Meet Amanda McMillan: the woman who runs Glasgow Airport

"The security officer said: 'Can you just taste that for me, please?'" McMillan recalls. "So this lady took a swig, then grimaced as if she was going to vomit. When he asked if she was OK, she replied: 'Oh yes, it's just I don't normally drink it, I usually rub it on my back.'"

It's an anecdote that succinctly surmises the often surreal world McMillan inhabits. Be it terrorist attacks, volcanic ash clouds, snow-clogged runways, boisterous hen and stag parties, shepherding lost passengers, greeting popstars or welcoming the Pope, it's all in a day's work for the managing director of Glasgow Airport.

Approaching her fifth anniversary in the job later this year, McMillan has some interesting tales to tell. Refreshingly, she doesn't always plump for the sanitised, air-brushed version of events – which admittedly can't be good for the blood pressure of her PR man seated opposite.

Nor is she the stuffy, corporate jargon-spouting executive one might expect, quick to dispense with any rigid formalities as we sip from chipped coffee mugs. "Irrespective of the role I'm in and responsibility I have, I'm still Amanda and like to have a wee laugh," she asserts. "I don't take myself all that seriously. I'm proud of the fact I haven't over-complicated anything. I think you can be highly professional without losing your sense of spirit and fun."

The youngest of two children, McMillan grew up in Linwood, Renfrewshire, just a few miles from the airport, where her father worked in the town's former car factory and her mother juggled a full-time job as a wool buyer with running the family home.

It's a staunch work ethic that has undoubtedly rubbed off on their daughter. When McMillan, 44, took over the reins in 2008, she became the first female managing director of Glasgow Airport and is currently one of only two women in Europe to hold that role, the other Sonia Corrochano at Barcelona El Prat.

Not that it didn't involve a steep learning curve. An accountant by trade who previously worked for drinks giant Diageo, by her own admission she knew little of the commercial side of airports when she joined BAA in 2005 as head of operations.

"I was still very much of the mindset of going down the pub with your pals and saying: 'I don't understand why there isn't a route to Barbados from Glasgow because I know at least six people who want to go, I'm sure we could fill a plane,'" she says. "Then you come in and learn there is a huge piece of economic analysis to determine whether a route is viable or not. It's pretty scientific."

She clearly caught on fast. Within three years, McMillan was in the top job. It's a tenacity the head of Scotland Yard's counter-terrorism command, who she spent 24 hours in a car park with following the 2007 terrorism attack, could perhaps testify to. While he was intent on preserving a crime scene, McMillan had her own goal: to get passengers back into the airport without delay.

A stand-off in the pouring rain finally ended at 2am when McMillan convinced the counter-terrorism chief to allow her to paint over the windows on a footbridge leading from the car park to the terminal building, preventing prying eyes from viewing the burned-out Jeep wedged between the front doors. "I think he was fed up with me in the end," she admits. "He said: 'If you can find someone to paint the windows at 2am, then on you go'. So I did."

McMillan is able to observe moments of black comedy amid the unfolding drama. Like the Glaswegian man who sought her out among the melee to compliment her Prada trainers. "By this point my hair had dried and re-dried about three times, I looked like crap, and this guy said: 'Oh, I love your shoes,'" she grins. "That could only happen in Glasgow."

Or when she telephoned her husband Fraser as the hours of fraught negotiations with the police ticked by. "I called to tell him what a nightmare it was, that there was 4000 Glaswegians wanting to go on their holidays and I couldn't possibly come home. He said: 'No, this is a nightmare. It's the first time I've had the two kids overnight on my own.'"

For McMillan, life comprises two distinct but equally important prongs: work and family. She and Fraser, 45, a lawyer and partner at Pinsent Masons in Glasgow, have two children Sophie, eight, and Rory, six. "I'm quite primitive in my ambitions and general well-being," she says. "I like putting my foot out of bed in the morning, having a challenge and my family around me. As long as I get all of that ticking every day, I'm happy."

When not being a "big kid" in swing parks, making pottery, playing bingo or cards – her children's current favourite pastimes – in the west end of Glasgow where they live, McMillan can often be found at their family holiday home near Kingussie. The latter is an area she first got to know as a youngster when she was packed off "like a refugee" to stay with her aunt in the summer months.

"I have fond memories of it being so quiet you could hear a pin drop, playing tennis, going cycling and swimming in the Gynack," she says.

It's a part of the world she still loves. "We take life at a slower pace there. It's quieter and calmer," she says. "I still like the same simple things: fresh air and going for walks. There's great beaches on the lochs and hills to climb."

Watching other people jetting off on their holidays on a daily basis, McMillan isn't immune to the lures of foreign climes, citing Rome among her favourites. She laughs when asked the destination of choice this summer. "We are going to Florida – the traditional Weegie holiday," she confirms.

Perhaps most pertinent in her line of work, McMillan appears to get what sets Glasgow Airport apart from any other in the world. Or rather, she gets Glaswegians. "Everyone I know thinks Glasgow Airport is a public service – they see it as being closer to a hospital or a school," she says. "The public don't care if I hit my business plan targets, they want to make sure this place is always open, efficient, friendly and something they can be proud of."

Pride is something McMillan talks a lot about and that in her own working-class roots is palpable as she recites stories in an unmistakable west of Scotland burr. Her childhood in Linwood was the result of her father Peter's job as an upholsterer in the factory once famed for producing the Hillman Imp. "The Linwood I knew was a formulaic town which came about because of the car factory," says McMillan. "It's where we went to school, where we played and where our dads worked. I'm not sure I had a huge horizon of what was outside that.

"I was on a school trip the day it was announced the factory was closing [in 1981]. There was only one kid on the bus whose dad didn't work there. I do remember feeling scared. There was a lot of gloomy things going on in the world, so it was hard to think your dad was part of that."

While she excels in the boardroom, McMillan cheerily admits to being somewhat lacking on the domesticity front. "You can't have it all," she says. "I don't think you can work, spend time with your kids and do everything else."

There is much hilarity as she reveals her signature culinary dish. "I phone Delizique [a deli in Glasgow]," she jokes. "To be fair I can do a Sunday dinner because you don't need to be a good cook to do that – you just have to be logical. It's about organisation which I can do standing on my head. We did an away day for work in a £10-a-bunk bothy and had a Ready Steady Cook challenge. I peeled and chopped the carrots, did all the prep, cleaned up afterwards and no-one noticed I couldn't cook."

She has an infectious sense of humour, not least when talking about taking a pen to her daughter's maths homework: "This question said: 'Six planes leave from Edinburgh Airport with 150 people on them'. I thought: 'Edinburgh? What's the teacher thinking?' So I got a pen out and changed it to Glasgow."

But asked about the future and McMillan is sanguine. "The trick in business is to never think you have got there," she says. "As one of the guys I work with says: 'It's all very well climbing the ladder, but if it's against the wrong wall there is not much point in getting to the top.' I think the secret is to keep putting it against a different wall – and always be pushing yourself."