Chief executives don’t often seem like they’re having much fun. Quietly riding high on the thrill of a deal, maybe, but embracing an ongoing sense of genuine joy? Not so much. Then there’s Federico Marchetti, chairman and CEO of the YOOX Net-a-Porter group (YNAP). I can’t vouch for his unmitigated happiness, but what he does have is a boyish enthusiasm for his role heading up the world’s biggest online luxury retailer.

Comprising YOOX (the site he founded in 2000 after a career in investment banking, on an instinct that shopping for luxury on the internet would be big business), Net-a-Porter and Mr Porter (they merged with YOOX in 2015), plus the operation of a handful of e-commerce sites on behalf of labels such as Armani and Valentino, Marchetti’s remit is vast.

In 2017 the group’s revenues were €2 billion (£1.8 billion), with half the sales coming via mobile devices. In 2018, YNAP was acquired by Richemont in a deal that valued it at €5.3 billion (£4.8 billion).

Marchetti, who turned 50 in February, posts pictures on Instagram of himself riding around his Milan office on a bike. He has decorated the open-plan working space with a statue of postmodern designer Alessandro Mendini in a patchwork jumpsuit (Marchetti is an avid art collector) and theatrical red velvet curtains.

Despite being on the cusp of celebrating its 20th anniversary, YNAP HQ still has a kooky, start-up feel. Before my interview, I am ushered into a darkened room, where I experience some of the technology the company is working on to transform the way we shop in the future, like the ability to take a photo of someone and see items similar to what they’re wearing, or to scan a shop window or bus ad and shop the look.

It is, he says, artificial intelligence that is the next big game changer. "For the simple reason that it makes the life of the customer much easier. In ’99 I was among the first to invent the luxury home page [with categories, images and stories designed to entice]. Soon, the home page won’t exist any more because we have over three million customers so that means over three million home pages, one for each person and their bespoke needs. Only technology can do that because it’s big data and artificial intelligence; they go together."

He stresses, though, that, "We always try to find the balance between human and machine." So, for example, he’ll still employ real stylists rather than attempting to rely on robots for great taste, and combine his Lamborghini-speed warehouse robots with people to pack the parcels and give a personal flourish.

All this data means Marchetti has some fascinating insights into the world’s shopping habits. The Japanese are particularly enthralling. "They never shop from the office; the strongest work ethic that I’ve seen is in Japan," he says. "We have same-day delivery in all the fashion capitals – London, Hong Kong, New York – but the Japanese don’t care about same-day delivery, they only care about the exact time you are going to deliver their parcel, and it could be in two weeks’ time but you need to tell them exactly when."

High-net-worth customers will now spend £200,000 a go, and during last winter’s Cyber Weekend (the late-November shopping peak that begins on Black Friday), the group received an order every 0.7 seconds. Marchetti has built up a personal rapport with many of his most loyal customers; his favourite part of the job, he says, is when someone tells him they married in something they bought via YNAP.

It is the unravelling of Net-a-Porter’s editorial flagship that has been the subject of British fashion-industry chit-chat this summer. Porter magazine was the ultimate luxe marketing tool when it launched in 2014 under former Harper’s Bazaar editor Lucy Yeomans – to be published six times a year as a vehicle to showcase NAP’s products. Now it is being pared back to biannual editions and the team has been restructured (Yeomans left in January to work on a new venture).

"You always work in a defined level of means," Marchetti explains, carefully. "We decided the split between print and digital was going to be more favourable to digital because that is where our customers want us to be. So we are investing heavily in video for Porter. Frankly, we felt that we were a little behind. And there will be podcasts, which is super-important for our customers. We’re keeping the print to two big issues, which I think will be amazing."

He is not concerned about the business implications of Brexit. Although he didn’t exactly see it coming, he was prepared, he says, pointing to the company’s logistical bases in both the UK and Europe. Good to know the nation’s Gucci habit won’t be dented by no deal.

On a personal note, however, he’s not feeling so breezy. His partner, Kerry Olsen, a journalist, is British so their daughter Margherita, eight, is ‘50/50’. "I’m more than worried, I’m sad, because I’ve always dreamed of a future where she could travel without a passport."

Marchetti’s own upbringing was humble. He was born in Ravenna on Italy’s north-east coast. His father worked for Fiat, and Marchetti remembers he would drive them to the mountains for family Christmas holidays before returning to the factory to complete the end-of-year inventories. When Marchetti was awarded an Italian knighthood in 2017, his greatest regret was that his "perfectionist" father was not there to witness the moment.

After studying economics at Bocconi University, Marchetti’s first job was with Lehman Brothers. There were other forays into banking and entrepreneurship before he formulated the YOOX idea in 1999.

We meet on the hottest day of the year, when even slick Milanese air con struggles to ward off the 39C heat. Marchetti is concerned about climate change and has introduced electric cars for staff and recyclable packaging. He began the YOOXYGEN sustainable fashion platform in 2009, when it still seemed like a niche interest, and he’s adamant that being more eco needn’t be a business sacrifice.

"I don’t think that there’s necessarily a trade off. Like with fur, we simply did a survey asking 5,000 customers, and the vast majority said they don’t want to buy fur any more. It means a few million pounds lost for us but it was a decision to satisfy our customers, and in the end you have to satisfy your customers, which means that loss that you make in three months, in the long term is not a loss."

Marchetti is a proud early adopter. He tells me that he had a brick of a mobile phone in his first year of university in 1989, and even then was desperate for this to be combined with a camera. When he lived in Ealing as a young teenager, having come to the UK to study English, he fell in love with a pair of big orange boots, which kept being reduced until he could afford them. Within three or four years, those Timberlands were a huge trend.

Today he looks cool in his signature round grown-up Harry Potter glasses, a grey Tom Ford suit, loafers handmade in Milan and a collarless shirt by Turkish designer Umit Benan. "I was wearing this type of shirt at a dinner with Richard Gere, about 25 years ago. He was pro-Tibet so he complained about my mandarin collar," Marchetti remembers.

His predilection for zaniness has resulted in some offbeat ideas, like the time he met Malcolm McLaren at a weekend house party in Connecticut in 2001. Over whisky by the fire, they came up with a Pac-Man-themed childrenswear collection, which remains one of his proudest collaborations to date.

Besides former Vogue Italia editor Franca Sozzani, Marchetti still cites McLaren as one of his great inspirations. "He told me that anything you launch must respect the three Ss: it needs to be stylish, sexy and subversive." With that mantra, the future of luxury shopping is sure to be anything but dull.​