The sailing is the first of several from China chartered by Germany-based shipowner and operator Schulte & Bruns Group to ferry new boxes for Schneider and cargo for the U.S. carrier’s customers. It comes as big shippers including

Walmart Inc.

and

Home Depot Inc.

are taking steps to organize their own oceangoing capacity to keep goods moving through strained distribution networks.

“We’re hearing from many of our customers that they’re significantly behind in their shipping. They’re looking for any solution,” said Jim Filter, Schneider’s chief commercial officer and senior vice president of the Green Bay, Wis., company’s intermodal business.

The dedicated voyages on general cargo ships, which can carry both bulk-loaded cargo and a limited numbers of containers, provide an alternative for hard-pressed shippers, which are paying to move the freight to help offset the vessel charter costs. Schneider also is counting on the charters to deliver at least 2,500 new containers by the end of the year to meet surging domestic demand for its intermodal service, which moves cargo by road and rail.

Schneider planned to move the 53-foot-long boxes set to arrive Thursday, which are loaded with items from electronics to clothing and merchandise for dollar-store discounters, by train from the Pacific Northwest, with many bound for the East Coast, Mr. Filter said.

General cargo vessels can carry only a fraction of the boxes big container ships haul on trans-Pacific routes. The largest boxships operating trans-Pacific services can accommodate the equivalent of 10,000 to 15,000 twenty-foot containers. Some equipment-leasing companies have hired multipurpose vessels to reposition containers, said John Fossey, the head of container equipment and leasing research for London-based Drewry Shipping Consultants Ltd.

Supply-chain disruptions around the world this year, including severe port congestion and delivery delays, have left empty containers more difficult to find because many have been tied up on the water or at jammed docks and cargo-handling facilities.

“We’ve never put our containers on a vessel this small before,” Mr. Filter said. The company began hunting for alternatives to deliver the new boxes in late spring, he said, when it became clear “we would have very few slots on our traditional vessels.”

Schneider didn’t disclose the cost of using dedicated vessels but weighed the option against the costs of both long delivery delays and skyrocketing container shipping prices this year.

Spot container shipping rates from Asia to the U.S. West Coast were 462% higher this week than the same time last year, according to Freightos Baltic Index. It can cost as much as $80,000 or $90,000 a day to charter a large container ship, and prices are up three or four times over the middle of last year, Mr. Fossey said, as companies have scooped up capacity to meet strong shipping demand.

“Every container ship that floats is basically in operation already today,”

Soren Skou,

chief executive of A.P. Moller-Maersk A/S, the world’s largest container shipping line by capacity, said earlier this month, adding, “there are no ships to lease anymore.”

Discount retailer

Dollar Tree Inc.

said Thursday it was turning to charter operations to keep its goods moving. The company said it would use a large vessel contracted for three years that is scheduled to make its first voyage within weeks.

The frenzied global shipping market also is making it harder for U.S.-based transport providers to get new equipment. Most shipping containers are made in China, and container lines give priority to loaded boxes over empty ones.

Intermodal containers such as Schneider’s boxes, which are used to move goods long distances by road and rail in the U.S. and Canada, pose additional problems. The 53-foot-long containers take up more space than the 40-foot and 20-foot boxes that dominate container shipping, and can’t be stacked as high, making them a headache for shipping lines trying to maximize available space.

Vessel owners favor loaded containers over empty boxes on Asia-to-U.S. lanes because they can command higher rates, so some intermodal operators and equipment-leasing companies anxious to get boxes into their domestic networks are arranging to fill them with U.S. bound imports.

“The system is so strained right now that anything that’s viewed as extraneous,” such as intermodal boxes, isn’t a priority, said Ted Prince, co-founder and chief strategy officer of transportation company Tiger Cool Express LLC. “The lines aren’t interested, the marine terminals overseas aren’t interested, and time is of the essence,” he said.

—Dave Sebastian contributed to this article

Write to Jennifer Smith at jennifer.smith@wsj.com