A single robot of a two-lane bin packing system has an end of arm tool (EOAT) that interfaces with two infeed lines and two bins on an ongoing basis so that the robot can pick a group of bags from a first bag group staging area on the first infeed line while a group of bags is being formed in a second bag group staging area by the second infeed line. In addition, by interfacing with two separate bins, one bin can be filled while another, full bin is being replaced with an empty bin. The EOAT thus operates constantly. The bag groups can be formed in layers by discharging bags on a reciprocating shuttle of a pick table assembly.