High-performance composites are widely used in industry because of specific mechanical properties and lightweighting opportunities. Current automation solutions to manufacturing components from prepreg (pre-impregnated precursor material) sheets are limited. Our previous work has demonstrated the technical feasibility of a robotic cell to automate the sheet layup process. Many decisions are required for the cell to function correctly, and the time necessary to make these decisions must be reduced to utilize the cell effectively. Robot placement with respect to the mold is a significant and complex decision problem. Ensuring that robots can collaborate effectively requires addressing multiple constraints related to the robot workspace, singularity, and velocities. Solving this problem requires developing computationally efficient algorithms to find feasible robot placements in the cell. We describe an approach based on successive solution refinement strategy to identify a cell design that satisfies all constraints related to robot placement.