  In this paper, we study a dynamic pickup and delivery problem with docking
constraints. There is a homogeneous fleet of vehicles to serve
pickup-and-delivery requests at given locations. The vehicles can be loaded up
to their capacity, while unloading has to follow the last-in-first-out (LIFO)
rule. The locations have a limited number of docking ports for loading and
unloading, which may force the vehicles to wait. The problem is dynamic since
the transportation requests arrive real-time, over the day. Accordingly, the
routes of the vehicles are to be determined dynamically. The goal is to satisfy
all the requests such that a combination of tardiness penalties and traveling
costs is minimized. We propose a cost function approximation based solution
method. In each decision epoch, we solve the respective optimization problem
with a perturbed objective function to ensure the solutions remain adaptable to
accommodate new requests. We penalize waiting times and idle vehicles. We
propose a variable neighborhood search based method for solving the
optimization problems, and we apply two existing local search operators, and we
also introduce a new one. We evaluate our method using a widely adopted
benchmark dataset, and the results demonstrate that our approach significantly
surpasses the current state-of-the-art methods.
