DALLAS >> Southwest Airlines returned to a relatively normal flight schedule today, as the focus shifts to making things right with what could be well more than a million passengers who missed family connections or flights home during the holidays, and many of whom are still missing luggage.

The Dallas carrier, which had canceled thousands of flights every day this week after a winter storm last weekend, reported less than 40 cancellations early today. While that was still more than United, American and Delta combined, its progress following one of the most chaotic weeks in aviation history for a single airline.

Federal regulators have vowed a rigorous review of what happened at Southwest, with all eyes on outdated crew-scheduling technology that left flight crews out of place after the storm hit, essentially shutting down almost all of the carrier’s operations.

However, Southwest passengers today reported relatively empty flights, some with one person to a row, as the carrier reshuffled routes and sent planes, and crews, to where they needed to be.

John and Rosaria Monte had been watching their Southwest flights closely this week as the airline struggled and their home city of Buffalo, New York, dug out for a deadly blizzard.

They had no trouble today flying from Buffalo through Chicago to see their daughter and enjoy some warmer weather in Dallas for New Year’s.

“My husband kept checking it (the flight schedule) through the night and early this morning and everything went accordingly,” Rosaria said. “They were super friendly everywhere and not a problem.”

Yet if even one leg of a flight was scheduled with Southwest this week, there were very different emotions.

“I’m still reeling from the experience,” said Theresa Kraus, arriving home today in Dallas after being stuck for four days stuck in Washington, D.C.

Kraus left late last week just before the storm to see her children for Christmas, and was supposed to return Tuesday.

“I paid my daughter’s roommate $100 to stay in her room and had my medication FedEx-ed to me,” Kraus said.

Kraus is a frequent flyer, and has grown frustrated with Southwest.

“It’s just the inconvenience of four days with not being able to get home,” she said.

U.S. Transportation Secretary Pete Buttigieg in a letter to Southwest CEO Robert Jordan late Thursday called the week of disruptions “unacceptable.”

“While weather can disrupt flight schedules, the thousands of cancellations by Southwest in recent days have not been because of the weather,” Buttigieg wrote. “Other airlines that experienced weather-related cancellations and delays due to the winter storm recovered relatively quickly, unlike Southwest.”

At airports across the country passengers had what could be described as a typical holiday week for travel. It was a stark contrast near Southwest Airline counters, where hundreds of people sat on bags or slept where they could, with the Southwest aircraft sitting on the tarmac yards away, but crewless.

Southwest begun accepting reservations again today after getting crews and planes into place, and executives have started on what is undoubtedly a long road to regaining the trust of travelers.

Southwest’s Robert Jordan said in an interview with ABC’s Good Morning America today that after safety, there is no greater focus than reimbursing customers and getting them reunited with their luggage.

“This has impacted so many people, so many customers, over the holidays. It’s impacted our employees. And I’m extremely sorry for that,” Jordan said. “There’s just no way almost to apologize enough because we love our customers, we love our people and we really impacted their plans.”

Executives with the airline said this week that it may be as much as a week to connect all Southwest passengers with their destinations.

The air travel industry is just now recovering from the pandemic, which reduced activity to levels not seen since the beginning of the jet age.

Jordan warned that the meltdown this week will “certainly” hit the carrier when it reports fourth quarter financial results at the end of January.

Company shares, which tumbled 8% this week, appeared to stabilize today.

AP Airlines Writer David Koenig contributed to this report from Dallas. AP Photographer Abbie Parr contributed from Chicago.