Dynamically scheduling ships to multiple continuous berth spaces in an iron and steel complex Lixin Tang a , Shaohua Li a and Jiyin Liu b a The Logistics Institute, Northeastern University, Shenyang 110004, China, b Business School, Loughborough University, Leicestershire LE11 3TU, UK E-mail: qhjytlx@mail.neu.edu.cn (Tang), j.y.liu@lboro.ac.uk (Liu) Received 30 September 2005; received in revised form 22 May 2008; accepted 8 June 2008 Abstract This paper studies the problem of dynamically scheduling ships to multiple continuous berth spaces at the raw material docks in an iron and steel complex with the objective of minimizing the total weighted service time. We propose two mathematical models and develop an improved Lagrangian relaxation algorithm to solve the problem. Based on the problem structure, six properties are observed that help speed up the procedures of solving the sub-problems, updating Lagrangian multipliers and obtaining feasible solutions, respectively. Computational results on 50 real data problems and 120 randomly generated problems show that the algorithm generates good solutions in short time and that using the properties can reduce by more than 80% the computation time of the algorithm. Keywords: transportation; berth scheduling; industrial applications 1. Introduction Being the most important steel producer in China, Shanghai Baoshan iron and steel complex (Baosteel) consumes over 50 million tons of raw materials annually. About 95% of the raw materials are brought in by ships to raw material docks in Baosteel. At the docks, the materials are discharged from ships by unloaders and then carried by conveyor belts to raw material yards. As the annual steel production rapidly increases, more and more raw materials are received at the docks. This brings an urgent need for more efficient berth scheduling to improve the productivity of these raw material docks. For management convenience, the entire quay of each raw material dock in Baosteel was partitioned into several berths. However, incoming ships to be served at the A preliminary version of this paper named ‘‘A Lagrangian heuristic for dynamically scheduling ships to berth’’ was presented at the IFORS Hawaii 2005 conference. Intl. Trans. in Op. Res. 16 (2009) 87–107 INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH r 2009 The Authors. Journal compilation r 2009 International Federation of Operational Research Societies Published by Blackwell Publishing, 9600 Garsington Road, Oxford, OX4 2DQ, UK and 350 Main St, Malden, MA 02148, USA.