Ask HN: How do you rank documents according to multiple criterias?

I work for a furnitures marketplace, and we are starting to rework our catalog system to make better use of our limited web real-estate.

I'm currently gathering insights from a bunch of companies to see how they tackle the ranking problem and would love to get feedbacks from you as well.

To be more precise, I'd mostly focus on pure ranking and not dwelve into personnalized recommendations or textual search results. An example would be ranking products according to their seller's ratings, probability of being in stock, shipping price, and number of user interactions.

Here are a few starter questions:

1/ Do you pre-score your documents with a batch / stream system and rank only on this score?

2/ Do you run multi-criterias queries on the database? Is the resulting ranking sequential or averaged?

3/ How do you collaborate with your data / marketing team on the ranking algorithm?

Thanks!