The head of Southwest Airlines has insisted that he will remain in post, despite mounting pressure from bosses of two hedge funds that have invested in the business.

Elliot Investment Management and Artisan Partners have both been critical of the management of the airline in recent years, as well as of a proposal to change seating and boarding arrangements, due to be formally announced in September.

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Elliot recently bought a $1.9bn share in the airline and reports suggest that it is seeking to replace Southwest CEO Robert Jordan and other executives. Meanwhile, Artisan has been clear in its desire for Southwest to ‘upgrade’ leadership.

Speaking to Associated Press journalists after a Politico event in Washington earlier this week,  Jordan said, “I have no plans to resign” and that Southwest will treat Elliott “like any other investor.”

“Elliott can provide us ideas. They can talk to other shareholders, but Elliott is not directing the company,” he said.

Southwest cancelled thousands of flights last year after a systems issue blamed on outdated software caused unplanned downtime.