Model and solution of sustainable bi-level emergency commodity allocation based on type-2 fuzzy theory

The allocation of emergency commodities is very important for efficient emergency response after a disaster. In this study, a sustainable multi-objective bi-level emergency commodity allocation model is established, providing a practical emergency commodity allocation strategy for humanitarian supply chains. First, type-2 fuzzy variables are used to describe uncertain transportation costs and handle them based on the conditional value-at-risk (CVaR) theory of type-2 fuzzy variables. Second, Karush-Kuhn–Tucker (KKT) conditions with complementary constraints are used, auxiliary variables are introduced, and global criteria are applied to achieve the equivalent transformation of the model. Finally, with the Wenchuan earthquake in China in 2008 as an example, we prove the necessity of introducing the CVaR for risk measurement and the practicability of using type-2 fuzzy variables to describe uncertain parameters by comparing this scenario with a risk-neutral situation and the proposed model with a model based on type-1 fuzzy theory. The novelties of this study include considering both the government and suppliers are decision-makers, exploiting CVaR to measure tail risk and using type-2 fuzzy theory to transform uncertain parameters. The contributions of this study include considering sustainability during the rescue process and proposing a CVaR formula based on type-2 theory.