This paper addresses the robotic scheduling problem in blocking hybrid flow shop cells that consider multiple part-types, different speed parallel machines at each stage, machine eligibility constraints and a single transportation robot to move the parts between stages. Initially, a mixed integer linear programming (MILP) model is proposed to minimise the makespan. Due to the complexity of the model, a simulated annealing (SA)-based solution approach is developed to solve the problem. This approach uses both simple insertion method and a new neighbourhood structure based on block properties while generating neighbour solutions, which yields two different SA algorithms respectively. The performance of proposed SA approach is assessed over a set of randomly generated instances. The computational results demonstrate that the SA algorithm is effective with the employed neighbourhood structure for this problem.