Currently gas powered drones have a capacity of carrying 5 ton load which cover most dry containers and have the ability to operate for 50 minutes. There could be multiple drones that are flying different routes concurrently to service ships that are not docked on the pier.
Docking could be expanded to other area of the pier from just where the cranes could reach.
Jeff Bezos of Amazon is focusing their efforts on commercial door to door delivery of products to end consumers from the distribution center. The focus of this problem is the leg of transport of containers to the distribution centers. The earlier leg of transport could be achieved by flying containers directly from the ship to the delivery 18 wheeler truck. Alternately, from the 18 wheeler truck unloaded and shipped via drone to the consumers home or business.
https://www.quora.com/How-long-does-it-take-to-unload-a-cargo-ship-at-Los-Angeles
http://www.vantagefreight.com.au/wp-content/uploads/2013/01/Container-Dimensions.pdf