You've Got My Attention
My travels take me to a variety organizations. Whether a government body a small business or a multinational corporation they all have one thing in common. Everyone is busy. Very busy.
Now lets relate this to you and your A3. As you enter someone's office, remember, they are busy. So the first thing your A3 needs to do is catch their attention. Why even discuss this issue? What makes it so important? What business objective is it supporting?
And that is the reason for starting your A3 with the "Background." The purpose of the background is to establish the business need met by addressing this issue. In your case, if there is a cascade of goals in your company, leverage that. For example, at the corporate level there may be an objective related to cash flow. When that cascades down to your site it may be in terms of an inventory goal. If your project has the potential to reduce inventory, then state this linkage in the background. It is that simple. If your company doesn't have a process for deploying goals, look within your department for objectives.
Another less obvious benefit is, if this linkage cannot be established then perhaps the A3 should be stopped NOW. There is no shame in the A3 process bringing consensus to the fact that a particular project should not even be pursued. Better to realize this early.