Robust emergency relief supply allocation with supplier selection and inventory pre-positioning

The growing threat of unexpected disasters makes disaster operations management increasingly important. This paper studies an emergency relief supply allocation problem with inventory pre-positioning and supplier selection, where suppliers are selected based on commitment quantity, compensation for interrupted regular business, and quantity-based or lead-time-based price discounts, which captures features of pre- and post-disaster purchasing. We consider uncertainties in both demand and facility disruption using budget-based uncertainty sets. A min-max robust model is formulated to simultaneously optimise supplier selection, emergency facility location, and inventory pre-positioning, aiming to minimise the total systemwide economic and deprivation costs. The deterministic equivalence of the robust model is given based on the special structures of budget-based uncertainty sets and the recourse function. We apply the robust model to a case of the 2019 Super Typhoon Lekima, where the robust model demonstrates superiority over deterministic and stochastic benchmark models, with more selected suppliers, more pre-positioned inventory, and less realised cost after disaster. Sensitivity analysis on the deprivation cost and the compensation rate further shows that the advantages of the robust model over benchmark models significantly increase with the deprivation cost. The numerical results also indicate the tradeoff between the economic and deprivation costs under different compensation rates.