In recent years lots of papers were published about ant algorithm-, and swarm intelligence applications on logisitcs. But are there any further findings for logistics provided by biomimetics?
Perhaps you might also consider artificial neural networks and evolutionary algorithms to be "biomimetic". I can't give any specific examples of use in logistics (although I vaguely recall seeing a few), but they definitely have uses anywhere that involves optimisation, such as in logistics.
Although I don't think I've seen any published research in the field of logistics, there are a few more biologically inspired optimisation methods that could potentially be useful in the field: the cuckoo search, the artificial bee colony optimisation (I'm not sure how it differs from ant colony optimisation), and something called biogeography-based optimisation.
I found a nice introductory book that shows a few more example (linked below), and there's also an international congress every year called "World Congress on Nature and Biologically Inspired Computing", which I'm sure has some more interesting examples for you.