By David Koenig / Associated Press

DALLAS — Southwest Airlines customers relaxing on Thursday evening got an email that may mean their summer vacation could be more stressful and expensive than they planned.

Southwest, the biggest operator of Boeing jets, is removing the grounded 737 Max from its schedule until at least Aug. 5, well past the peak of the summer high season.

Company president Tom Nealon wrote in his email that the airline was taking the Max out of its schedule two months longer than previously planned to reduce the need for last-minute changes during the summer travel season. The decision, he wrote, would make the schedule more reliable.

Unless Boeing can quickly fix software on a flight-control system implicated in two deadly crashes, other airlines are likely to follow Southwest’s example and remove the Max from their schedules for an extended period.

That, in turn, ratchets up pressure on Boeing to fix its best-selling plane so it can return to flying soon.

Last month, Boeing and federal officials said privately that the company would finish a software fix before the end of March. Instead, it was delayed by an unexpected problem that Boeing hasn’t fully described, and the company is now aiming to complete its work by late April.

CEO Dennis Muilenburg said Boeing pilots have flown 96 test flights totaling 160 hours with the new software and will operate more flights in the coming weeks to prove that the fix works.

When Boeing does complete its work, it must be submitted to the Federal Aviation Administration for approval. Foreign regulators including in Europe and China will then do their own reviews — significant because foreign airlines account for about 85% of Max orders, according to analysts for financial services firm Cowen.

It remains uncertain how willing passengers will be to board the Max after crashes in Indonesia and Ethiopia killed all 346 people on board.

The longer the planes sit on the ground, the more money airlines lose. Southwest already figures that just the first three weeks the Max had been grounded, along with other setbacks, cut first-quarter revenue by $150 million.

Southwest is already canceling about 90 flights a day because its 34 Max jets have been grounded since mid-March. That’s a small percentage of Southwest’s 4,000 daily flights during summer. Still, unless the airline finds replacement planes quickly — and that can be a complicated process — Southwest will scrap about 10,000 flights that could have carried nearly 1.8 million people between now and early August.

American Airlines doesn’t expect its 24 Max jets to be flying before June 5, and it too is canceling about 90 flights a day.

United Airlines, with 14 Max planes, says it is shuffling its fleet and mostly covering flights that were scheduled with the Max in mind.

Without those planes, travelers will have fewer flights to choose from, and fewer planes to carry passengers whose flights are canceled for other reasons such as bad weather. There could also be fewer fare sales.

“Travelers who have not already booked their summer reservations may end up paying a slightly higher airfare,” said Henry Harteveldt, a travel-industry analyst with Atmosphere Research Group. “But it’s not going to be the summer from hell.”

Harteveldt said he expects airlines that don’t have Max jets — a list that includes Delta, JetBlue, Alaska and Spirit — will court travelers with price-cutting.

The cost of the Max crisis to Boeing also rises the longer the plane is grounded and jets coming off the assembly line pile up around Seattle.

Airlines in China and Norway have said publicly they want Boeing to compensate them for their grounded planes. While other airlines have kept silent, analysts expect Boeing will make concessions that could total hundreds of millions of dollars.

The Chicago-based company also faces a growing number of lawsuits by families of the crash victims.

Since its launch in 2017, the Max had emerged as Boeing’s best-selling jet. Fewer than 400 have been delivered, but about 4,600 are on order.

Boeing stopped deliveries of the plane shortly after it was grounded, and it announced last week that it was cutting production of 737s from 52 to 42 a month.

The company took no new orders for the 737 Max in March — not even before the March 10 crash of one in Ethiopia — and only 10 in the first three months of the year, down from 112 in the same period last year. The decline could be explained by the fact that many airlines that want the plane had already placed orders.

Boeing hasn’t provided numbers on the financial impact from the Max crisis. Company leaders are expected to do so when they report first-quarter earnings later this month.