Reliable design of a congested disaster relief network: A two-stage stochastic-robust optimization approach

The preparedness of humanitarian relief networks can be enhanced by pre-positioning resources in strategic locations and using them when disasters strike, a strategy that gives rise to a two-stage planning problem. This paper presents a novel two-stage stochastic-robust optimization approach for integrated planning of pre- and post-disaster positioning and allocation of relief resources, while taking into consideration the uncertainty about demand for relief services and disruptions in the relief facilities and the transportation network. The proposed approach enables planners to effectively use limited historical data and imperfect experts' opinions to obtain robust solutions while avoiding the over-conservatism of classical robust optimization methods. The objective sought is to minimize the expected total time victims need to receive assistance, including both access time to facilities and waiting/service time in them. Congestion in relief facilities is accounted for by modeling them as queuing systems and penalizing waiting time. A decomposition method based on column-and-constraint generation is implemented to solve the problem, whereas the nonlinear terms corresponding to queuing in the second-stage problem are handled using a direct search procedure. Applicability of the proposed approach is demonstrated through a real case study and the numerical results are analyzed to draw managerial insights.