The dynamic stochastic container drayage problem with truck appointment scheduling

In this work, a stochastic dynamic version of the container drayage problem is studied. The presented model incorporates uncertainty in the form of stochastic loading and unloading times at both terminals and customers, as well as stochastic travel times, conditionally dependent upon the departure time, allowing robust planning with respect to varying processing times. Moreover, the presented model is dynamic, allowing flexible orders and having the capability of re-solving the optimization problem in case of last-minute orders. Finally, the model also incorporates a truck appointment system operating at each terminal. First, a description of the general model is given, which amounts to a mixed integer non-linear program. In order to efficiently solve the optimization problem, and linearize both the objective and the conditional chance constraints, it is reformulated based on time window partitioning, yielding a purely integer linear program. As a test case, a large road carrier operating in the port of Antwerp is considered. We demonstrate that the model is efficiently solvable, even for instances of up to 300 orders. Moreover, the impact of incorporating stochastic information is clearly illustrated.