Column generation-based stochastic school bell time and bus scheduling optimization

Given a trip plan (a sequence of bus stops), the integrated school bell time and bus scheduling problem simultaneously optimizes the school bell time and bus routes (the assignment of buses to serve trips at a specific time) while maintaining the minimum level-of-service requirements. The objective is to minimize the total number of buses and the total vehicle time. The previous efforts focused on the deterministic problem. However, uncertainty...