Hi Nathan,
One way that comes to mind is to give each of your items a reference point in a reference scheme.
You could use either a cartesian framework or a polar framework.
So, for example if you had X,Y and Z axes, then you could state facts such as :
Podium is at Room_X(23)
Podium is at Room_Y(15)
Podium is at Room_ Z(23)
You could set the constraints so that the X.Y & Z coordinates of an object were required to be together.
The reference point for each object (e.g. the Podium) would be the point from which its own dimensions were measured.
This approach allows you to give dimensions to each object and values to the size of the room.
The two sets of data could then be used to see if it is permissible to put an object at a particular point.
Hope this helps
Ken