Calculus For Truckers

Published 12 years ago
Calculus For Truckers

BERNARD JOHNSON IS a trucker and a math problem. From his home in Columbia, S.C. the 49-year-old drives for Schneider National, one of the country’s largest freight haulers. Johnson pulls trailers filled with everything from TVs to toilet paper on as many as 25 trips a month for stretches of up to 500 miles.

The Green Bay, Wis. Company has to design the most efficient routes for Johnson and 13,000 other drivers. With diesel at $4 a gallon, this is not an equation it can afford to get wrong. “It’s like a big jigsaw puzzle,” says Ted Gifford, an operations research scientist at Schneider. At any given time the company has 10,000 trucks on the road, with another 33,000 trailers available and waiting to be picked up. Drivers are on the road between four days and three weeks at a time— alone and in pairs—and Schneider must get them back to their homes by a certain date. Drivers have to take breaks according to government regulations.

Schneider’s Ted Gifford helped design a computer model that simulates operations.


Their customers are only open during certain hours. “We want to avoid the situation where a driver may live in Alabama, and it’s time for him to go home, and he’s in Minnesota,” says Gifford. “And we don’t have any freight for him to get home, so he has to drive empty.” For most of its 76-year history Schneider, which grossed $3.1 billion last year, has relied on pilot projects to answer these key logistical questions. Whichever department was considering a policy change would carve out a group of 20 to 200 drivers, make them function as a separate business and test the results. The pilot projects cost “hundreds of thousands of dollars,” but results were often ambiguous. All too often a system that worked well for a sample of 20 drivers wouldn’t work when scaled up to the whole company. “You could spend more on the pilot than what you’d save making the policy change,” says John Nienow, a senior logistics engineer. To test another variable the only choice was to rerun the entire pilot and therefore double the cost.

In 2003 Schneider decided to invest in a fleet-wide “tactical planning simulator” that would use software algorithms to mimic the decision making of human dispatchers on an inhumanly large scale. Schneider looked to one of the leading practitioners of logistics simulation, Warren Powell, a professor of operations research and financial engineering at Princeton University. The algorithms that came out of Powell’s lab in the 1980s had changed the industry’s “less-than-truckload” segment (consisting of parcels and smaller freight) by mapping out a more efficient way to plan routes and using terminals that break down shipments.

One model, called SuperSPIN, had been embraced by Yellow and Ryder to survive the recessionary late 1980s. Powell’s software was also behind the launch of Roadway Package Systems, which later became FedEx Ground. What interested Schneider, a full-truckload carrier, was Powell’s work in the field of approximate dynamic programming, which is a way to make decisions in the presence of uncertainty. Schneider needed a model that could take into account the nonobvious and sometimes random variables that affect the efficiency of thousands of drivers over weeks of time and at a high level of detail. “Warren gave us a really nice hammer, and we had to take our problems and make them look like nails,” says Nienow.

A team of Schneider and Princeton engineers spent two years and “between $2 million and $5 million” developing software for the simulator, which lives on an eight-processor server in Green Bay. The simulator, which Schneider launched in mid-2005, pretends that it’s assigning freight and gathering orders based on a scenario posed to it by Schneider’s analysts. That could be something such as adding more drivers in Chicago, adding an hour in mandated break time for drivers or having a big customer change the location of its distribution center. The simulation runs forward in time for three weeks in order to approximate the value of having a truck and driver at a certain location at a certain time, and gets a first result. Then it runs backward in time to the “present”, reconciling the results with those that happened in the simulated future. Then it runs forward three weeks again and then backward, continuing to improve its estimate. It does that until it “converges” and starts to make only minor changes. For each three-week run, it makes hundreds of thousands of decisions. Gifford estimates that the simulator has helped Schnei- der save tens of millions of dollars. The simulator has, for example, allowed Schneider to justify price hikes to customers.


In 2008 a customer wanted to restrict the number of hours that Schneider could drop off goods. Schneider ran the simulator. “We showed that we could limit the hours but that doing so would cost us $600,000 more,” says Gifford. “We went back to them and said, ‘This is the impact of restricting your hours.’” The customer ultimately decided not to limit its hours. One of Schneider’s biggest challenges is maintaining its fleet size, since drivers often burn out and leave the company. Schneider regularly uses the simulator to determine how many jobs to offer and where it’s best to hire drivers. The model can determine the marginal value of hiring ten new drivers who live in central Illinois, say, based on the number of times that freight departs from the Midwest. In the future Schneider wants to use the simulator to decide which new business to pursue. The company currently employs three different fleets of drivers: long-haul truckers who live in one city but can travel all over the country, regional drivers who drive within a 500-mile radius of their homes, and dedicated fleets for specific customers.

A decisionto increase one of those fleets can affect the others: When Schneider creates a regional business, for example, it cannibalizes some work that the long-haul fleet is doing. “The thing that’s so powerful is that when someone presses us on the impact of different policy changes, we have the facts, we have the data. We can produce reports and analysis so that if someone else brought in their scientists, they would have to agree,” says Gifford. “The value is to be able to take these complex business opportunities and give them a good, solid analysis.”