Representatives with Elliott Investment Management, the Florida-based hedge fund that has accumulated a 11% stake in Southwest Airlines and pushed for leadership changes, said the plan shared with shareholders represented "another promise of a better tomorrow from the same people who have created the problems we face today.

Southwest Airlines held a conference call with investors Thursday to lay out a plan for long-term profitability. The Dallas-based airline posted a profit in the second quarter but losses in the prior two quarters.

Southwest isn’t the only Texas company Elliott has invested in.