggage reunification.

The penalties include the ability to levy fines.

“It would be an unfair and deceptive practice not to fulfill this commitment to passengers,” Buttigieg wrote, specifically referring to alternative travel reimbursements.

“The Department will use the fullest extent of its investigative and enforcement powers to hold Southwest accountable if it fails to adhere to the promises made to reimburse passengers for costs incurred for alternate transportation.”

Those fines could be substantial.

“The airline said to me that they were going to go above and beyond what’s required of them,” Buttigieg said Thursday in an interview with NBC News. “I’m looking to make sure they actually do that, and if they don’t, we are in a position to levy tens of thousands of dollars per violation per passenger in fines.”

Regrets and repairs

The airline’s chief commercial officer, Ryan Green, offered his regrets Thursday over the collapse of services, promising to rebuild customer relations that have sunk to rock bottom.

“My personal apology is the first step of making things right after many plans changed and experiences fell short of your expectations of us,” Green said in a video.

“We’re continuing to work to make this up to you, and you’ll continue to hear about that soon. But for now, we’re focused on restoring the reliability and level of customer experience we expect of ourselves, and you expect of us.”

His remarks came as Buttigieg made his own scathing assessment Southwest’s troubles, calling the situation a complete “meltdown.”

“You’ve got a company here that’s got a lot of cleaning up to do,” he said.

People want to know: What caused this?

Ask Southwest Airline employees about their company’s technology. You won’t get many raves.

While Southwest grew from a Texas-based discount airline operating three planes into one of the nation’s largest, union officials representing Southwest workers say the company did not keep pace with technology changes. And they say they’ve been raising concerns for years.

“We’ve been harping on them since 2015-ish every year,” Mike Santoro, a captain and vice president of the Southwest Airlines Pilots Association, told CNN.

They and the airline itself described an internal process that requires multiple departments to manually redesign the airline’s schedule — a system that works “the vast majority of the time,” the airline said in a statement.

When something goes wrong, the Southwest software — including the crew scheduling system tool — leaves much of the work of rebuilding that delicate network to be done manually.

Some understanding passengers

Some passengers were taking all of this in stride and showed some sympathy for Southwest.

Several people at Hartsfield-Jackson Atlanta International Airport spoke to CNN’s Nick Valencia on Thursday about their travel experiences with Southwest this holiday season.

“I mean, it’s just par for the course. This is flight travel, everyone’s trying to get everywhere at the same time. Unfortunately, Southwest took the brunt of this year’s travel unfortunate situation,” Roderic Hister told CNN.

When asked what he thought about the lack of lines at the Southwest counters at the airport, Hister said: “Maybe speaks to the improvements that they’re trying to make, because there’s not long lines, people aren’t here complaining. So, maybe you know, the efforts to redeem themselves are working.”

Winston Williams, standing near Hister, said he intends to still use the airline in the future. “I like Southwest. I mean, the bags are free,” Williams said.

Damaged reputation

But plenty of folks are still taking a hard line with Southwest.

Elaine Chao, who served as secretary of transportation during the Trump administration, described the Southwest Airlines breakdown as “a failure of unbelievable proportions.”

She told CNN it was “a perfect storm of all the things that have been going on with the company. It’s going to take them a very long time” to rebuild trust with consumers, she added.

Phil Dengler, co-founder of the travel advice website The Vacationer, concurs.

“It is going to take a long time for Southwest Airlines to earn back public trust. While the extreme weather affected other airlines, Southwest experienced a true meltdown at the worst possible time,” he said Thursday in an email to CNN Travel.

“A large portion of Americans only fly once per year, and they want a problem-free experience. I believe many people are going to pause when booking their next flight and they see Southwest Airlines as the cheapest option,” Dengler said.

“While the low prices are enticing, this meltdown is going to cause many travelers to explore other low-cost options.”

What customers should do

Dengler cautions to proceed carefully regarding these promised refunds.

“Southwest says, ‘We will honor reasonable requests for reimbursement for meals, hotel and alternate transportation,'” he said. “While Southwest is being vague on how much they will reimburse, I would avoid any expensive hotels or restaurants. Use Google Hotels to find nearby hotels near the airport where you are stranded.”

And he also cautions about piling up a big tab.

“Do a few Google searches such as ‘free things to do near me.’ I doubt Southwest is going to reimburse tours or other paid activities, so I would not book any expensive excursions that you cannot afford.”

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CNN’s Andy Rose, Andi Babineau, Adrienne Broaddus, Dave Alsap, Nick Valencia, Devon Sayers, David Goldman, Leslie Perrot, Carlos Suarez, Karla Cripps and Ross Levitt contributed to this story.