MESQUITE, Texas—In the sticky Southern heat, hundreds of workers streamed in for the 11 a.m. shift last month at United Parcel Service Inc.'s UPS 0.24% local package-sorting facility, one of dozens nationwide that help it move millions of parcels daily.

In a windowless room, a 30-year-old analog control panel about the size of a chest freezer monitors operations, with rows of green and red lights indicating when something goes awry in the building's web of conveyor belts.

"Thirty years ago, this was top-notch," UPS plant engineering manager Dean Britt said of the control panel. Today, the panel's computing capabilities "can probably fit on your phone," he said, "and not even a good phone."

The site, and other similar UPS facilities, haven't automated much over decades—despite a rush of new warehouse technology in many industries. Today, the company is paying a price.

'Thirty years ago, this was top-notch,' says a UPS engineer about the analog control panel, above, in the company's Mesquite, Texas, distribution facility. Photos: Brandon Thibodeaux for The Wall Street Journal

As UPS tries to satisfy America's 21st-century shopping-and-shipping mania, parts of its network are stuck in the 20th century. The company still relies on some outdated equipment and manual processes of the type rival FedEx Corp. discarded or that newer entrants, including Amazon.com Inc., never had.