When Nafis Muhammad first started driving for UPS in New Jersey, he had a hard time keeping up. Like all UPS drivers, he had a lot on his plate. In the morning, he would get his packages, plus their addresses and promised delivery times, and he’d have to plan a route that got him back to the delivery center in a standard eight-and-a-half hour work day.

“If you don’t know your area, you’re not doing it in eight-and-half hours — you’re doing it in ten. And they’re like, ‘let’s go, step it up,’” Muhammad said.

He eventually got faster. Then, a few months ago, his delivery center started using a software program that tells him, one by one, what order to deliver the packages in — making the job, as he puts it, “ten times easier.”

The program is called ORION, for “On-Road Integrated Optimization and Navigation,” and its complicated algorithm crunches data on the packages for a given route on a given day to come up with the most efficient order of delivery.

UPS says the software is helping prepare for the record number of packages — 700 million — it’s expecting to deliver between Thanksgiving and December 31. The shipping company’s on-time delivery rates dropped around the holidays in 2013 and again, to 91 percent, after Cyber Monday last year, according to Shipmatrix, which tracks the delivery performance of shipping companies.

ORION does have limitations. One of the biggest: it doesn’t recalculate for unexpected delays once drivers are out in the field. In those cases, they end up having to play catch up.

UPS plans to release a new version of ORION that does recalculate by 2018, said Jack Levis, senior director of process management at the company. But even as it is, the software program is already on track to save UPS 100 million miles and $300 million to $400 million a year in fuel and personnel costs, Levis said. “Which is why we didn’t wait for all these final things,” he said. “We said, you know, ‘this is enough that we can make an impact to the business.’ So we put it out there even though it wasn’t perfect.”

The cost savings are crucial for UPS, which has to keep its prices down to compete for business from online retailers. Around the holidays, though, it may be the time savings that matter most.