A novel fuzzy bi-objective vehicle routing and scheduling problem with time window constraint for a distribution system: A case study

During the transportation of dangerous, the risk is an important factor that should be considered due to the potentially serious consequences of the accident. Regardless of risks, time is the primary issue that should be considered in the transportation of hazardous materials. This paper introduces a bi-objective model of vehicle routing and scheduling for hazardous material allocation problems under fuzzy conditions to minimize the total allocation time and risk. In the proposed model, the fuzzy inference system and fuzzy failure mode and eects analysis are used for the rst time to identify and calculate high-level risks, instead of the previous simple methods. Moreover, the Jimenez method and fuzzy goal programming are respectively utilized to convert the fuzzy biobjective model into the same crisp and single-objective one. In addition, in order to deal with the NP-hardness of large-scale problems, two meta-heuristic algorithms, invasive weed optimization, and genetic algorithm, are used, and multiple sensitivity analyses are performed to prove the eectiveness of the proposed method. The performance of the proposed algorithms is also assessed through a comparative study. Finally, the proposed model is applied to a real case study to prove the validity of the model.