I am working on a Django app, and I would like my Database migrations to be run when deploying on Heroku.
So far we have simply put the following command in the Proc
You can create a file bin/post_compile which will run bash commands after the build.
Note that it is still considered experimental.
Read here for more buildpack info.
See here for an example
Alternatively, Heroku is working on a new Releases feature, which aims to simplify and solve this process. (Currently in Beta).
Good luck!