A robust bus evacuation model with delayed scenario information

Due to natural or man-made disasters, the evacuation of a whole region or city may become necessary. Apart from private traffic, the emergency services also need to consider transit-dependent evacuees which have to be transported from collection points to secure shelters outside the endangered region with the help of a bus fleet. We consider a simplified version of the arising bus evacuation problem (BEP), which is a vehicle scheduling problem that aims at minimizing the network clearance time, i.e., the time needed until the last person is brought to safety. In this paper, we consider an adjustable robust formulation without recourse for the BEP, the robust bus evacuation problem (RBEP), in which the exact numbers of evacuees are not known in advance. Instead, a set of likely scenarios is known. After some reckoning time, this uncertainty is eliminated and planners are given exact figures. The problem is to decide for each bus, if it is better to send it right away—using uncertain information on the evacuees—or to wait until the the scenario becomes known. We present a mixed-integer linear programming formulation for the RBEP and discuss solution approaches; in particular, we present a tabu search framework for finding heuristic solutions of acceptable quality within short computation time. In computational experiments using both randomly generated instances and the real-world scenario of evacuating the city of Kaiserslautern, Germany, we compare our solution approaches.