An exact algorithm for the container drayage problem under a separation mode

In this paper, we consider the container drayage problem under a separation mode in which a container can be separated from the truck during (un-)loading operation, and some emptied containers should return to the depot for maintenance. The problem is equivalently transformed into a variant of the asymmetric vehicle routing problem with time windows (a-VRPTW) based on a determined-activities-on-vertex (DAOV) graph. We present an arc-flow formulation and propose a branch-and-price-and-cut algorithm to exactly solve it. Computational results on a set of randomly generated instances show that the proposed algorithm outperforms CPLEX in terms of efficiency and effectiveness and the separation mode is advantageous over the stay-with mode.