pp. Restructuring a company's workforce to find the optimum mix of jobs performed locally and jobs moved to foreign countries.
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The hype in the U.S. may die down as more companies figure out what work they can send overseas, and how to manage it from afar. In the meantime, the real innovation seems to be in finding new ways to sell it to an uneasy public. The latest term making its way through corporate America: "right-shoring."
—Brad Stone, “Should I Stay or Should I Go?,” Newsweek, April 19, 2004
Whatever the truth of the matter, there is no doubt that customers with complex queries requiring local understanding do not respond well to far-off operators repeating parrot-fashion a series of learned responses. Convergys, one of the world's biggest providers of "contact-centre services", advises companies to shift simple queries offshore while retaining the more complex ones on the same shore as the caller. It calls this process "rightshoring", and estimates that about 80% of the companies that it is working with in Britain are planning to split their call-centre operations in this way.
—“Relocating the back office,” The Economist, December 13, 2003
2003 (earliest)
With companies falling over themselves to move chunks of their IT overseas it was only a matter of time before consultants coined a cheesy term for it.

We have had offshore outsourcing and "nearshore" outsourcing — but now brace yourselves for "rightshore".
—“Downtime,” Computer Weekly, July 08, 2003
The term Rightshore ™ is a trademark of Cap Gemini Ernst & Young, with a filing date of May 27, 2003.