Design a Relief Transportation Model with Uncertain Demand and Shortage Penalty: Solving with Meta-Heuristic Algorithms

In this paper, a fuzzy multi-objective optimization model in the logistics of relief chain for response phase planning is addressed. The objectives of the model are: minimizing the costs, minimizing unresponsive demand, and maximizing the level of distribution and fair relief. A multi-objective integer programming model is developed to formulate the problem in fuzzy conditions and transformed to the deterministic model using Jimechr('39')nez approach. To solve the exact multi-objective model, the e-constraint method is used. The resolved results for this method have shown that this method is only able to find the solution for problems with very small sizes. Therefore, in order to solve the problems with medium and large sizes, multi-objective cuckoo search optimization algorithm (MOCSOA) is implemented and its results are compared with the NSGA-II. The results showed that MOCSOA in all cases has the higher ability to produce higher quality and higher-dispersion solutions than NSGA-II.