DOI stands for Dry Operating Index. It gives an indication of the position of the centre of gravity at dry operating mass. It's really a moment (mass multiplied by the distance from a defined datum) which is usually reduced to a smaller workable number by multiplication with a constant. This makes calculations easier as indexs are just added to each other.
Normally the operator will be able to supply the figures for the dry operating mass and index. For air transport they are required to weigh their Aircraft ever four years and record these figures in a weight schedule.
Here's a loadsheet for a CRJ I found with google. If you want I could guide you through it.