Running out of stock fast.

I just launched a product a week ago. I did a smaller batch of 1000 units and I have sold over a third in a week; this is great. I’ve already started on my next batch and my lead time is 3 weeks + Amazon’s time to distribute through to the FCs.

I have heard that it is better to close your listing than to run out of stock to slow the decline in rank.

I’m ranking at around 5K in the top level category and 10 in the subcategory right now.

Considering these factors, what is my best option? Do I raise prices to not run out? Do I close it before I run out? Do I close after I run out? Obviously I stop PPC.

Advise from people who’ve navigated this would be appreciated. Thanks!