Robust optimization of evacuation instructions, applied to capacity, hazard pattern, demand, and compliance uncertainty

In the evacuation problem, departure time, route, and destination instructions are optimized to increase the effectiveness of the evacuation (i.e., more arrivals at the destinations). In literature, evacuation instructions are mostly optimized for a problem without uncertainty (the so-called nominal problem): one specific scenario regarding the system, the hazard and the evacuees is assumed. In this paper, the robust evacuation problem is formulated to create instructions dealing with the uncertainty. So-called scenarios are used that are specific representative realizations of the various uncertainties. The effectiveness of a set of instructions is based on the worst-case performance. By solving the problem, a guarantee can be given on the number of arrivals, either absolute or relative to the number of arrivals in the solution for the nominal problem. An earlier presented optimization method is extended to solve the robust problem. In a case study, the robust evacuation problems are solved under system, hazard, demand, and behavior uncertainty. The results show that for the specific case study, the guarantee on the number of arrivals by applying the relative robustness evacuation instructions is equal to 96.1%, compared to a guarantee of 85.3% in case that only nominal problems are solved.