Integrated Quay Crane and Yard Truck Scheduling Based on Constraint Programming

A Mixed Integer Programming(MIP) model and a Constraint Programming(CP) model to tackle the integrated quay crane and yard truck scheduling problem for inbound containers are proposed, which aims to minimize the makespan of unloading process. The CP model is developed with OPL modeling language and employs OPL's special constructs designed for scheduling problems, e.g., interval variables sequence variable etc. To improve solving efficiency, a special concept called extended operation task is proposed which is used to define interval variables. Besides, a new lower bound is given to evaluate the quality of solutions. Computational experiments on varied scales of instances are carried out to test the CP model and the MIP model. The results indicate that the CP model does not outperform the MIP model for small instances. For medium and large instances, the MIP model can not be solved within time limit, whereas the CP model is effective for finding high-quality solutions and can efficiently solve large problems with fast convergence rate. On average, the gap between the objective values of the CP model and the lower bounds is 2.19%~8.28%.