Southwest has been the airline most admired in the United States for a long time. Its excellent crews more than make up for a lack of IFE with industry leading humor (do a YouTube search for examples). But today’s Southwest is nothing like the Southwest of even three years ago. Take a look at its fleet growth – we include AirTran after 2011. Southwest has grown into a huge airline.
Typically, airlines seek economies of scale. So a bigger airline should achieve lower costs through sheer size and efficiencies. It does not look like Southwest’s growth has achieved the benefits of size yet. Perhaps, Southwest developed its systems and culture to such an extent that the acquisition of AirTran in 2011 disrupted the business much more than expected.
The combined fleet started to shrink as the AirTran 717s have been moved over to Delta. Besides digesting AirTran, Southwest also undertook another significant change by starting to move away from the 737-700 to the larger -800. As of the 1Q14, the airline had 54 737-800s (7.8% of the fleet) in service. The larger aircraft was expected to cause disruptions because it takes more time to load and unload. Southwest is famous for quick turns, and anything disrupting this negatively impacts operations.
But taking a look at the top ten most delayed Southwest aircraft in the first three months of 2014; not one is a 737-800. The table lists the top ten most delayed tail numbers for each month in the first quarter 2014. It would seem the delays are probably not related to the new larger 737-800. Indeed it is the 737-300 that seems to most frequently have delays. The 737-300 represents ~19% of the fleet but accounts for 16 of the top 30 delayed tail numbers. 
There are growing delays in Southwest’s system. The following charts illustrate this well. Let’s start with Atlanta where Delta is by far the biggest carrier. Southwest is growing at Atlanta, but is by far not a big airline at the airport despite it being the former home of AirTran.
Note we count a delay as any flight that does not meet its scheduled departure time – we not use the FAA 15 minute window. Our view is that schedule is defined and must be met because operational impacts follow a delay; a morning delayed departure can disrupt schedule for the rest of the day, as the delayed aircraft moves through the system.
When we look at the delays at Atlanta, the following chart illustrates how Southwest has been struggling. Delta, accounting more than half the traffic at one of the world’s busiest airports, is doing relatively well. Southwest has a relatively light schedule yet is running significant and growing delays.
The problem is not Atlanta focused. Take a look at the next charts for some other key airports for Southwest. The airline is a big player in Baltimore.
Next note that Southwest is again running over the average at the airport.
Next let’s look at Phoenix. Southwest accounts for approximately one-third of the departures.
Yet it runs late here too.
How about Dallas Love, where the airline is based and has a near monopoly? As the chart shows, even as new entrants try build traffic, Southwest accounts for over 90% of departures.
Yet Southwest is seeing increasing delays here too; and they are growing. 
Departure delays can sometimes be made up during a day, but often they can’t because of the numerous exogenous factors that plague airline operations.  That said, there is a financial impact for airlines that run into schedule challenges.
Using a combination of data sources (including Form 41, on-time) , we estimated the cost of those delays for Southwest at the airports we have shown. The following chart shows not only that the costs as significant, but they are rising.
Southwest is suffering indigestion, and now seems to be running into the kind of operational challenges faced by the other majors. Perhaps it is a maturing nature of their operations. But certainly its business model is changing.  When Southwest was the upstart, scrambling to achieve the famed 15-minute turn was the rule rather than the exception.  Today, the palpable tension that was once omnipresent in the race against the clock seems missing, based on our observations.
The 737-800 takes longer to load and unload. But it would not be a source of more delays as long as this assumption is baked into the schedule.
I understand the -700s turn in 30 minutes on average. The -800s are budgeted for 45 minutes, which seems to be adequate. Easyjet is 25 minutes, by comparison!