Developing New Methods for Efficient Container Stacking Operations

By Amir Gharehgozli, Erasmus University, November 2012



The first containers were introduced to the world in April 1956 when Malcolm McLean moved fifty-eight 35-foot containers from Newark to Houston by a refitted oil tanker, “SS Ideal X” (see the figure). Nowadays, containerized transportation has become an essential part of intermodal freight transport. More than 90% of all cargo is now transported by ships. Most of this cargo is handled in containers. A large terminal handles millions of containers on an annual basis. For example, the terminals in the Port of Rotterdam has handled more than 11 million containers in 2010. Container terminal managers attempt to efficiently manage the logistic process of the terminals to keep up with the increasing number of containers to be handled. The stacking area is particularly critical since most of the containers transiting through a container terminal must be stored for a certain length of time, possibly in different blocks. Efficiently managing block operations can significantly improve the overall performance of the container terminal.

In this dissertation, we first study how to minimize the makespan to stack and retrieve a set of containers
in a block of containers. In Chapters 2 and 3, a single automated stacking crane (ASC) handles the requests. The block has multiple input/output (I/O) points. The ASC must move retrieval containers from the block to the I/O points, and must move storage containers from the I/O points to the block. We formulate theproblems as continuous time integer programming models and propose exact and heuristic solution methods to solve them. The numerical experiments reveal that the optimal makespan results are significantly shorter than results obtained by heuristics commonly used in practice such as first-come-first-served and selecting the nearest request. In Chapter 4, two ASCs carry out the requests. The ASCs can never pass each other and must operate sufficiently far from each other. We formulate this problem as an integer programming model and propose a metaheuristic algorithm to solve it. The results show that the proposed algorithm significantly outperforms other heuristics and truncated CPLEX.

In Chapters 2–4, we consider that locations as well as destination sides of retrieval containers and I/O
points of storage containers are known. Note that in Chapter 2, each storage location has a given storage
location in the block. In contrast, in Chapters 3 and 4, each storage container can be stacked in a location
selected from a set of open locations suitable for stacking that container. Storage locations can be determined using the methodology discussed in Chapter 5, where we use a stochastic dynamic programming model to decide where to stack each incoming container in a block. The objective is to minimize the expected number of reshuffles. The number of states of the dynamic programming model is overwhelming. We propose a decision-tree heuristic algorithm to solve real instances. The heuristic uses the results of the exact model for small-scale problems to generate generalized decision trees. These trees can be used to solve problems with a realistic number of piles. For small-scale problems, the trees can quickly make optimal decisions. For large-scale problems, the decision-tree heuristic significantly outperforms stacking policies commonly used in practice. Those policies perform well as long as the utilization of the block is low. However, since they are myopic, as the utilization increases, they start performing similar to random stacking which results in reshuffles. Using the decision trees, we can compare the performance of a shared-stacking policy, which allows containers of multiple ships to be stacked on top of each other, with a dedicated-stacking policy. Shared-stacking appears to outperform dedicated-stacking.

Finally, in chapter 6, we conclude the dissertation and summarize the contributions and findings. Together,
the exact and heuristic methods developed in this dissertation can be used by container terminal
operators to increase the performance at the stacking area, which consequently affects the whole terminal