When someone comes up with an idea, the way in which they are treated by management is very important. If management treats people and their ideas with respect, then those people are much more likely to come back and share more ideas.
Think about the psychology of it. When people are challenged to come up with innovative ideas, they may feel unsure of their ability to do so. When they do come up with an idea, they will probably feel a bit proud, a bit excited, but also still a bit uncertain and nervous. They won't be sure their idea is any good, and they'll wonder how it will be received.
So they will feel vulnerable. Treat them gently. Regardless of the quality of their idea, thank them for going to the effort of producing it and for having the courage to share it.
Make sure they feel their contribution is valued. If they have a good experience with the first idea they share, then it's far more likely they will come back with more. And the next one could be the idea that is really valuable. If they have a bad experience, then they won't want to go through the process again.
Earlier I suggested that organisations about to embark on, for example, a new advertising campaign, should request staff to submit ideas via email. That's a great way to harvest ideas for specific campaigns when timeframes are tight, but if you want to set up a pipeline to access innovative ideas from staff on a regular basis, then ...