Before revision:  The input is {\em   a set of items I = \{ 1 ,  , N \} with corresponding sizess_1, ...,s_N \in (0 , 1 , partitioned into n groupsG_1, ...,G_n. The goal is to pack the items in a minimum number of unit size bins, such that no two items of the same group are packed in the same bin.
After revision:  The input is {\em a set of items I = \{ 1 ,  , N \} with corresponding sizess_1, ...,s_N \in (0 , 1 , partitioned into n groupsG_1, ...,G_n. The goal is to pack the items in a minimum number of identical (unit-size) bins, such that no two items of the same group are packed in the same bin.