Block-matrix-based approach for the hybrid vehicle routing problem with fuzzy travel time and transportation type selection

In this study, we propose a novel hybrid model for the vehicle routing problem that combines fuzzy travel time and transportation type selection between milk-run and cross-dock strategies to derive an optimal transportation plan. Furthermore, we present a novel block-matrix-based approach for the hybrid model to explore optimal transportation plans in an intuitive, reasonable, effective, and efficient form. The proposed block-matrix-based approach derives an optimal transportation plan by solving a hybrid vehicle routing problem that considers not only fuzzy travel time, but also transportation type selection between milk-run and cross-dock strategies. An extended biogeography-based optimization (BBO) algorithm is proposed to effectively derive a transportation plan with the optimal degree of plant satisfaction by extending the operators of migration and mutation, and introducing a novel self-adaptive mutation rate, as well as a secondary mutation operator.