SCDA: School Compatibility Decomposition Algorithm for Solving the Multi-School Bus Routing and Scheduling Problem

Safely serving the school transportation demand with the minimum number of buses is one of the highest financial goals of school transportation directors. To achieve that objective, a good and efficient way to solve the routing and scheduling problem is required. Due to the growth of the computing power, the spotlight has been shed on solving the combined problem of the school bus routing and scheduling problem. We show that an integrated multi-school bus routing and scheduling can be formulated with the help of trip compatibility. A novel decomposition algorithm is proposed to solve the integrated model. The merit of this integrated model and the decomposition method is that with the consideration of the trip compatibility, the interrelationship between the routing and scheduling sub-problems will not be lost in the process of decomposition. Results show the proposed decomposed problem could provide the solutions using the same number of buses as the integrated model in much shorter time (as little as 0.6%) and that the proposed method can save up to 26% number of buses from existing research.

School bus routing by maximizing trip compatibility

School bus planning is usually divided into routing and scheduling due to the complexity of solving them concurrently. However, the separation between these two steps may lead to worse solutions with higher overall costs than that from solving them together. When finding the minimal number of trips in the routing problem, neglecting the importance of trip compatibility may increase the number of buses actually needed in the scheduling problem. This paper proposes a new formulation for the multi-school homogeneous fleet routing problem that maximizes trip compatibility while minimizing total travel time. This incorporates the trip compatibility for the scheduling problem in the routing problem. Since the problem is inherently just a routing problem, finding a good solution is not cumbersome. To compare the performance of the model with traditional routing problems, we generate eight mid-size data sets. Through importing the generated trips of the routing problems into the bus scheduling (blocking) problem, it is shown that the proposed model uses up to 13% fewer buses than the common traditional routing models.

Understanding and Visualizing the District of Columbia Capital Bikeshare System Using Data Analysis for Balancing Purposes

Bike sharing systems' popularity has consistently been rising during the past years. Managing and maintaining these emerging systems are indispensable parts of these systems. Visualizing the current operations can assist in getting a better grasp on the performance of the system. In this paper, a data mining approach is used to identify and visualize some important factors related to bike-share operations and management. To consolidate the data, we cluster stations that have a similar pickup and drop-off profiles during weekdays and weekends. We provide the temporal profile of the center of each cluster which can be used as a simple and practical approach for approximating the number of pickups and drop-offs of the stations. We also define two indices based on stations' shortages and surpluses that reflect the degree of balancing aid a station needs. These indices can help stakeholders improve the quality of the bike-share user experience in at-least two ways. It can act as a complement to balancing optimization efforts, and it can identify stations that need expansion. We mine the District of Columbia's regional bike-share data and discuss the findings of this data set. We examine the bike-share system during different quarters of the year and during both peak and non-peak hours. Findings reflect that on weekdays most of the pickups and drop-offs happen during the morning and evening peaks whereas on weekends pickups and drop-offs are spread out throughout the day. We also show that throughout the day, more than 40% of the stations are relatively self-balanced. Not worrying about these stations during ordinary days can allow the balancing efforts to focus on a fewer stations and therefore potentially improve the efficiency of the balancing optimization models.