Terminal and yard allocation problem for a container transshipment hub with multiple terminals Der-Horng Lee ⇑ , Jian Gang Jin, Jiang Hang Chen Department of Civil and Environmental Engineering, National University of Singapore, Singapore article info Article history: Received 14 February 2011 Received in revised form 16 June 2011 Accepted 31 July 2011 Keywords: Terminal allocation Yard allocation Container ports Transshipment abstract This paper presents an integer programming model for the terminal and yard allocation problem in a large container transshipment hub with multiple terminals. The model inte- grates two decisions: terminal allocation for vessels and yard allocation for transshipment container movements within a terminal as well as between terminals. The objective func- tion aims to minimize the total inter-terminal and intra-terminal handling costs generated by transshipment flows. To solve the problem, we develop a 2-level heuristic algorithm to obtain high quality solutions in an efficient way. Computational experiments show the effectiveness of the proposed approach. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction In container transshipment hubs, the management of transshipment flows is an important issue to which port operators pay close attention. Transshipment containers are temporarily stored in storage yards after being discharged from inbound vessels, and wait to be loaded onto outbound vessels in the near future. This transshipment movement generates container flows between quay side and yard side. As transshipment containers do not need to move out of the terminal gates, the re- lated operations concentrate on storage yards and along the quay. Consequently, management for transshipment flows, including berth allocation, yard allocation and so on, is required to achieve a high productivity. The Port of Singapore is one of the world’s busiest transshipment hubs and handles one-fifth of the world’s total trans- shipment throughput. Along with the increase of containerized maritime shipping, the Port of Singapore has set up five ter- minals phase by phase and another one is under construction in order to meet the increasing demand. It is often the case that a large transshipment hub consists of several terminals which are close to each other. Fig. 1 presents such a multi-terminal transshipment system with three terminals in Singapore. For such a multi-terminal system where many handling resources are involved, operations are complex and there are some unique issues calling for attention which are different from traditional ones in the management of a single terminal. One problem comes from inter-terminal traffic and it is what the port operators concern most. This is because inter-terminal traffic contributes to the whole operational cost to a large extent. In the case that two related vessels berth at two different terminals, for example, T1 and T3 in Fig. 1, there exists an inter-terminal container movement operation which needs a lot of resources including yard cranes and yard trucks. When inter-terminal traffic volume becomes high, not only does cost in- crease, traffic congestion may also occur. Take Fig. 1 as an example, there is only one traffic corridor indicated by the dotted arrows between T1 and T3 and high traffic could lead to high costs and traffic congestion. Fortunately, inter-terminal traffic 1366-5545/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.tre.2011.09.004 ⇑ Corresponding author. Address: Block E1A #07-16, 1 Engineering Drive 2, National University of Singapore, Singapore 117576, Singapore. Tel.: +65 6516 2131; fax: +65 6779 1635. E-mail address: dhl@nus.edu.sg (D.-H. Lee). Transportation Research Part E 48 (2012) 516–528 Contents lists available at SciVerse ScienceDirect Transportation Research Part E journal homepage: www.elsevier.com/locate/tre