We consider a flow shop type manufacturing cell consisting of m machines and a material handling robot producing multiple parts. The robot transfers the parts between the machines and loads/unloads the machines. We consider the cyclic scheduling of the parts and the robot moves with the objective of maximizing the throughput rate. We develop a mixed integer linear programming formulation of the problem. The formulation is improved with several valid inequalities and reformulations of the constraints. We also develop a hybrid metaheuristic algorithm for this strongly NP-Hard problem. The algorithm is modified to handle both 1-unit and multi-unit robot cycles. Multi-threading is used to parallelize the algorithm in order to improve its efficiency. After calibrating the parameters of the heuristic algorithm, an extensive computational study is performed to evaluate its performance. The results of this study revealed that the developed heuristic provides near-optimal solutions in reasonable solution times. The effects of parallelization and the benefits of considering multi-unit cycles instead of 1-unit cycles are also quantified. Our computational tests show that multi-unit cycles improve the throughput rate by 9% on the average. The improvement can reach to 20% depending on the problem parameters. (C) 2017 Elsevier Ltd. All rights reserved.