A two-stage optimization model for relief distribution to disaster survivors under two-fold uncertainty

Disasters are unforeseen occurrences requiring extensive transport deployment to support and relieve victims. Sometimes, this transportation is not feasible directly from some supply points to some destination points. Due to this tragedy, it is unclear precisely what is available at supply points, what is needed at destinations, how much transportation capacity there is, and what the routes are like. In this study, we investigate a two-stage multi-item fixed charge four-dimensional transportation problem using the concept of big data theory under the two-fold uncertainties. Here, the model’s parameters such as unit transportation costs, availabilities of items at the suppliers, fixed charges, capacities of conveyances, and demands of the items at the retailers are considered type-2 zigzag uncertain variables. Using big data theory and based on uncertain programming theory, two novel uncertain models are developed such as chance-constrained programming and expected value programming model. These two uncertain models transformed into the deterministic form via uncertainty inverse distribution theory. A critical value based reduction method with three categories (i.e., expected value, pessimistic value, and optimistic value) is applied to reduce the type-2 zigzag uncertain variable to the type-1 zigzag uncertain variable. The genetic algorithm and particle swarm optimization techniques have been proposed to find the optimal solution for the two deterministic models. The efficiency of our proposed approach is demonstrated with a real-life numerical example.