I'm going to guess Heroku. They pioneered PaaSes, which are intended to solve this problem. Spoiler: they solve this problem. There's also my fave, Cloud Found

I'm going to guess Heroku. They pioneered PaaSes, which are intended to solve this problem. Spoiler: they solve this problem. There's also my fave, Cloud Foundry -- try Pivotal Web Services or BlueMix. These PaaSes have a buildpack model and basically, it Just Works. Or OpenShift, though maybe its shift to a pure docker-y model will put you back where you started. Disclaimer: I work for Pivotal Labs, part of the company which donates the most engineering to Cloud Foundry.