Hub transportation problem with chance constrained due dates

Traditional public transportation systems provide efficient mass transportation solutions between designated stations. Despite its advantages, public transportation systems suffer from being restricted to serve a fixed area. This reduces its accessibility considerably, particularly in remote areas. Hub transportation systems overcome this problem by offering shuttle services to serve passengers who face such restrictions. These systems are highly time sensitive, as shuttles are required to return to their station by a due time to ensure that all passengers are served on time. From a decision making perspective, it is essential that the routing decisions made for shuttles are reliable against changes in travel times. To achieve this, we propose a chance constrained programming approach within a column generation framework that guarantees that the final solution remains feasible (with respect to meeting the due time) for at least a given probability of travel time scenarios. We introduce a sampling-based approach to reduce the size of the problem, and introduce procedures that maintain chance constraint feasibility under this framework. Computational experiments reveal that our approach yields routing decisions that remain immune against travel time uncertainty.