How suggest ship date in constraint plan can publish to OM

We are running ATP constraint plan every day. The demand and supply picture changed every day so the constraint plan is changing Sugg ship date based on the current demand and supply. I want to publish Sugg due date to SSD at the order line.

The reason is, Currently we are using unscheduled and scheduled in order management to reflect the new SSD based on the supply-demand calculated by ATP. However, it has a problem, when we are unscheduling sales orders then other lower priority demand is taking away the onhand and firm supply that pushed SSD of higher priority sales order to later at the time of scheduling again.