Location and inventory pre-positioning problem under uncertainty

In humanitarian logistics, the location and inventory pre-positioning problem (LIPP), making decisions on facility location, inventory pre-positioning, and allocation, is critical to post-disaster rescue efficiency. Since post-disaster conditions are complex and uncertain, it is challenging for planners to make LIPP decisions and perform rescue activities. To reduce operational costs while also guaranteeing service levels to customers, it is necessary to take uncertainties into account when making decisions. This study explores a service-oriented LIPP under two types of uncertainties, i.e., uncertain customer demand and third-party supply. We propose a two-stage robust optimization framework to solve the problem, considering the service-level constraints and minimizing the total cost. We develop two algorithms to solve the problem. Specifically, a column-and-constraint generation algorithm is utilized to solve the original two-stage robust model, and an improved row generation algorithm is developed to tackle the affinely adjustable robust counterpart model. Simulation results show that both algorithms can provide satisfying solutions. A case study based on a power grid company in China is conducted to perform sensitivity analysis and compare models, producing several managerial insights.