In this study, we consider the mass production of identical parts consisting of a specific number of operations in a robotic manufacturing cell. The throughput of the cell depends on the robot move sequence, which in turn depends on the assignment of these operations to the machines. Despite this relation, the robot move sequencing and line balancing problems discussed in the literature are not integrated, but they are instead solved sequentially. This study is one of the very first to attempt this integration. We formulated the problem as a mixed-integer linear programming formulation. However, in order to be able to solve real-sized problem instances of this NP-hard problem, a parametric heuristic algorithm is developed. The performance of the developed solution methods is tested with an extensive computational study. The results indicate that the heuristic algorithm performs efficiently.