Automated guided vehicles (AGVs) have been regarded as a promising means for the future delivery industry by many logistic companies. Several AGV-based delivery systems have been proposed, but they generally have drawbacks in delivering and locating baggage by magnet line, such as the high maintenance cost, and it is hard to change the trajectory of AGV. This article considers using multi-AGVs as delivery robots to coordinate and sort baggage in the large international airport. This system has the merit of enlarging the accuracy of baggage sorting and delivering. Due to the inaccurate transportation efficiency, a time-dependent stochastic baggage delivery system is proposed and a stochastic model is constructed to characterize the running priority and optimal path planning for multi-AGVs according to the flight information. In the proposed system, ultra-wideband technology is applied to realize precisely positioning and navigation for multi-AGVs in the baggage distribution center. Furthermore, the optimal path planning algorithm based on time-window rules and rapidly exploring random tree algorithm is considered to avoid collision and maneuverability constraints and to determine whether the running path for each AGV is feasible and optimal. Computer simulations are conducted to demonstrate the performance of the proposed method.