In recent weeks, Apple Inc. has accelerated plans to shift some of its production outside China, long the dominant country in the supply chain that built the world’s most valuable company, say people involved in the discussions. It is telling suppliers to plan more actively for assembling Apple products elsewhere in Asia, particularly India and Vietnam, they say, and looking to reduce dependence on Taiwanese assemblers led by Foxconn Technology Group. Turmoil at a place called iPhone City helped propel Apple’s shift. At the giant city-within-a-city in Zhengzhou, China, as many as 300,000 workers work at a factory run by...