Provenance (tracking of goods) and Regulatory compliance seem to be the most important use cases related to supply chain, and these can be broken down into several sub-segments.
By documenting the provenance of goods as they move thru the supply chain, the breadth of recalls can be reduced and problems within the supply chain can be more readily isolated, diagnosed, and resolved. Regulatory compliance can be verified as goods move thru the supply chain as well (inspections, quality controls, etc). Tracking of goods can assist with inventory management and inventory tracking, especially when components are manufactured in several different countries and assembled in another.
As for change in practices, blockchain will demand more digitalization of the applications/processes at the various steps within the supply chain. For example, there are often delays at import terminals/ports due to missing paperwork (bills of lading, etc.) By going digital, this information can be transferred in real time so that terminals can plan and execute more efficiently without compromising privacy. But this, as do other scenarios, will require shippers, receivers, etc. to digitalize their information, and/or export their information into the blockchain system via an API.