Integrated risk averse and possibilistic humanitarian logistic model with social costs and material convergence

Abstract A stepwise development is proposed for the construction of a model that comprehensively solves the disaster planning and response problem. In addition to traditional logistics costs, the suggested approach incorporates response time sensitivity, social costs related to post-disaster deprivation, the impact of material convergence, and measurable and epistemic uncertainty. Starting from a stochastic model based on previously published scenarios, the global costs of the scenarios are minimized using the expected value of the parameters, in a risk-averse bi-objective function that also optimizes the robustness of the model by minimizing the variability of the parameters whose probabilities are known. Finally, the complexity arising from imprecise parameter values with unknown probabilities is addressed by using chance-constrained fuzzy programming to optimize the risk associated with inter-scenario cost variability and feasibility of the constraints. This formulation is applied to real case study data, demonstrating that both the overall costs and the social cost component of the costs decrease progressively from the base formulation. The model allows the decision-maker to test the sensitivity of the results and thus set the uncertainty parameters and the incorporation of multiple objectives accordingly.