A robust chance constraint programming approach for evacuation planning under uncertain demand distribution

This study focuses on an evacuation planning problem where the number of actual evacuees (demand) is unknown at the planning phase. In the context of mass evacuation, we assume that only partial information about the demand distribution (i.e., moment, support, or symmetry) is known as opposed to the exact distribution in a stochastic environment. To address this issue, robust approximations of chance-constrained problems are explored to model traffic demand uncertainty in evacuation networks. Specifically, a distributionally robust chance-constrained model is proposed to ensure a reliable evacuation plan (start time, path selection, and flow assignment) in which the vehicle demand constraints are satisfied for any probability distribution consistent with the known properties of the underlying unknown evacuation demand. Using a path-based model, the minimum clearance time is found for the evacuation problem under partial information of the random demand. Numerical experiments show that the proposed approach works well in terms of solution feasibility and robustness as compared to the solution provided by a chance constrained programming model under the assumption that the demand distribution follows a known probability distribution.