Humanitarian logistics planning under uncertain demand and third-party supply capacity: a distributionally robust optimisation approach

Effective humanitarian logistics planning is crucial given the increasing frequency and intensity of disasters. This study explores two primary relief supply strategies: inventory pre-positioning and post-disaster third-party supply. Pre-positioning can enhance relief efficiency but is challenged by inaccuracies in demand forecasting, while post-disaster third-party supply offers greater flexibility but faces uncertainties in supply capacity during chaotic disaster scenarios. To address these challenges, we develop a two-stage optimisation framework under uncertain demand and third-party supply capacity. In the first stage, decisions are made concerning relief facility location, contract establishments with third-party suppliers, and inventory pre-positioning before disasters. The second stage focuses on the distribution of relief items from both relief facilities and third-party suppliers in the post-disaster phase. To capture the uncertainties, we use a distributionally robust optimisation (DRO) approach. In this approach, we construct a scenario-wise ambiguity set based on limited historical data and reformulate the DRO model into a tractable mixed-integer linear programming model. We validate the effectiveness of our proposed model through comprehensive numerical experiments and a real-world case study of the Pu'er Earthquake. Our out-of-sample experiments demonstrate that the scenario-wise DRO framework achieves superior performance compared to the stochastic programming approach and the classical moment-based DRO model. The results provide evidence that the decisions obtained by the DRO approach can hedge against the uncertainties. Additionally, we conduct sensitive analyses on various key parameters to provide managerial insights and practical guidance for humanitarian logistics decision making.