Abstract: Highlights•A special case of SDLBP-1 used in many studies is proved polynomial solvable.•Two lower bounding schems and a strenghtened integer programing model are presented.•A branch, bound, and remember algorithm is proposed to solve general SDLBP-1 instances.•The proposed BB&R algorithm is a state-of-the-art exact algorithm for the SDLBP-1.•The BB&R algorithm can be easily truncated into an efficient heuristic.
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