This paper studies a robotic cell in which multiple single-armed robot manipulators are equipped for transporting parts between the machines. Compared with most previous studies, processing time window is considered in this paper, i.e. identical parts are processed successively on multiple machines with upper and lower bounds on processing times. The problem discussed in this paper aims at finding optimal cyclic solution for the robot, that is, a sequence of robot moves that can be repeated endlessly and that can achieve the goal of minimum cycle time. Based on the description and analysis, the problem is formulated as a mixed-integer programming model with the objective of minimizing the cycle time. The commercial software CPLEX is used to solve the proposed model. This paper also presents a relaxed mathematical model to compute the lower bound of cycle time. In order to be more efficient, a model-based heuristic algorithm is constructed. Computational experiments on benchmark and randomly generated instances validate the feasibility and efficiency of the proposed heuristic algorithm.