Cincinnati ? Swiffer kitties? Just attach little dusting pads to your felines’ paws, so they can help keep your floors clean while making their rounds.

A bit farfetched? Executives at consumer-products king Procter & Gamble Co. thought so, too, and sent the idea to the discard pile.

P&G also rejected pitches from outside inventors for a bellybutton lint brush, a Knees and Toes body wash to complement Head and Shoulders shampoo, and a “man handle” to keep marital harmony in the bathroom by making it easier to raise and lower the toilet seat.

But there are success stories, too. The original Swiffer duster was developed by a Japanese company that P&G teamed up with to take it global.

That’s why P&G keeps the door open to proposals. The once insular company is now considered a leader among the companies in many industries who are listening to outsiders they once might have shunned, including other businesses.

“We don’t care where good ideas come from, as long as they come to us,” said Jeff Weedman, a vice president who helps lead P&G’s effort to solicit ideas online or from scouting by P&G employees around the globe. “We’re not going to use everything that shows up, but we want to be the preferred partner.”

Others noted for “open innovation” include IBM Corp., whose online “innovation jams” in the past decade included a 2006 session it said had 150,000 participants from more than 100 countries, and Eli Lilly & Co., which in 2001 created an InnoCentive branch to draw scientific help from around the globe.

Jeff DeGraff, a professor who focuses on managing innovation and creativity at the University of Michigan’s Ross School of Business, said P&G has helped popularize the approach.

“P&G was the poster child for this movement, showing large companies with growth challenges that this is not just for Silicon Valley or Ann Arbor (Mich.),” DeGraff said.

A.G. Lafley, who took over as CEO in 2000 with a mandate to change a huge company whose stock was plummeting, in 2001 set a goal of more than tripling the share — he estimated it then at 15 percent — of innovations from the outside. By the time he stepped aside in July, about half of P&G’s new products used ideas, ingredients or technology that originated outside the company.

Going outside can help bring products to market faster and cut development costs, Weedman said, while it gives the innovator access to P&G’s global marketing might — and a share of its sales.

P&G still filters out most ideas it receives from outsiders because of patent or ownership issues — or because they’re just “not P&G businesses,” Weedman said.

That was the case with a recent proposal that the company combine its hygiene and beauty capabilities to create a home embalming kit.

P&G passed.