This article investigates a new collision-free routing problem of a multirobot system. The objective is to minimize the cycle time of operation tasks for each robot while avoiding collisions. The focus is set on the operation of the end-effector and its connected joint, and the operation is projected onto a circular area on the plane. We propose to employ a time-space network (TSN) model that maps the robot location constraints into the route planning framework, leading to a mixed integer programming (MIP) problem. A dedicated genetic algorithm is proposed for solving this MIP problem and a new encoding scheme is designed to fit the TSN formulation. Simulation experiments indicate that the proposed model can obtain the collision-free route of the considered multirobot system. Simulation results also show that the proposed genetic algorithm can provide fast and high-quality solutions, compared to two state-of-the-art commercial solvers and a practical approach.