Robot makers are getting close to solving part of that puzzle.

Siemens AG and Honeywell International Inc. have built machines that pull packages from the back of a tractor-trailer and place them on conveyor belts, whizzing the parcels off for sorting. Making robots that can load trucks is more complicated, although clearing that hurdle isn't far off.

"The biggest challenge in our world is: Every single package is different in size, shape, weight, color, material," said Ted Dengel, managing director of operations technology at FedEx's ground-delivery unit. "It makes it a very tricky problem."

The devices, unveiled at a recent automation conference in Chicago, hold out the promise of increasing productivity while reducing the need for one of the most grueling jobs in logistics. Couriers are relying on automation to grapple with the rise of online shopping, which is fueling record demand but pressuring profit margins. Amazon's plan to handle more of its own shipping and offer more one-day deliveries is only upping the ante.