Improved Classical and Quantum Algorithms for the Shipment Rerouting Problems

We study a shipment rerouting problem, which generalizes many NP-hard routing problems and packing problems. This problem has ample and practical applications in vehicle scheduling and transportation logistics. Given a network of hubs, a set of shipments needs must be delivered from their sources to their respective destinations by trucks. The objective is to select a set of transportation means and schedule travel routes so that the total cost is minimized. This problem is NP-hard and only classical approximation algorithms were known to have been studied for some of its NP-hard variants. Prior to our research, a quantum algorithm, based on the Ising model, generates an exact solution for a variant of this problem. In this work, we design classical exact and approximation algorithms as well as a quantum algorithm for this problem. The algorithms that we design use novel mathematical programming formulations and/or new insights on solving packing and routing problems simultaneously. Such algorithms take advantage of the network infrastructure, the shipments, and transportation means. We give provable running time bounds. We conduct extensive experiments and show that our classical solutions are empirically better than the up-to-date quantum algorithms in the noisy intermediate-scale quantum (NISQ) era.