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Scientific Programming
Volume 2018 (2018), Article ID 3450726, 9 pages
Research Article

Stowage Planning in Multiple Ports with Shifting Fee Minimization

1School of Information Management & Engineering, Shanghai University of Finance and Economics, Shanghai, China
2Glorious Sun School of Business & Management, Donghua University, Shanghai, China
3School of Economics & Management, Tongji University, Shanghai, China

Correspondence should be addressed to Ming Liu

Received 21 August 2017; Revised 20 December 2017; Accepted 10 January 2018; Published 1 February 2018

Academic Editor: Emiliano Tramontana

Copyright © 2018 E. Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper studies the problem of stowage planning within a vessel bay in a multiple port transportation route, aiming at minimizing the total container shifting fee. Since the access to containers is in the top-to-bottom order for each stack, reshuffle operations occur when a target container to be unloaded at its destination port is not stowed on the top of a stack at the time. Each container shift via a quay crane induces one unit of shifting fee that depends on the charge policy of the local container port. Previous studies assume that each container shift consumes a uniform cost in all ports and thus focus on minimizing the total number of shifts or the turnaround time of the vessel. Motivated by the observation that different ports are of nonuniform fee for each container shift, we propose a mixed integer programming (MIP) model for the problem to produce an optimal stowage planning with minimum total shifting fee in this work. Moreover, as the considered problem is NP-hard due to the NP-hardness of its counterpart with uniform unit shifting fee, we propose an improved genetic algorithm to solve the problem. The efficiency of the proposed algorithm is demonstrated via numerical experiments.