The path planning problem of logistics robots is mainly subjected to the time cost of the operation of the mathematical model. To save the time of refilling process in the fast medicine dispensing system (FMDS), the optimization procedure is divided into two steps in this study. First, a new mathematical model called the multiple steps traveling salesman problem model (MTSPM) is proposed to optimize the replenishment quantity of each picking and establish picking sets. Second, an improved ant colony optimization (IACO) algorithm is employed, considering the effects of velocity, acceleration, and deceleration in the refilling route during the development of the new model. Simulation results and operational results demonstrated that MTSPM-IACO was better than both the order picking model (OPM) and MTSPM-ACO in terms of saving refilling time. Compared to the OPM, the optimization of the refilling time of MTSPM-IACO was more than 1.73% in simulation and 15.26% in operation. Compared to MTSPM-ACO, the optimization of the refilling time of MTSPM-IACO was more than 0.13% in simulation and 1.67% in operation.

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