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APMT said the Charleston business was seen as a non-core asset.
Such an alliance could have a "competitive edge," according to industry consultant Drewry.
Box volumes at the southeast port grew more than 25% last month.
Trade Promotion Authority, a bill that grants the president authority to conclude trade deals without congressional interference, moved forward in the Senate Thursday morning.
Together with Dynamex, the two units will offer final mile delivery in more than 70 markets.
Energy and Water Development Appropriations Bill substantially increases funding to the Army Corps of Engineers for waterway and port infrastructure projects during fiscal year 2016.