Want to get the best deal on airfares, figure out how big your reception area needs to be, work out the best radiation treatment for liver cancer or cut waiting times for call centres?
First do the math. The secret is all in the algorithms, say Canada's top researchers.
Algorithms, they say, are taking over the world. They hold the answers to everything from designing better cars to finding the perfect mate.
"What computational sciences, algorithms especially, do is greatly improve accuracy. They make things much more predictable," says Tamas Terlaky, director of McMaster University's School of Computational Engineering and Science in Hamilton, Ont.
"If we have good enough data, today's computers are powerful and fast enough for us to apply mathematical computation to finding better ways to do almost anything you can think of."
Algorithms are a math process, a set of rules used to calculate outcomes. They are also iterative, says Oded Berman, Sidney Cooper Chair of Business and Technology at the University of Toronto's Rotman School of Management. This means they can run through hundreds of thousands of small improvements and each one increases accuracy.
Dr. Berman, along with colleagues Opher Baron and Dmitry Krass, recently won themselves a footnote in history by creating an algorithm that can be used to reduce waiting times in facilities as diverse as hospitals or call centres.
What made their algorithm different was that it takes into account three key variables: how many facilities are needed, where to put them and how large they need to be to balance consumer demands.
The problem with previous attempts to apply mathematical principles to decide the best place to locate any kind of facility - from a Starbucks outlet to a manufacturing branch plant - was that those efforts used very specific assumptions, which limited their usefulness to only specific case studies rather than to a variety of situations.
"The end result was you wound up providing lousy service or paid too much for your facility," Dr. Berman explains.
The Rotman trio tested their new algorithm on a computer model. In fact, they ran it on 4,000 different cases involving up to 210 facilities.
The results were so gratifying they published a paper, "Facility Location with Stochastic Demand and Constraints on Waiting Time" (available online, for the mathematically inclined, at http://www.rotman.utoronto.ca/pdf/facilitylocation.pdf).
The trio hasn't yet found a commercial client interested in using their algorithm, but that is part of the research game, says Dr. Berman. "We may work at a business school but in truth we are researchers and scientists, not business people."
At McMaster, meanwhile, advanced mathematics is being put to very practical uses.
For example, Dr. Terlaky says his school and a team from the University of Waterloo are working with oncologists from Toronto's Princess Margaret Hospital to find the optimal level of radiation that can be used in treating liver cancer.
"We are working with Dr. Laura Dawson, a PMH oncologist, to find out how much radiation is most effective," he says.
"Laura Dawson doesn't understand the math but she doesn't need to. She knows the treatment - we know the math."
What has propelled the giant leaps forward in creating mathematical formulas to increase accuracy is a happy combination of data and computing power.
The data becomes the basis for analysis; the more of it available to sift through, the greater the accuracy.
The power and speed of today's computers means computational tasks that would have taken decades in the 1990s can be done in a matter of minutes today.
"Today, thanks to computational science we can produce huge savings for industry, more effective diagnosis and treatment for medicine, better design for products and better management of resources," Dr. Terlaky says.
"These great advances come at a time when almost all organizations have accumulated masses of data," says Rotman's Dr. Baron, associate professor of operations management. "It becomes historical data which can be analyzed to predict the future.
"Mathematical models are bound to play a greater role in business and even personal decision making," Dr. Baron predicts.
One of the nifty properties of algorithms is their widespread application, Dr. Terlaky says. He points to online discount travel sites such as Expedia.ca.
"Those sites adjust airline fares twice a day depending on buyer response," Dr. Terlaky says. "And the algorithm they use is basically the same as the one used for cancer diagnosis."
Another popular website, MapQuest, uses algorithms to work out optimal routes for drivers.
Utility companies, meanwhile, use algorithms to determine the "sweet spot" for prices they charge, the prices that give them the competitive edge with consumers as well as the best bottom-line profit in a deregulated market.
"What it comes down to is one of those basic principles: if you can't measure, you can't manage," says Dr. Berman. "Computational sciences take measurement a huge leap forward."
Algorithms at a glance
What they are
An algorithm is more than a mathematical equation. It's a formula or set of steps or rules used to solve a problem. It can range from a simple cookie recipe to something as complex as the procedures to follow for landing a vehicle on Mars.
General properties
An algorithm receives input and generates output. It is carried out in discrete, stepwise fashion, with the results of each step determined only by inputs and the results of the previous step. It also has a clear stopping point.
Uses
Algorithms can be used to design circuit patterns for microprocessors, analyze stock-trading trends and create Sudoku puzzles. Computer programs are essentially elaborate algorithms. To sharpen a digital photo, for example, an algorithm has to process each pixel in the image and determine how to change them to make the image clearer.
Key players
The word algorithm derives
from algoritmi, the Latinized name of 9th-century Persian mathematician Mohammed ibn-Musa al-Khwarizmi, the father of algebra.
In 1801, France's Joseph Jacquard invented the automated weaving loom, one of the earliest machines with functions that were controlled by algorithms; fabric patterns were determined by cards punched with holes that controlled thread selections. (Today, a jacquard fabric is one with an intricate pattern.)
In 1842, the first algorithm for a computer was written by Ada Byron (daughter of the poet Lord Byron) for English mathematician Charles Babbage's "analytical engine." He was the first person to propose the idea of a programmable computer, but his device was never built.
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