In a Project num of data connections are limited.So After moving the workbooks to production,Go to Admin Tab->choose data connections and u are able to see the list of connections and below search option .Enter the each server name and its details and choose search,u are able to see all the workbooks used this connection.Select all workbooks and by using the edit option u can able to replace the dev server details with production server details.
Search by Connection Attributes Server Port
If you have 10 data connections in your project.you have to do this only 10 times.Its not at all laborious work.
I hope it will helpful to you
Here is a tool that could speed up the time associated with this process: Power Tools For Tableau. (Enterprise Deployment Tool). You can fill out a form on the website if you would like to get more information on this tool.