Scheduling and Routing for a Bus-Based Evacuation with a Constant Evacuee Arrival Rate

This paper introduces a variant of the vehicle routing problem adapted for bus‐based, regional evacuation planning, where evacuees arrive at predetermined pickup locations at constant, location‐specific rates. This arrival process more realistically portrays evacuee arrival behavior, presenting an important distinction from the current transit‐based evacuation literature. In this problem, capacity‐constrained buses are routed, potentially multiple times, to transport all evacuees to a depot/shelter such that the last pickup, and the end of the arrival process, occurs at a location‐specific time, determined by risk considerations. The problem seeks to minimize the total waiting time at these locations (total exposure) and exploits efficiencies by allowing service choice. The structural properties of this problem guide the choice for two important strategic parameters: the maximum number of pickups allowed on each location and the fleet size. It is shown that, depending on the problem instance, increasing the maximum number of pickups may reduce both the fleet size requirement and the total exposure and that, past a certain threshold, there exists a maximum number of pickups (or a range of potential values, if the problem cannot be solved to optimality) that guarantees an efficient usage of the available fleet and equitable reductions in exposure across pickup locations.