Berthing ships at a multi-user container terminal with a limited quay capacity Akio Imai a,b, * , Etsuko Nishimura a , Stratos Papadimitriou c a Faculty of Maritime Sciences, Kobe University, Fukae, Higashinada, Kobe 658-0022, Japan b World Maritime University, P.O. Box 500, S-201 24 Malmo, Sweden c Department of Maritime Studies, University of Piraeus, 80 Karaoli & Dimitriou Street, GR185 32 Piraeus, Greece Received 27 October 2005; received in revised form 10 March 2006; accepted 26 May 2006 Abstract This paper addresses a variation of the berth allocation problem at multi-user terminals, as ships which would normally be served at the terminal but their expected wait time exceeds the time limit, are assigned to an external terminal. The objective of the problem is to minimize the total service time of ships at the external terminal. A genetic algorithm based heuristic is developed and a wide variety of numerical experiments showed that the heuristic developed performed well in reducing external terminal usage and thus may be helpful in the efficient management of busy ports during extreme peaking conditions. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Berth allocation; Terminal management; Container transportation; External terminal; Heuristic; Mathematical programming 1. Introduction While there are many container ports in the world with heavy traffic that serve as Dedicated Terminals to specific shipping lines, there is also another type of container terminals, operating as Common User Terminals also known as Multi-User Terminals (MUT) offering services to any shipping lines. These terminals are gen- erally configured with a long quay comprising several berths, having the capability of serving more than one ship at a time and it is not very likely that a particular calling ship is served at a specific berth every time it calls. Most of such terminals employ the First-Come-First-Served (FCFS) principle for their daily operations. It is worth to note that essentially the concept of MUT is independent from the number of berths at the ter- minal of concern; however, from the viewpoint of berth scheduling complexity, we base this study on an MUT with a specific number of berths, e.g., 4–8 berths. The MUTs are mostly state-owned in developing countries and privately-owned in developed countries. 1366-5545/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.tre.2006.05.002 * Corresponding author. Tel.: +81 78 431 6261. E-mail address: imai@maritime.kobe-u.ac.jp (A. Imai). Transportation Research Part E 44 (2008) 136–151 www.elsevier.com/locate/tre