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

AbstractPost-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.Keywords: Humanitarian relief logistics networkrobust optimizationbi-level goal programmingmultiple objectives AcknowledgmentsThe authors are especially thankful to the Editor-in-Chief, the Associate Editor and the anonymous reviewers for their valuable comments, which helped the authors to improve the article greatly.Disclosure statementNo potential conflict of interest was reported by the author(s).Data availability statementThe authors confirm that the data supporting the findings of this study are available within the article; further reasonable inquiries can be directed to the corresponding author.Additional informationFundingThis work is supported by the National Natural Science Foundation of China [No. 61773150]; the Operations Research and Management Innovation Team of Hebei University [grant number IT2023C02]; the Humanities and Social Sciences Research Program of the Ministry of Education [No. 20YJC630001]; the Science and Technology Project of Hebei Education Department [No. QN2021080]; the Post-Graduate's Innovation Fund Project of Hebei University [No. HBU2022ss008].