Dear Prabhu,
You try below possibilites which may help you in resolving this issue.
1. Set a Billing block in the Sales Order, Once upon Delivery of the material to customer (based on the notification recieved by the vendor) Unblock the billing document from SO and Create Billing document.
Please note that in the item category setting should be order related billing.
2. You can shipping notification function configured for Vendor Delivery the material to customer based on that you can bill the customer.
3. You can look for some enchancement if this needs to be done automatically (Workflow configuration).
Regards
Muralidhar Shetty