This sounds like one of those just-in-time delivery systems that were all the rage in manufacturing back in the 90s, but applied to retailing. They always were

This sounds like one of those just-in-time delivery systems that were all the rage in manufacturing back in the 90s, but applied to retailing. They always were brittle; there's little or no slack in the system, so if something unusual happens, the process breaks. If the system is new, and it seems to be, it probably needs some fine-tuning. Any workable system needs a little bit of slack in it to account for the variable and the unexpected. The question is how much. And it's not free.