Making the world better through clever mathematical modelling may seem like science fiction, but it is core business for Optima Corporation.

Optima uses mathematical modelling to improve efficiency and cut spending. As an example, the software it has developed has been used to significantly improve ambulance response times.

In January Optima scored a success in Florida, where the Lee County Emergency Medical Services and Emergency Dispatch Centre deployed two versions of its software - live and predict - to make the best use of resources.

In one case, a decision to relocate an ambulance hub made using Optima live cut the response time to three minutes, instead of the typical eight to 10 minutes.

Optima's predict tool, which builds "what if" scenarios, is aimed at helping make strategic planning decisions.

The software has already helped Lee County save US$750,000 ($1.1 million), says Optima chief executive Chris Mackay.

Although maths opens up endless possibilities, Mackay is keen to keep Optima focused on emergency services.

"There are about 15,000 emergency services in the US, of which about 1500 are the right target for us, conservatively valued at US$800 million," he says.

The Lee County project will give Optima more credibility when it talks to other US emergency services.

Cracking the US market has been a long courtship. "We have done a lot of flights and done a lot of exhibitions," says Mackay. "Our guys have for the last four to five years been toddling up to these trade shows with their suitcases to profile our business to them. We are starting to see some attention.

"They now realise we are not a fly-by-night operator. The export road is a long-haul one but you have just got to do it. Once you get one or two major deals, the momentum starts snowballing."

So far, Optima has implemented 24 projects in six countries. Locations include Toronto, Las Vegas, San Francisco and San Bernardino. It is beginning to build a relationship with St John in New Zealand, and also has some customers in Europe, where it hopes to expand.

Revenue has doubled from 2008 levels. "We are still learning about the industry which is constantly seeing a high pace of change," says Mackay. "Our numbers will grow quickly."

The Auckland-based company was founded in 1998 by Auckland University's Professor David Ryan and Dr Andrew Mason, together with graduate Dr Paul Day - experts in advanced operations research. Today a fifth of its staff have doctorates. Initially developed out of the Icehouse business incubator with $1 million from angel investors and venture capitalists, Optima is today owned by its founders, venture capitalists, investors, staff and management.

One of its most celebrated achievements is the work done with Air New Zealand, which estimates that it has saved nearly $15 million a year by using Optima's system for crew scheduling.

Like all high-growth companies based in New Zealand, Optima has come to a crossroads - needing to make a leap of faith and put resources into key markets.

"You really have to be there," says Mackay. "We currently have a New Zealand-based guy who travels three to four times per year to Europe, spending every day in a different country sometimes. We will soon be appointing a direct representative in US and Europe.

"We are not going to be able to create the growth we want by doing it all from New Zealand. We can implement and support from New Zealand - for that we can do remotely. For sales, we need the face-to-face contact."

The groundwork done in the US, for instance, has made Optima optimistic that potential clients will now understand what is on offer.

"One of our major challenges has been to educate the market - to tell people hey, you need to start considering this technology. In many cases it is almost frontier-land to them," Mackay says.

The other challenge the company faces is ramping up its capability.

"We have a whole bunch of 'rocket scientists' who are very special people. As we take on new developers, it would take us between six and 12 months to get them up to speed, before they can become commercially productive. New business analysts are very similar. We need between six and 12 months to bring them up to speed."

The company is also going to need more money. "We are cashflow positive but for us to continue our growth track, we need to invest in our sales capability. We will be looking at capital raising to support that."

The use of computer modelling is exciting, with applications across many industries. For now, Optima is content to make emergency services its main playing field.