UPS Astronomical Math

Marcus Wohlsen
June 13, 2013

The Astronomical Math Behind UPS' New Tool to Deliver Packages Faster

In a sense, all business boils down to math. But some companies have tougher equations to solve than others.

At UPS, the average driver makes about 120 deliveries per day, says Jack Levis, the shipping giant's director of process management. To figure out how many different possible routes that driver could travel, just start multiplying: 120 * 119 * 118 * . . . * 3 * 2 * 1. The end result, Levis likes to say, far exceeds the age of the Earth in nanoseconds.

If that number sounds big, imagine having to make those calculations for 55,000 drivers every day. Until recently, UPS used a software tool that gave drivers a general route to follow but allowed wide latitude for human judgement along the way. Over the next five years, however, the company will roll out widely a more exacting algorithm designed to steer drivers away from well-worn paths toward often counterintuitive routes calculated to make delivery faster.

Called ORION, or On-Road Integrated Optimization and Navigation, UPS' data-drenched route optimization tool aims to deliver the best answer yet to the traveling salesman problem, the classic computational conundrum that shows just how hard it is to find the shortest distance among a series of points on a map. The size of the numbers involved means simple arithmetic is out. Instead, ORION depends on heuristics, the field of math and computer science devoted to finding answers that are good enough, and that get better based on past experience.

Of course, finding the shortest distance is only one of many variables in play for UPS. Promised delivery times, different types of customers and the types of packages being delivered and picked up are just a few of the additional factors ORION must take into consideration. And Levis is quick to emphasize that UPS doesn't discount the value of driver wisdom accumulated during years on a route. The best system, he says, is one that relies on both human and algorithmic intelligence, not just one or the other.

Still, computers simply have far more raw calculation power than humans. That capacity combined with the massive amount of data needed to feed that brainpower are what Levis hopes add up to superhuman intelligence: "How do we come up with ways that are better than what humans would have come up with on their own?"

Here's a few more numbers that play into the math behind UPS' quest for efficiency:

$30 million—The cost to UPS per year if each driver drives just one more mile each day than necessary. By that same logic, the company saves $30 million if each driver finds a way to drive one mile less.

15 trillion trillion—The number of possible routes a driver with just 25 packages to deliver can choose from. As illustrated by the classic traveling salesman problem, the mathematical phenomenon that makes figuring out the best delivery routes so difficult is called a combinatorial explosion.

55,000—The number of "package cars" (the brown trucks) in UPS' U.S. fleet. If the figures involved in determining the most efficient route for one driver are astronomical in scale, imagine how those numbers look for the entire fleet.

85 million—The number of miles Levis says UPS' analytics tools are saving UPS drivers per year.

16 million—The number of deliveries UPS makes daily.

30—The maximum number of inches UPS specifies a driver should have to move to select the next package. This is accomplished through a meticulous system for loading packages into the truck in the order in which they'll be delivered.

200 million—The number of addresses mapped by UPS drivers on the ground.

74—The number of pages in the manual for UPS drivers detailing the best practices for maximizing delivery efficiency.

100 million—The reduction in the number of minutes UPS trucks spend idling thanks in part, the company says, to onboard sensors that helped figure out when in the delivery process to turn the truck on and off.

200—The number of data points monitored on each delivery truck to anticipate maintenance issues and determine the most efficient ways to operate the vehicles.

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