Integrating Public Transport in Sustainable Last-Mile Delivery: Column Generation Approaches

We tackle the problem of coordinating a three-echelon last-mile delivery system. In the first echelon, trucks transport parcels from distribution centres outside the city to public transport stops. In the second echelon, the parcels move on public transport and reach the city centre. In the third echelon, zero-emission vehicles pick up the parcels at public transport stops and deliver them to customers. We introduce two extended formulations for this problem. The first has two exponential sets of variables, while the second has one. We propose column generation algorithms and compare several methods to solve the pricing problems on specially constructed graphs. We also devise dual bounds, which we can compute even when the graphs are so large that not a single round of pricing completes within the time limit. Compared to previous formulations, our models find 17 new best known solutions out of an existing dataset of 24 from the literature.