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

This study proposes a novel model for the vehicle routing problem that considers transportation type selection between milk-run and cross-dock strategies under uncertain environment with fuzzy travel time to derive an optimal transportation plan. Furthermore, a novel block-matrix-based approach for the transportation type selection to explore optimal transportation plans in an intuitive, reasonable, effective, and efficient form is presented. 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.