Packing objects into bins to minimize the number of bins

Question

There is a list of objects. Each object cannot be in a bin with some other objects. How can I find the minimum number of bins required to hold all the objects (and the objects in them)?

My current algorithm:

For each object in the list, see if any of the currently existing bins will hold it. If yes, stick it in the first bin we come to that will hold it. If we exhaust the list of bins without finding a bin, create a new bin and stick the object into it.

Will this algorithm find the minimum number of bins? If not, what algorithm will (NP-hard algorithms OK: I have only about 12 objects)?

Feel free to add any tags you think appropriate - I'm not sure which one is