Two-stage stochastic facility location problem with disruptions and restricted shortages

In this study, we consider a reliable facility location problem where an uncertain disruptive event might affect the demand of the nodes, the allocation costs, and the available capacities at the facilities. We assume that the decision maker decides the locations and the types (size and reliability levels) of the facilities under uncertainty, while the allocation and shortage decisions are made in response to the realizations of the uncertain parameters. Motivated from a humanitarian facility location problem, we enforce an upper bound on the risk of shortages under any scenario using the popular risk measure conditional value-at-risk (CVaR). We formulate the problem as a two-stage stochastic programming model, and solve it using the L-Shaped method accelerated with additional enhancements. Our computational experiments show the value of our modeling scheme, and the effectiveness of our solution method