Column generation for the collaborative multi-stop truckload shipping problem in daily regional distribution

Multi-stop truckload shipping offers less-than-truckload shippers a promising way to reduce their freight costs by consolidating freights en route, which is similar to ridesharing in the mobility industry. One significant challenge in practical implementation is designing attractive multi-stop routes that to shippers while conforming to carriers' requirements. It is crucial to develop an efficient optimisation algorithm to automate bundling decisions. However, this routeing problem is complicated by a nonlinear inseparable cost structure and new routeing decisions in the first pickup and last delivery points. We introduce a new variant of pickup and delivery model and propose a column generation algorithm to efficiently solve real-world multi-stop routeing problems. The algorithm utilises a new specialised labelling procedure that exclusively generates labels for pickup sequences and establishes new dominance rules. Theoretical results on the label dominance, algorithm complexity, and optimality gap are also established. We conduct a real-world case study, comparing our methodology against the enumeration method and a heuristic method documented in the literature. The computational results demonstrate the high efficiency of our method and reveal important insights for practitioners.