A Dynamic Distribution Model of Urban Mobile Stations Considering Passengers' Arrival Punctuality

The existing distribution model for urban mobile stations (UMS) has not considered the uncertainty in the arrival times of passengers to the service stations, resulting in discrepancy between the optimization outcomes and practical scenarios. This discrepancy can cause the inability to provide services for early-arrival and delayed passengers. To address the detrimental impact of the time uncertainty on optimization solutions, A dynamic facility-distribution model based on the probability function of passengers' arrival punctuality is proposed. In response to the layout optimization problem of UMS, a comprehensive mathematical model and evaluation indexes for the optimization of dynamic facility distribution are proposed. A punctuality probability function with a normal distribution form is introduced to estimate the difference between passengers' actual and declared arrival times. Based on the location distribution of passengers during different service periods, the ripple-spreading algorithm and genetic algorithm are adopted to optimize the positions of service stations and to compute the optimal paths between passengers and stations. Finally, based on empirical data on the road network and passengers' distribution in Tianjin, simulation experiments are conducted to compare the dynamic facility distribution models considering passengers' punctual arrival and passengers' arrival with probabilities. The results indicate that the optimization model considering the probability of passengers' arrival time outperform those of the model considering the passengers' punctual arrival, with a 4.31% enhancement in the evaluation indexes of the dynamic facility distribution model. Specifically, the average path length of passengers to arrival stations decreases by 0.35%, the total excess distance beyond acceptable distances for passengers decreases by 6.26%, and the total excess capacity beyond stations' service capacity decreases by 4.13%. Therefore, the proposed model effectively considers the uncertainty in arrival times and optimizes facility layout based on passengers' actual arrival times more efficiently. In practice, the proposed model has the feature of high portability and can be applied to many other dynamic problems, such as dynamic location choice of logistics services.