Dynamic Stochastic Optimization of Relocations in Container Terminals

In this paper, we present a mathematical model and formulation to minimize the number of container relocations in storage systems, like container terminals and warehouses. Container relocations are necessary when a container to be retrieved is not at the topmost position in a stack. We consider a dynamic setting, which allows for continual stacking and retrieving of containers, without restrictive assumptions on container arrival and departure sequences, and on possible relocations. We generalize our objective function to include operational delays due to relocations, and jointly minimize the number of relocation moves and delay. We apply our method to the special case of only container retrievals, and compare our results with those of existing approaches. Further, we study the impact of uncertainty on the number of relocations, by extending our formulation to the setting with incomplete information on stacking and retrieval times. Using a two-stage stochastic optimization framework, we show that lack of information results in more relocations; and having partial information significantly closes the gap to the optimal solution with complete information.