How are logistics and logic related?

Logistics follows the same pattern of other plural nouns—such as ballistics, linguistics, statistics, or physics—that represent fields of study and take either a singular or plural verb.

Logic, used strictly in the singular, is a science that deals with the formal principles of reason. If a visitor walks in the house with a wet umbrella, it is logical for one to assume that it is raining outside. Logistics, which involves such concerns as the delivery of personnel or supplies in an efficient manner, can often employ logic, such as by reasoning out the path least likely to interrupt the flow of a delivery:

As with many other areas of the economy, the digital revolution is having a profound effect on delivery logistics. The combination of mobile computing, analytics, and cloud services, all of which are fueled by the Internet of Things (IoT), is changing how delivery and fulfillment companies are conducting their operations.
—Andrew Meola, Business Insider, 14 Oct. 2016

Both logic and logistics ultimately derive from the Greek logos, meaning "reason." But while logic derives directly from Greek, logistics took a longer route, first passing into French as logistique, meaning "art of calculating," and then into English from there.