Upward scalable vehicle routing problem of automobile inbound logistics with pickup flexibility

Motivated by the inbound logistics of a famous automobile manufacturing company, we introduce the upward scalable vehicle routing problem (for order pickup) with time windows (USVRPTW), where the pickup from each supplier can be adjusted upward by a certain degree (pickup flexibility) based on the order volume, thus increasing the vehicle utilization and reducing logistics cost. We solve the USVRPTW exactly by a branch-and-price algorithm, where the flexibility affects the pricing problem, leading to the elementary shortest path problem having to consider resource allocation except the resource constraints. The consideration of resource allocation adds many new properties to the shortest path problem, based on which we design a tree search algorithm. We develop a heuristic algorithm based on the bipartite graph to generate initial columns for the column generation (CG) process. The algorithm can also be adopted as an efficient method for solving large-scale problems due to its ability to find near-optimal solutions quickly. We also propose the penalty stabilization method and the drill-down strategy to accelerate CG. Numerical experiments show that our designed branch-and-price algorithm outperforms the commercial solver Gurobi. The efficiency of the tree search algorithm, the heuristic algorithm, and the CG acceleration methods is also verified. Real-data experiments illustrate that the low increase in driving cost can significantly improve vehicle utilization, proving the significance of flexibility. We then provide management insights to reveal that adopting the proposed flexibility mechanism can reduce logistics cost.