Logistics are a great place for this technology, but first you must purge your mind of Cryptotokens and their economics. They aren't applicable for a logistics use case.
To understand this, first you have to understand why we structure mining. In the case of Bitcoin or Ethereum, you need a method that allows any arbitrary computational device to verify and add to a given blockchain. In lieu of trusting that device, the blockchain makes it do a massive amount of busywork, called mining, to prove it isn't bullshitting the network. Different implementations have different busywork, but it's designed to make it hard to change the network by arbitrary devices. This is why we can allow any untrusted device on the network.
In the case of logistics, we are already operating under some amount of trust. This is through a mechanism of certification of goods, suppliers, verifying the goods are what they say they are, and the verification of those approvals and certifications. Even in a trusted environment, managing that coordination of certifying and verifying is slow, bureaucratic, and grows with the size of the logistic network. Additionally, many supply chains generally certify new entrants before allowing them to contribute. This creates a barrier to entry when establishing trust in the same way busywork creates a barrier for devices. Then there are whole units of auditors that go through and recheck all those certifications to make sure the whole chain is authentic with regards to the goods moving through it.
Blockchain technology is a mechanism of creating certifications (signing a transaction) and verifying those certifications (miners/verifiers on a chain) that can operate in a decentralized but coordinated way. It allows for the whole system to better coordinate information and certification that used to be done manually.
Did you notice I never mentioned tokens?