Modelling a bi-level multi-objective post-disaster humanitarian relief logistics network design problem under uncertainty

Abstract

Post-disaster humanitarian relief logistics focuses on managing the supply and shipment of relief items. Owing to the complexity arising from the hierarchical decision relationship and the uncertainties of demand and transportation, it is challenging to develop an effective humanitarian relief logistics network (HRLN). A globalized robust bi-level multi-objective HRLN model involving uncertainties in transportation time, transportation cost and demand is developed to address this problem, in which an upper-level decision-maker focuses on the allocation problem and a lower-level decision-maker considers the supply problem. For tractability, the goal programming approach is employed to trade off conflicting timeliness, satisfaction and operational cost objectives. The proposed globalized robust bi-level HRLN model is reformulated as its globalized robust counterpart formulations under two different perturbation structures. The primal–dual approach is adopted to transform the bi-level models into equivalent mixed-integer conic programs. A case study concerning an Iranian earthquake is conducted to prove the performance of the proposed model. Globalized robust models are more flexible and able to immunize against uncertainty by comparison with traditional robust optimization and deterministic solutions. The managerial insights of using the globalized robust bi-level optimization approach are reported for disaster response management. The design of an emergency aviation network to circumvent the effects of COVID-19 could be considered in future research.