A chance-constrained two-stage stochastic programming model for humanitarian relief network design

We consider a stochastic pre-disaster relief network design problem, which mainly determines the capacities and locations of the response facilities and their inventory levels of the relief supplies in the presence of uncertainty in post-disaster demands and transportation network conditions. In contrast to the traditional humanitarian logistics literature, we develop a chance-constrained two-stage mean-risk stochastic programming model. This risk-averse model features a mean-risk objective, where the conditional value-at-risk (CVaR) is specified as the risk measure, and enforces a joint probabilistic constraint on the feasibility of the second-stage problem concerned with distributing the relief supplies to the affected areas in case of a disaster. To solve this computationally challenging stochastic optimization model, we employ an exact Benders decomposition-based branch-and-cut algorithm. We develop three variants of the proposed algorithm by using alternative representations of CVaR. We illustrate the application of our model and solution methods on a case study concerning the threat of hurricanes in the Southeastern part of the United States. An extensive computational study provides practical insights about the proposed modeling approach and demonstrates the computational effectiveness of the solution framework.