Abstract
Accidents, bad weathers, traffic congestions, etc. led to the uncertainties of travel times in real-life road networks, which greatly affected the quality of individual’s life and the reliability of transportation system. This paper addressed the school bus routing problem in such a stochastic and time-dependent road environment. Firstly, the problem was set based on a single-school configuration, and the students were picked up at their homes, which was in line with the current situation of school bus systems in China. Thus, it could be regarded as an independent problem of school bus route generation in random dynamic networks, which could be solved as a variant of extended Vehicle Routing Problem. However, due to the fluctuation and uncertainty of link travel times, the arrival time at each stop including the destination was varying. Therefore, the selection of optimal path connecting the current service node with the next one was treated as a sub-problem in this study, where the reliability of travel times in the stochastic and time-varying network was highly concerned by such time-rigid commuters. To this end, a Robust Optimal Schedule Times model with a hard time windows constraint was built to generate a most cost-reliable route for school buses. By the use of Robust Optimization method, it was intended to minimize the worst-case total cost which combined the cost of earlier schedule delays with the disutility of travel times. It was also proved that the proposed model could be converted into solving a conventional problem in deterministic dynamic networks for a reduction of computation complexity, which provided the potential of applying to the practical problems. Finally, the validity of the proposed model and its performance evaluation was analyzed through a small-scale computational instance, where all the link travel times in the simulated network were attributed to both time-varying and stochastic. Then, a mathematical programming solver was used to find the exact optimal solution. The results indicated that the model was valid, and the necessity of considering the stochastic and time-dependent nature of transportation networks was also confirmed in the case study.
Highlights
For the sake of convenience and safety, the school bus system is usually adopted to deliver students from certain stops to their respective schools in the morning, and return them back after school
Since the reliability of travel times was highly concerned by such time-rigid commuters, a hard time window constraint was employed in the model, and the cost of earlier schedule delays combined with the disutility of travel times were proposed as the evaluation index
In order to School bus routing problem and stochastic and time-dependent transportation network generate a most cost-reliable route for school buses, a Min-Max approach derived from Robust Optimization (RO) was applied to STD instances, and the ROST model was formulated which minimized the upper bound of the total cost of all the feasible solutions
Summary
For the sake of convenience and safety, the school bus system is usually adopted to deliver students from certain stops to their respective schools in the morning, and return them back after school. SBRP can be regarded as a combinatorial optimization problem which have specific assumptions and constraints [1] It consists of several sub-problems which can be summarized as “bus stop selection problem”, “route generation problem”, “school bell time adjustment problem” and “route scheduling problem” [2]. The variability in travel times was attributed to both dynamic and uncertainty in the real world, and modelling the SBRP in a stochastic and dynamic network was in line with the reality [12] In this context, the optimal path problem in STD networks which sought the efficient path connecting the current service node (including the bus depot) to the one was regarded as a sub-problem of bus route generation.
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