A branch-price-and-cut algorithm for the local container drayage problem with controllable vehicle interference

This paper investigates a local container drayage problem with controllable vehicle interference (LCDP&CVI) under the tractor-and-trailer separation mode in which a tractor can be coupled or decoupled with a trailer at a customer location or a terminal. The container drayage requests proposed by customers should be fulfilled by a set of vehicle fleets, and each vehicle fleet comprises of a certain number of tractors and trailers that should be matched to each other. The controllable vehicle interference (CVI) means that the routes of any tractors from different vehicle fleets are independent of each other, implying that the interference between tractors is restricted only to the tractors from the same vehicle fleets. A mixed-integer linear programming (MILP) model is proposed for the LCDP&CVI. To exactly solve the problem, we develop a branch-price-and-cut algorithm based on the reformation of the MILP model, including a master problem and a pricing sub-problem. The pricing sub-problem that deals with the temporal synchronization constraints is formulated as the multi-vehicle shortest path problem with interference. By adding the tractor to the temporal-spatial network, a new representation of the pricing sub-problem is constructed, which enables us to solve the sub-problem by the multi-label method. In addition, the symmetrical elimination and dominance rules are incorporated into the multi-label method to enhance its effectiveness. Extensive numerical experiments are conducted to validate the proposed model and solution algorithm. For small-scale instances, the proposed solution algorithm is able to solve instances with up to 24 requests to optimality within two hours, which outperforms significantly the commercial MILP solver in terms of efficiency and effectiveness. For large-scale instances, the proposed algorithm can yield competitive solutions that are superior to the heuristic algorithms reported in the literature. Our experimental results also show that the controllable vehicle mechanism can strike a good balance between computational efficiency and operational costs by meticulously designing the structure of vehicle fleets.