In 2003, California was ravaged by some of the deadliest forest fires in its history, with up to 13 blazes raging across the state.

The impact was devastating: more than 2,000 homes were destroyed, 22 people were killed, and billions of dollars of damage was inflicted as 800,000 acres of land went up in flames.

At its peak, more than 11,000 fire fighters and 81 planes and helicopters attacked the blazes. Behind the scenes, hundreds of response teams across the state were trying to work out how to cope with the scale of the disaster.

But while confusion reigned on the ground, a series of complex algorithms coded by a group of mathematicians was quietly calculating the optimum method of response to the challenge.

The group is part of a rapidly growing unit in IBM, the Centre for Business Optimisation, which comprises mathematicians, researchers and consultants. Its role in the disaster gives an insight into how IBM is reshaping itself from a server company to a service provider.

William Pulleyblank, vice president of the Centre for Business Optimisation, says events such as forest fires and hurricanes are among the toughest problems to deal with.

'The critical issue is that once a wildfire starts, you have 18 hours to respond to it,' he says.

'We're working with the US Federal Government on the maths modelling to optimally allocate fire-fighting resources and to better predict how the fires will burn, so the decision and response can be made within the 18-hour window.'

The centre specialises in devising approaches to complex scenarios to help anyone from disaster response units to business leaders dealing with rapidly changing markets. Best known for his work on developing IBM's Blue Gene, the world's most powerful supercomputer, Pulleyblank has now moved on to lead a team that aims to use IBM's varied resources to solve complex problems.

He realised early on that if IBM was going to be really effective in solving difficult business issues, it needed a unit that drew on a range of strengths from IBM's research, development and consulting divisions.

'If there has been one trend at IBM over the past 10 years, it has been that we've been looking for broader-impact things that we can attack,' he says. 'At one point we'd worry about how to store a company's digital data. Today we're looking at companies and seeing how they can run their businesses more efficiently, and deal with disruptions more effectively.'

Pulleyblank describes how pricing, for example, has changed dramatically as businesses shift away from the legacy of fixed catalogue pricing to dynamic online pricing.

'It's just an example of the kinds of much more complicated business transactions that have to be supported,' he says.

A lot of the unit's initial work has centred on markets with clear needs, such as tightening up supply chains and optimising shipping schedules. Beyond that, IBM has approached more unusual areas and pitched unique ideas to companies through its consulting business.

One challenge involved building a system that can help an airline deal with major disruptions such as a blizzard that shuts down an airport.

'That's a situation where you need real-time response with an enormous level of complexity. Scheduling is disrupted, staff may be there but they've passed the maximum amount of time they're allowed to fly in a shift, and so on,' says Pulleyblank.

'And all of this happens under enormous time pressure, all of which becomes a major logistical challenge.'

The idea is to get the research brains to solve a unique issue, and then pass it on to IBM's consulting group to develop it into a more general package that can be sold on to other businesses. So far, the centre has developed four offerings, based on initial one-off engagements with early clients, ranging from fraud detection to pricing optimisation. Behind all of these programs are complicated algorithms.

'Within our research group we have access to some of the best mathematical minds you can find. The real challenge is that we're having to study mathematical models that don't actually exist in nature,' says Pulleyblank.

'Statistics will look at a lot of data and give you an overall view of it, but a lot of the time we're looking for the outlying data. That's the opposite of statistics. I want to know where the anomalous behaviour is happening.'

The centre's goal is to grab a chunk of an emerging market, which it calls business performance transformation services. IBM believes it will be worth some $500bn (£267bn).

'No one knows the number, but it's a big number. It's about companies wanting a capability but not being able to do it themselves, so they look for someone who can help,' says Pulleyblank.

'We're on a very steep growth curve now. We're looking at going from tens of millions [of dollars] this year to hundreds of millions next year because we think there's that much opportunity out there.'