That list is going to include the decision makers, your team and anyone else in the organization who stands to benefit from or be affected by the project you are working on and the processes that it will implement or change.
As the Six Step Guide to Practical Project Management says: “It’s a chance to benefit from the collective knowledge of your organisation in the one session.”
Plan out the objectives. Brainstorming sessions can be random enough without a poorly planned meeting making it further chaotic. Know what you want and need to accomplish. If you don't go into the meeting or brainstorming session with clear objectives, how can you possibly hope that the session will be productive?
Focus on each stakeholders' area of expertise. Certainly most stakeholder input is helpful during brainstorming sessions. But when you have certain stakeholders offering information or ideas that fall far outside their individual area of expertise, your brainstorming meeting is going to suffer from time wasting discussions and potentially bad information being used to make important project decisions.
Put out an advanced agenda. Productivity starts with being well-informed and prepared to contribute. The best way that you can ensure your stakeholders are coming to your project meetings and brainstorming sessions prepared and ready to participate is to let them know what the topics are and what the expectations will be for the meeting. Knowing what the plan and objectives are help them come to the table with contributions in hand – thus eliminating a lot of chin rubbing and head scratching during the meeting as they are seeing the expectations of them for the first time. Don't let that be the case at your meeting – expect them to come prepared and make that possible by giving them information about the meeting up front.
Stick to the timeframe and schedule. Want the most productivity out of your stakeholders during project meetings and brainstorming sessions? Want to ensure that they are there in their seats for such sessions when you need them to be? One of the best ways to ensure that is to have the reputation of that project manager who only calls necessary meetings AND sticks to the proposed timeframe and schedule for the meeting. If your proposed one hour meetings always last two or three hours then those busy stakeholders who have conflicts for the second and third hours are going to skip your meeting knowing they won't get out in time. Suddenly, you've lost a lot of brainstorming power and knowledge just because you aren't an organized or reliable meeting facilitator. Your poor reputation precedes you.
Keep the discussions on topic. We've all been to those meetings that go off topic several times leaving several people in the room frustrated and often causing you to run out of time and not accomplish everything on your agenda without running over time (see above). . . which I strongly advise against doing. In order to avoid that, you will need to be a strong facilitator who keeps attendees focused on the meeting/brainstorming session agenda and objectives so you can get the information disseminated and the decisions made that need to be made.
Take good notes and follow up. Finally, you must ensure that everyone leaves with the same understanding and on the same page. How? Well, you can ask at the end if there are any questions and then follow-up with a high-level summary of what was decided and/or accomplished. Do this at an absolute minimum. However, I highly recommend a next step. Follow up the meeting by distributing your notes and ask for everyone's input or changes – if they have any – by noon the next day. Stress that it is imperative that all stakeholders be on the same page and have the same understanding and expectations. This follow-up should take care of that.
Brainstorming to come up with solutions to project issues can be extremely powerful and time-efficient ways to solve complex issues. This is especially true when you have a room full of people – key stakeholders – who have a strong vested interest in the success or failure of the project you are leading. It's a win-win. Still, the process must be handled logically and must be well planned out. Otherwise, it can just end up being a huge waste of everyone's time. The time of up to ten people doesn't come cheap and you could easily throw away a lot of money on a single meeting that accomplishes nothing.