You can define Order entry dead line site wise. here you can specify the time before which a company has to receive the sales order for that day.
For example you have order entry dead line for Monday as 2.30 PM the sales orders that are received before that time on the particular day will be treated as if they are received on that day and after that time will be treated as if they are received on the next business day.
You can attach these deadlines to the groups and groups can be attached to the customer - which you were mentioning.
You need to actually look into Inventory Management → Setup → Distribution → Order Entry Dead lines and groups.
If you have some specific reasons for the delivery - you can make use of this field - which will be printed on your packing slip based on the selection of shipment details in AR-> setup → form setup → Packing slip.
Thanks for the explantion with good example.