Designed would be someone sitting down with the intention of creating an item or process to be used in the future. "We designed the safety procedure to ensure nobody was hurt." Devised is more improvisational. To me, it would imply that someone created something useful in a stressful situation. "He devised this handy contraption to trap fish after being trapped on an island." Developed would be something that occurred after a situation arose. "We developed this safety plan after Brandon got trapped on an island and had to catch fish to survive."

These words are all pretty similar though we would use them differently. Designed means to plan in detail for a specific purpose. Deivised is rather similar it is to plan or invest something with careful thought. Developed is a little different. It more of a process than a plan.