Warehouses and distributions are so full that some shippers are holding product on chassis, leading to increased prices passed on to consumers and further snags in the US supply chain, especially inland rail ramp pools.

Paul Brashier, vice president of drayage and intermodal for ITS Logistics, told CNBC in an interview this week that the practice of leaving containers on chassis both prevents those chassis from being use to move new containers and leads to increased per diem charges and fees for the shipper — which are then passed on to the consumer.

The fees shippers are charged for the dwelling chassis "can lead to tens of millions of dollars in penalties," Brashier told CNBC, adding that per diem charges will likely tick up in Q2 and Q3. "These are on top of charges for warehousing, which are still at historic highs. Late fees and warehouse fees are passed onto the consumer, which is why we are not seeing products fall as much as they should."