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Assembly line balancing with station paralleling

We consider the NP-hard problem of assembly line balancing with station paralleling. We assume an arbitrary number of parallel workstations can be assigned to each stage. Every task requires a specified tooling/equipment, and this tooling/equipment should be available in all parallel workstations of the stage to which the task is assigned. Our objective is to find an assignment of tasks to stages so as to minimize sum of station opening and tooling/equipment costs. We propose two branch and bound algorithms: one for optimal solutions and one for near optimal solutions. We find that optimal solutions can be found quickly for medium sized problem instances; for larger sized problems we find high quality solutions in reasonable solution times.