A new dynamic shape adjustment and placement algorithm for 3D yard allocation problem with time dimension

This paper studies a yard allocation problem at a container terminal, namely the 3D yard allocation problem with time dimension (3DYAPT), that determines the container storage locations in a given storage block to satisfy requirements from batches of arrived containers. The objective is to minimize the two-dimensional area of the storage block occupied for temporarily storing the containers within a given planning horizon (time dimension). The 3DYAPT is challenging and proved to be strongly NP-hard since it requires dynamically adjusting the shape of the allocated area when placing containers from the same request. We formulate the 3DYAPT as an integer linear programming model and develop a simulated annealing-based dynamic shape adjustment and placement algorithm (SA-DSAP). The simulated annealing-based algorithm comprises a novel dynamic programming procedure with several speed-up techniques that sequentially computes the storage space solution given a particular sequence of requests. Extensive computational experiments are conducted, showing that SA-DSAP is capable of finding optimal solutions very efficiently for nearly all small instances. For large instances, we also find that SA-DSAP produces significantly better heuristic solutions than the existing algorithm from the literature.