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It is only fitting that a service pitched for traveling sellers should find themselves facing a particularly nasty version of what is known as a travel-seller problem. Stated simply: Given the seller and a certain number of cities, what shortcut should it take before returning home? This is a classic resource allocation puzzle that rears its ugly head in industries ranging from logistics (especially freight) to design schemes, yes, flesh and blood travel sellers: How to minimize cost and maximize traffic efficiency? Back in 2002, it was an issue facing DayJet, a new air taxi service hoping to take off this spring. Based in Delray Beach, Florida, DayJet will fly planes, but its business model is not built around its growing fleet of flogging new Eclipse 500 light aircraft. It is built on mathematics and silicon, and an almost prophetic force that, in turn, came out of them. We are a software and logistics company that happens only to make money flying planes, insists Ed Iacobucci, IBM veteran and co-founder of Citrix Systems, who launched DayJet as his third act. The advent of affordable air taxis has heralded a steady drumbeat of press over the past few years, with understandable fixation on sexy new technologies that are usually credited with making the market possible: airplanes. The Eclipse 500 is a clean sheet design for a tiny jet that seats up to six and costs about $1.5 million (the Federal Aviation Administration could clear it for mass production as early as next month). It is also the most economical certified aircraft in the sky. Cessna, meanwhile, rolled out his own, if more expensive, very light (VLJ), with a Honda set to appear in 2010. No less authoritative than the dilemma of the author of the innovator and professor of Harvard Business School Clayton Christensen mused in the press that the E500 and its ilk could radically change the airline airline breaking the hub and talking the system we all know and despise. But Jakobucci, who has long written a check for more than 300 orders and options on the first Eclipse planes, doesn't rely on a plane to make or break it. Instead, it's his company's software platform and the new way it attacks travel-seller problems that will set DayJet apart. On the first day of operations flying from five cities in Florida with only 12 planes, DayJet dispatchers will already have millions of interconnected flight plans to choose from. As the geographical track of the company spreads (with luck) across the southeast- and as its fleet expands the also-computing capability only gets worse. Factor in variables such as the availability of pilots, airplane maintenance schedules, and downpours that wet the peninsula like summer clocks, and well, you get the idea: Finding the shortest, fastest and least expensive combination of routes can take every computer in the universe for the rest of time. I knew the complexity and how it would degenerate as soon as you reached the threshold, Jacobucci said. So he didn't try to find the best solution. Instead, DayJet began looking for a family of options that create positive (if imperfect) results by following a discipline known as the science of complexity. For the past five years, without planes, pilots or customers, DayJet has operated every aspect of its business thousands of times a day, every day, in silicon. Feeding on any data they could find, Jakobucci and his colleagues were determined to see how the business would actually ever behave. When DayJet finally starts flying, they will switch to real-time flight data, using their operating system for shuttles back and forth as computers cruise around bits and bytes. Iacobucci is an expert in operating systems, he has done so for decades at IBM and Citrix. Because of this, it has zero interest in the loose goose world of Web 2.0. The next big business opportunities he sees are in a series of operating systems designed to simulate activities in the real world. DayJet looks the first, but it has no doubt that there will be others, and that new companies, and even new industries, will appear overnight as computers tease answers from previously intractable problems. Which brings us back to the traveling merchants. Iacobucci says its computer models predict that DayJet's true competitors are not airlines, but Bimmers and Benzes- it says that 80% of its revenue will come from business travelers who would otherwise drive. In other words, DayJet, which in March closed an additional round of funding for $50 million, is creating a market where it is not, which is an amazing mathematical achievement. To there, all Iacobucci needed was five years, a professor with a bank of 16 parallel processors, two so-called Farmers and a pair of Russian rocket carriers, which, it turns out, are neither Russian nor rocket launchers. It's a lot nastier than any other airline planning job we've ever done, said Georgia Institute of Technology professor George Nemhauser, whose graduate students help map the scale of DayJet's mountain planning dilemma. You can think of it as a travel-seller problem with a million cities and this is a problem DayJet has to solve every day. Using the school's computing power, Nemhauser and his students figured out how to calculate a near-perfect solution for 20 aircraft in a matter of minutes of computing time and a solution for 300 aircraft in 30 hours. But as impressive as this is, in the real world, it's not nearly enough. This is because in order for DayJet's booking system to succeed, Iacobucci and the company need a response and price in less than five seconds, the limit for those driven by Orbitz or Expedia. Because DayJet doesn't have a preset schedule, and because overbooking is out of the question (DayJet will fly two pilots and three passengers maximum) - any request to add another customer to the equation given the day requires its software to crunch it all over again. One of Jacobucci's oldest buddies and investors, former Microsoft CFO and Nasdaq Chairman Mike Brown, pointed him to a label-way to cheat the math. Brown resigned with his stock options to pursue his pet projects while bleeding edge themes such as image recognition, artificial intelligence, non-linear optimization, and computational modeling. His dabblings led him first to Wall Street, where he invested in a trading algorithm called FATKAT and ended up in Santa Fe, New Mexico, a land of zero for the complexity of science. Iacobucci says 80% of its revenue will come from travelers who would otherwise drive. In other words, DayJet creates a market where it didn't exist, an amazing mathematical feat. Invented by scientists from the nearby Los Alamos National Laboratory in the 1980s, the science of complexity is a gumbo of ideas taken from such diverse fields as biology, physics and economics. At its core is the belief that any seemingly complex and totally random system or phenomenon - from natural selection to the stock market - arises from the simple behavior of thousands or millions of people. Using computer algorithms to stand up for these individual agents, the scientists found that they could build fantastically powerful and detailed models of these systems, if only they could nail the right set of rules. When Brown arrived in the city in the late 1990s, many scholars-in-residences at the Santa Fe Serene Institute center dedicated to the contemplation of complexity, hastened to commercialize their favorite research topics. Prognosis Co. was profitable gaming games Street by identifying and using small pockets of predictability in capital flows. Clothes called Complexica worked on a simulator that could basically model the entire insurance industry, acting as a giant virtual brain to anticipate the consequences of any disaster. And BiosGroup is perfecting models based on agents that today fall under the headline artificial life. By the time Jacobucci mentioned his logistical dilemma to Brown in 2002, most Santa Fe Info Mesa startups were bouncing around in the wreckage of dotcoms. But Brown knew that Bios produced a surprisingly elegant solution a few years ago, creating virtual ants that, when turned free, showed how a few false assumptions or bottlenecks could throw the entire system out of impact. The Bios model, built from Southwest's cargo operations, for example, cost $60,000 and found a way to save the airline $2 million a year. Brown suggested That Jakobucci supplement his set of tools with a healthy dose of complexity science. Iacobucci has already worked hard to create an optimizer program that used non-linear algorithms and other mathematical labels to create planning solutions in seconds.