Five decades ago, a young Texas Instruments Inc. accounting manager named Pete Pyhrr pioneered a technique to help businesses shave costs. It led to a book deal, a People magazine interview and some consulting gigs, including as an adviser to then-Georgia Gov. Jimmy Carter.

Then things mostly turned quiet for Mr. Pyhrr and his arcane tool, known as zero-based budgeting, until the Brazilians behind private-equity firm 3G Capital Partners LP came along.

...