Robust-fuzzy-probabilistic programming for humanitarian aid logistics under uncertainty: A facility location and flow allocation study with deprivation cost analysis

In this research, the modeling and solving of a humanitarian aid logistics problem under uncertainty have been discussed. Considering the uncertainty in the model parameters, the study used the robust-fuzzy-probabilistic programming concept. This model incorporates the facility location concept and optimal flow allocation. The results indicate that as the uncertainty rate increases, more people are affected by the accident and there is an increased demand for relief items at the accident scene, leading to higher costs related to the supply and transportation of items and for assisting the injured. Additionally, by examining the effect of deprivation cost on the model's outcomes, it is evident that with an increase in deprivation cost, the model aims to increase the amount of goods transferred to fully meet the demand, resulting in decreased deprivation-related costs but increased costs associated with product transfer. Consequently, the overall cost of the relief logistics network increases. Finally, by examining the effects of the objective function weighting coefficient on the problem's objective function values, it is observed that with an increase in this weighting coefficient, the objective function values increase due to higher volumes of relief items being transferred. ey contributions of the paper include the analysis of deprivation costs and the investigation into the impact of uncertainty on logistics costs. The study reveals that heightened uncertainty and increased affected populations significantly elevate relief logistics costs. Specifically, a 90% increase in uncertainty leads to a 19.46% rise in total costs, driven by amplified demand and logistical challenges.