As customer service/ team leader of 3PL warehousing how will you be successful in solving conflict with your supplier with regards to their supply?

By identifying and thorough examination of the reason for conflict, this issue can be resolved.

Need to identify the type of issues first.
Secondly need to study their trend of supply.
Plan your dedadlines keeping in mind the possibilities of issues in the supply.
Help the supplier in case you have a long term relationship or if they are monopoly suppliers.
In case you have other options, then start looking for other competitive suppliers and let the news reach the current supplier that you are hunting.
Hope this will help.
Last but not the least have close communication with them at regular basis and try to understand their side of the problem and ask them to be transparent as well as you be eager to support them.
this will build long term relationship.