Appointment arrangement algorithm... Please?

I've posted this same question in at least a dozen forums. To date there have been no one has attempted to solve it... except me with complete and total failure. :( I don't think it's really that hard, I just don't know how to do it.

I want to arrange appointment items in a fashion similar to Microsoft Outlook or MS Schedule +. It is highly probably that there will be several overlapping appointments on any given day.

The algorithm I am looking for is to arrange the appointments as efficiently as possible using as few "columns" in a particular day as possible.

For example, if there are 10 appointments in one day, I don't want to have 10 skinny columns in the day. The appointments should be sorted so that they line up in as few columns as possible.

I'm lost and would like some help with this. If you have even an inkling of how to do it, it is more than I have.

Thanks.