Journal article
Liner Shipping Cargo Allocation with Repositioning of Empty Containers
This paper is concerned with the cargo allocation problem considering empty repositioning of containers for a liner shipping company. The aim is to maximize the profit of transported cargo in a network, subject to the cost and availability of empty containers. The formulation is a multi-commodity flow problem with additional inter-balancing constraints to control repositioning of empty containers.
In a study of the cost efficiency of the global container-shipping network, Song et al. (2005) estimate that empty repositioning cost constitutes 27% of the total world fleet running cost. An arc-flow formulation is decomposed using the Dantzig-Wolfe principle to a path-flow formulation. A linear relaxation is solved with a delayed column generation algorithm.
A feasible integer solution is found by rounding the fractional solution and adjusting flow balance constraints with leased containers. Computational results are reported for seven instances based on real-life shipping networks. Solving the relaxed linear path-flow model with a column generation algorithm outperforms solving the relaxed linear arc-flow model with the CPLEX barrier solver even for very small instances.
The proposed algorithm is able to solve instances with 234 ports, 16,278 demands over 9 time periods in 34 min. The integer solutions found by rounding down are computed in less than 5 s and the gap is within 0.01% from the upper bound of the linear relaxation. The solved instances are quite large compared to those tested in the reviewed literature.
Language: | English |
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Publisher: | Taylor & Francis |
Year: | 2011 |
Pages: | 109-124 |
ISSN: | 19160615 and 03155986 |
Types: | Journal article |
DOI: | 10.3138/infor.49.2.109 |
ORCIDs: | Pisinger, David |