The only formations with the structures and the lift capacity are the two Log Bdes. However, it would take weeks to deploy them and all their equipment (assuming that it isn't deployed in Iraqistan), by which time it would be too late. Additionally, if this relief op is enforced as opposed to being requested by the host nation then it would need considerable FP elements to protect the loggies. With our final 'spare' BG about to deploy to Kosovo, it would appear that the cupboard is somewhat bare.
Still, I suppose that they could always mobilise the TA (he said with his tongue very firmly in his cheek)!