Introducing a novel multi-objective optimization model for vehicle routing and relief supply distribution in post-disaster phase: combining fuzzy inference systems with NSGA-II and NRGA

Each year, natural disasters cause many life losses as well as countless damages all over the world. So, implementing an efficient and effective relief supply distribution system to save human lives is of vital importance. To this end, we introduce a model to deal with two interdependent problems: vehicle routing problem (VRP) as well as relief distribution scheduling among demand points regarding three objective functions: First objective function is minimizing operational costs which include fixed and variable costs of using available heterogeneous fleet according to the designated route. Also, for more proper modeling of reality in the complex decision space of the response phase, two qualitative objective functions are introduced in this study: the importance of unmet demand and the importance of late-satisfied demand. For evaluating introduced qualitative indexes, we employ Fuzzy Inference Systems (FISs) to encapsulate decision makers' knowledge and human reasoning process. To solve the proposed model, FISs were embedded in Non-Dominated Sorting Genetic Algorithm II (NSGA-II) and non-dominated ranked genetic algorithm (NRGA). Then algorithms were implemented on two categories of problems with small and large sizes and the performances of the algorithms were compared based on four criteria. The results of statistical tests showed that both algorithms have the same performance in small-size problems. However, NSGA-II outperforms NRGA in terms of runtime in large cases. As the objective functions are constructed based on FISs, the model can be adapted to various situations just by defining linguistic rules in the way that humans think and reason. Also, since the output of the algorithm is a trade-off among the objective functions in the form of Pareto optimal solutions, decision-makers can choose the best appropriate solution according to the circumstances.