Solving Large-Scale Vehicle Routing Problems with Unsplit Demands via Limited Information

Abstract

This paper addresses the capacitated vehicle routing problem with unsplit stochastic demand (UCVRP), in the limited information regime. We integrate ideas from region partitioning and online bin packing to propose a provably near-optimal and scalable algorithm. Our algorithm performs double partitioning: it first assigns routes to each vehicle a priori and then solves the recourse problem via a highly-efficient online bin-packing algorithm. One salient feature of our algorithm is that each driver only needs to know the information of a small number of customers, even when the total number of customers is extremely large. We characterize the performance of the algorithm and its convergence rate to the optimal offline solution with respect to the amount of customer information through asymptotic analysis. Moreover, we analyze the impact of adding additional overlapping routes and show in heavy traffic scenarios, additional overlapping does not improve the rate of convergence to the optimal solution except by constants. Finally, the effectiveness of the algorithm is further verified through numerical simulations.

Keywords: vehicle routing, region partitioning, online bin-packing, process flexibility, asymptotic analysis

JEL Classification: C61