Set a call forwarding number based on a defined schedule

We have a rotating on-call schedule. When an on-call person takes over, they forward the on-call phone number to their own cell-phone. This is a process which must be done manually each week, as the on-call changes over from one person to the next. I've checked the most obvious potential app (IF by IFTTT) but it doesn't seem to support setting call forwarding. Is there a way to set a call forwarding number based on a defined schedule?