As someone with over 20 years experience developing decision support models for domestic and international airlines, here's my take.

Southwest Airlines is a domestic carrier flying a point to point schedule, using the same fleet type to eliminate the need to train pilots on multiple aircraft type and also reduce training costs for transitional training from a narrow to a wide-body jet. All pilots can (theoretically) fly all planes in their fleet, tremendous training and labor savings. When flight crews "bid" on their flights, having only one aircraft type also reduces the complexities of bid lines down to basic seniority. (Let's ignore over water to Hawaii, m'kay?)

So, getting SWA back in the air should be over simplified compared to every carrier who got their planes and crews back flying the same or next day - get it? SWA has a single fleet and all of their crew is qualified to operate those jets or crew the cabin - so "wat da problem is"??? US Gov, inquiring minds want to know!!!

At all airlines, crews and planes are scheduled, and optimized, using decision support models which take into account how many hours the crew (pilots and flight attendants) can fly by law and contract; how long each tail# can fly until it needs to be flown into a maintenance base for an A/B/C/D check for scheduled maintenance, and how to get the maximum airtime out of the asset per day - in perfect weather conditions.

There are also decision support systems that monitor pricing of competitors every second of the day and why your airfares change from one browser refresh to another, yield management models which run overnight taking input from industry load data from the past year in the market SWA flies to help predict the passenger "load" which sets fares and also permits manual inputs for special events such as a World Series, or Super Bowl etc which would spike demand and drive airfares higher.

And there are Air Operations systems which are similar to the named product which take into account weather and crew events and help an airline re-plan based on where crew is currently. These Ops systems should have interfaces built to the crew (pilot and flight attendant) systems to know where they are located as well as where the jets are. Those values, along with the number of hours the crew has worked, would be used to re-calculate the crew and fleet assignments with the associated fleet and crew scheduling decision support models.
These DSS ran on either big iron multiple CPU Unix servers or multiple CPU Linux servers - point being the computational power was outstanding and yes, CPLEX was typically a library utilized by our PhD's. There was a lot of money spent on the hardware and the people who developed these models - it wasn't cheap but then none of the clients ever experienced this type of problem with scheduling and yes, the clients are named in the weather impact article alongside SWA, but they are up and running either same or next day...

My world had a common database and data model where all data was integrated from various systems regardless of if it was our system or not because a decision support system without current and accurate data is like having corn cobs for toilet paper vs. Charmin... painful and not a lot of value.
This is the one time I'm looking forward to the gov looking under the hood of private industry and revealing where the technical and management issues are. You can't blame the technical teams as they're only paid what SWA pays to hire both FTEs and contractors, and why I've never had a phone call that lasted beyond finding out what the position paid. We all know, you get what you pay for, but again, my opinion, and I'm greedy!!!