In this work, the focus is on a rarely studied problem in the technical literature - the inbound containers (importation) process delivery, with reach stackers for moving the containers . In this process, customers schedule their containers withdrawal in one of the several allowable time windows - two hours time, without fixed arrival order. Containers pre-segregation occurs in the night before the effective delivery day. Thirty containers are stacked by time windows in six stacks five containers high and a buffer area allocated for subsidiary movements. The purpose of this work is to identify and to evaluate comparatively the key performance indicators associated with the thirty containers maximum delivery levels in each time window. The model is necessarily a simulation one, because it involves the container stack packing (random), its access and movement by reach stacker equipment (with typical access policies) and the truck arrival for withdrawing the container (also random). Two different sequencing rules are compared - first in, first out (FIFO) and smallest processing time (SPT). Solving the model in a FIFO delivery discipline, the conclusion is that the two hours time window is insufficient to deal with the 30 (thirty) containers delivery in a Poisson process arriving trucks. The second delivery system studied - a decision process applied in the waiting queue (based on selecting the container with the minimal expected unproductive movements), more promising results have been obtained, although insufficient to pick up all the containers. Alternative scenarios were then offered to solve the problem.