Karen Smart has resigned on the same day political leaders and unions met with airport bosses to discuss the “concerning” situation.
Travellers have faced long delays and chaotic scenes with queues trailing outside terminals to reach check-in and hordes of people waiting to get through security and to pick up luggage at the country’s third busiest airport.
Piles of suitcases have been left in terminals after travellers abandoned the wait to reclaim their baggage and instead left for home.
The airport, along with much of the aviation industry, has struggled to recruit staff made redundant after the pandemic shutdown airports and travel.
As the Easter getaway increases travel, similar problems have hit other airports including Heathrow and Birmingham.
Manchester Mayor Andy Burnham had suggested that the police could be called in to assist after the chaotic scenes at the airport, and was due to meet with bosses today.
“I have been in touch with colleagues at Greater Manchester Police at the weekend to see what we can do to support the airport,” he said.
”It’s a difficult moment for airports around the world having laid low for the pandemic, they’ve had to scale up very quickly. We understand the challenges that we’ve got.
“But at the same time, we don’t want to see the scenes that we saw at the weekend and we obviously need to work with them to work through those issues and make sure we’re managing those things and giving the right information to the public and being clear about the plan to get things to an acceptable level.”
Greater Manchester Police’s assistant chief constable Wasim Chaudhry said: “As a member of the local resilience forum, Greater Manchester Police supports partner agencies in producing plans to prevent and mitigate the impact of incidents on our local communities.”
Manchester Airports Group, which also runs Stansted and East Midlands airport, is partly owned by the 10 local authorities of Greater Manchester, with the biggest stake held by Manchester Council.
Mr Burnham has said although the airport was run independently of the Greater Manchester Combined Authority, which he heads as mayor, it matters “hugely” to the city-region.
A statement on the talks, which also involve union Unite, are expected from Mr Burnham on Wednesday.
A spokesperson for Manchester Airports Group previously said: “We have regular discussions with a wide range of interested parties about the recovery of Manchester Airport following the impacts of the pandemic.
“We have been using these conversations in recent weeks to explain our response to the staffing and other operational challenges our sector is facing as it recovers.
“This includes launching a large-scale recruitment drive as well as exploring ways in which our existing colleagues can support our operation.”
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