Fuzzy green vehicle routing problem for designing a three echelons supply chain

In this study, a three-echelon fuzzy green vehicle routing problem (3E-FGVRP) is considered for designing a regional agri-food supply chain on a time horizon. To account for the variability associated with the quantities requested by customers, it is assumed that the demands are fuzzy numbers simulated by a time-dependent algorithm.
Moreover, the vehicle fleet and distribution centres are considered with a defined capacity. The credibility theory of fuzzy sets is used to implement a multi-objective fuzzy chance-constrained programming model, where the total costs and carbon emissions are minimised. The resolution of the 3E-FGVRP is conducted by using a non-dominated sorting genetic algorithm. The multiple-criteria decision-making ELECTRE III method is applied to select the best solutions belonging to each Pareto front. Finally, the validity of the model is demonstrated by performing an optimisation procedure with three different initial random sets of populations. The application of the model to a case study of the Sicilian agri-food context confirms the robustness of the model, and the optimal configurations of the three-echelon supply chain can be found.