They way I have seen this issue managed created questions about efficiency, but worked well. It actually required a procedural or process change. A rule was applied to shipments that required them to be ready to ship within 24 hours of opening of the pick up window OR shipped by requested ship date. It was a little more expensive, but since the majority of orders required no special handling it was deemed worth the cost.
Hope this helps!
Would it be possible to create a location such as "Ready to Ship", then measure your performance against that location. Depending on your systems, you may have to pull data from your inventory movements into the "Ready to Ship" location as well as shipping history to get your actual service levels, but I would not expect that to be a difficult problem to solve. Good luck!
As per my understanding goes service level for you can be looked at from 2 ways :
1.Fill Rate-Inventory available against the order
2.Shipment Efficiency-Order dispatched to customer
Also,your Inventory Management system,I suppose must be having location (docking / shipping) with inventory againt each order.
You IT team can create 2 reports:1.Customer Orders VS Shipped Order, 2. Customer Order VS (Order lying at the docking area + Shipped Order)