Contractors widening a 1.6-mile-long section of Interstate 75 in southwest Florida elected to build outside the box by using global-positioning technology to control two of the largest rubber-tired gantry cranes ever to work on a U.S. highway project.

Using GPS to guide a gantry, or straddle, cranes marks a first for a highway application, say executives at gantry-crane manufacturer Mi-Jack Products Inc., which supplied equipment for the Florida bridge project. Equally unusual is the size of the company’s twin MJ-70 Travelift ...