Inter-School Bus Scheduling Under Stochastic Travel Times

Stochastic disturbances occurring in real world operations could have a significant influence on the planned routing and scheduling results for inter-school buses. An optimal schedule might therefore lose its optimality when applied in actual operations where stochastic disturbances occur. In this study we employ network flow techniques to construct an inter-school bus routing and scheduling model, considering the characteristics of inter-school buses for class attendance, under stochastic travel times. The model is formulated as a special multiple commodity network flow problem which is characterized as NP-hard. To efficiently solve realistically large problems a problem decomposition and variable fixing method, coupled with the use of CPLEX mathematical programming solver, is employed to develop a solution algorithm. Finally, computational tests are performed using data from an allied university system in Taiwan. The test results show that the model and the solution algorithm are good and therefore could be useful for actual operations.