A fuzzy bi-level optimization model for multi-period post-disaster relief distribution in sustainable humanitarian supply chains

In the aftermath of large-scale natural disasters, supply shortage and inequitable distribution cause various losses, hindering humanitarian supply chains’ performance. The optimal decisions are difficult due to the complexity arising from the multi-period post-disaster consideration, uncertainty of supplies, hierarchal decision levels and conflicting objectives in sustainable humanitarian supply chains (SHSCs). This paper formulates the problem as a fuzzy tri-objective bi-level integer programming model to minimize the unmet demand rate, potential environmental risks, emergency costs on the upper level of decision hierarchy and maximize survivors’ perceived satisfaction on the lower level of decision hierarchy. A hybrid global criterion method is devised to incorporate a primal-dual algorithm, expected value and branch-and-bound approach in solving the model. A case study using data from the Wenchuan earthquake is presented to evaluate the proposed model. Study results indicate that the hybrid global criterion method guides an optimal strategy for such a complex problem within a reasonable computational time. More attention should be attached to the environmental and economic sustainability aspects in SHSCs after golden rescue stage. The proposed bi-level optimization model has the advantages of reducing the total unmet demand rate, total potential environmental risks and total emergency costs. If the decision-agents with higher authorities act as the leaders with dominant power in SHSCs, the optimal decisions, respectively taking hierarchical and horizontal relationships into account would result in equal performance.