Last-mile logistics via cargo tunnel: exact optimization approaches for the cargo tunnel scheduling problem

To relieve congested city centers, cargo tunnels are a recently revitalized last-mile delivery concept that is currently evaluated in various capability studies in different parts of the world. Under the cargo tunnel concept, freight is lifted into a tunnel at an easy-to-access outskirt depot and loaded onto electrically-powered autonomous cargo vehicles, rail cars, or maglev shuttles. These small shuttles move the goods underground through the tunnel toward small inner-city hubs, where environmentally-friendly vehicles such as cargo bikes take over the final transport leg toward urban customers. A central decision task in this context is the cargo tunnel scheduling problem, where a given set of shipments to be transported through the tunnel must be assigned to the departure slots of tunnel vehicles, such that neither vehicle capacities nor storage capacities in the hub are violated, all shipments reach their destination hubs in time, and the utilization of tunnel vehicles is minimized. This paper is dedicated to deriving exact solutions for this optimization problem. We present three alternative solution approaches, namely, two mixed integer programs and a Dantzig-Wolfe decomposition based on column generation and branch-and-price. An extensive computational study evaluates the performance of these exact solution methods. Furthermore, we show that a lack of shipment consolidation, long unloading times, and scarce storage capacities within the inner-city hubs bear the risk that significant parts of the tunnel capacity remain unused.