Optimization of yard operations in maritime container terminals
Author(s)Borjian Boroujeni, Setareh
Massachusetts Institute of Technology. Operations Research Center.
Cynthia Barnhart and Patrick Jaillet.
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With the continuous growth in international container shipping, many container terminals in maritime ports face congestion, particularly during peak hours of service, and when there is limited space in the storage area. Thus, there has been increasing interest in improving operations efficiency in container terminals. An efficient terminal, in general, is one that discharges containers from the ships in a timely manner and delivers containers to customers with a reasonable wait time. Moreover, a key performance measure in the storage area is the number of moves performed by yard cranes. Due to limited space in the storage area, containers are stacked on top of each other, forming a column of containers that can be accessed by yard cranes only from the top. Therefore, in order to retrieve a container that is covered by other containers, the blocking containers must be relocated to other slots. Because such relocation moves are costly for the port operators and result in service delays, one of the main challenges in the storage area is to plan the moves such that the number of relocations is minimized. This problem is referred to as the Container Relocation Problem (CRP). The CRP in its most simplified setting is concerned with finding a sequence of moves that retrieves all containers in a pre-defined order with a minimum number of relocations, assuming that no new containers are stacked during the retrieval process. Also, it is often assumed that the non-blocking containers cannot be relocated (i.e., repositioning moves are not allowed), an assumption that can result in a sub-optimal solution. Other variants of the container relocation problem include the dynamic CRP and the CRP with incomplete information. The former involves minimizing the number of relocations when containers are continuously stacked in and retrieved from the storage area, and the latter refers to the case that the departure times of containers are not fully known in advance. For example, a probabilistic distribution of container departure orders, or approximate departure times (in the form of time windows) might be known. Another important efficiency metric, in addition to the number of relocations, is customer wait times during the retrieval process. In particular, when repositioning moves are allowed in the system, there is a trade-off between the total number of relocations (including repositionings) and wait times, because such repositioning moves make the retrieval process faster for trucks arriving in the future. Also, it might be desired to prioritize some customers so that those prioritized experience shorter wait times. For example, in terminals with appointment systems, shorter waiting time guarantees can be given to customers who book in advance a time slot for picking up their containers. In this thesis, we propose optimization models that capture service-based and cost-based objectives and study different service policies. In the first part of this thesis, we study the CRP with complete information using an optimization model and heuristic approach. In particular, we formulate CRP (with no restrictive assumptions on repositioning moves) as an Integer Program that minimizes the weighted sum of the number of relocations and the total wait time of customers. Our integer program provides the optimal sequence of moves for retrieving containers subject to various service policies. For example, it can be used by port operators to minimize customer wait times, or to give different waiting time guarantees to different customers to reflect relative priorities. Moreover, by assigning different weight factors to the two objectives, one can use our model to plan repositioning moves. We also extend our model to the dynamic CRP and illustrate how the flexibility in the stacking process can be exploited to optimize jointly the sequence of moves and the stacking position of containers. Additionally, we propose a class of flexible retrieval policies. We demonstrate that flexible policies can result in fewer relocations and shorter wait times, thereby benefiting both the port operators and customers. In the second part of this thesis, we study the CRP with incomplete information in a 2-stage setting where the departure times of a subset of containers are initially known and the departure times of other containers are revealed at once at a later time. The contributions are twofold. First, we propose an approximate stochastic optimization algorithm, called ASA*, which is a branch-and-bound framework combined with a sampling technique, and to the best of our knowledge is the first optimization algorithm proposed for this problem. We provide theoretical bounds on the approximation errors and present numerical results showing the computational tractability and efficiency of our algorithm. Second, we use the ASA* algorithm and a myopic heuristic to study the value of information, that is, the effect of the number of containers initially known on the number of relocations. In the last part of this thesis, we introduce a simulator that is capable of integrated simulation of port operations, including the retrieval process, the stacking process, and other aspects such as allocating cranes to containers and allocating trucks to cranes. Our simulator captures the practical details of operations that cannot be modelled in an optimization framework and is capable of simulating long periods (e.g. a week) of realistic-scale operations.
Thesis: S.M. in Transportation, Massachusetts Institute of Technology, Department of Civil and Environmental Engineering, 2015.Thesis: S.M., Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2015.Cataloged from PDF version of thesis.Includes bibliographical references (pages 107-109).
DepartmentMassachusetts Institute of Technology. Department of Civil and Environmental Engineering.; Massachusetts Institute of Technology. Operations Research Center.
Massachusetts Institute of Technology
Civil and Environmental Engineering., Operations Research Center.