The Service Desk Team is working thousands of tickets related to hardware accessories. These are a lot of small tasks and inefficient manual deliveries. We are looking for a Self Service Portal for ordering and direct delivery, without going through IT. Has anyone implemented this kind of Self Service? What about Amazon's capabilities - as they are good at shipping items globally? How do we control this?

An alternative would be to outsource this and let a vendor handle all of it from ordering to distribution against a pre agreed catalog. So similar to the Amazon idea but using a vendor that specializes in enterprise IT equipment.

We use self-service ordering in ServiceNow and delivery is pick-up by the staff at the corporate post office. It is an interesting idea to use Amazon for a distributed enterprise. In the past I have used central shipping negotiated with an enterprise service provider. This had several economic benefits but it was before the capabilities to set up custom stores easily in the web2.0 marketplace. Following with interest.

This is classic use case in many organization. there are few ways to address it, If there is ITSM tool then build workflow for self service portal and list all the items which employee can purchase it directly, since its corporate purchase the asset has to go with proper PO.
the other option if ITSM not available is build portal in SharePoint Online or any Cloud based service tool, list all the products and have approval flow,send direct purchase to the supplier.