1. ¹University of California, San Diego, CA, USA
2. ²Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

Correspondence: Y Zhu, Department of Computer Science and Engineering, University of California, San Diego 9500 Gilman Drive, Mail Code 0404 La Jolla, CA 92093-0404, USA. E-mail: y2zhu@cs.ucsd.edu

Received November 2004; Accepted August 2005; Published online 28 December 2005.

Abstract

In this paper, we examine crane scheduling for ports. This important component of port operations management is studied when the non-crossing spatial constraint, which is common to crane operations, is considered. We assume that ships can be divided into holds and that cranes can move from hold to hold but jobs are not pre-emptive, so that only one crane can work on one hold or job to complete it. Our objective is to minimize the latest completion time for all jobs. We formulate this problem as an integer programming problem. We provide the proof that this problem is NP-complete and design a branch-and-bound algorithm to obtain optimal solutions. A simulated annealing meta-heuristic with effective neighbourhood search is designed to find good solutions in larger size instances. The elaborate experimental results show that the branch-and-bound algorithm runs much faster than CPLEX and the simulated annealing approach can obtain near optimal solutions for instances of various sizes.