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Erratum to: Shipping Optimisation Systems (SOS): tramp optimisation perspective

The Original Article was published on 10 July 2017


Unfortunately, the original PDF version of this article [1] contained some errors. The equation 8, 11, 13, 14, 15, 16, 17, 19, 22 all displayed incorrectly in the section of Appendix 1. The correct equations can be found below and the original article of PDF version has been updated to reflect this change.

$$ {V}_j^k\ge {V}_i^k-{v}_i{\sum}_{z\in Z}{x}_{ijz}^k,\kern0.75em i\in L,j\in E,\kern0.5em \mathrm{and}\kern0.5em k\in S,\kern0.5em \mathrm{where}\kern0.5em {\sum}_{z\in Z}{x}_{ijz}^k=1, $$
$$ {V}_j^k\ge {V}_i^k+{v}_i{\sum}_{z\in Z}{x}_{ijz}^k,i\in D,j\in E,\mathrm{and}\kern0.75em k\in S,\kern0.5em \mathrm{where}\ {\sum}_{z\in Z}{x}_{ijz}^k=1, $$
$$ {W}_i^k\ge {W}^k,i\in D,\kern0.5em \mathrm{and}\ k\in S,\kern0.5em \mathrm{where}\kern0.75em {\sum}_{z=3,4}{x}_{igz}^k=1,g\in G, $$
$$ {V}_i^k\ge {V}^k,i\in D,\mathrm{and}\ k\in S,\mathrm{where}\kern0.75em {\sum}_{z=3,4}{x}_{igz}^k=1,g\in G, $$
$$ {N}_i^k\ge {N}^k,i\in D,\mathrm{and}\ k\in S,\mathrm{where}\ {\sum}_{z=3,4}{x}_{igz}^k=1,g\in G, $$
$$ {W}_i^k\ge {W}_{0,}^k\ i\in D, and\ k\in S, where\ {\sum}_{z=1,2}{x}_{ijz}^k=1,j\in E, $$
$$ {T}_j^k\ge {T}_i^k+{t}_i+{\sum}_{z\in Z}{t}_{ijz}^k{x}_{ijz}^k,i\in {E}_f,j\in {E}_g,\mathrm{and}\ k\in S,\mathrm{where}\ {t}_{ifz}^k=0,\mathrm{and}{\sum}_{z\in Z}{x}_{ijz}^k=1, $$
$$ {T}_j^k\ge {a}_i,j\in E,\mathrm{and}\ k\in S,\mathrm{where}{\sum}_{i\in Ef}{\sum}_{z\in Z}{x}_{ijz}^k=1, $$
$$ {T}_g^k\le {T}^k,g\in G,k\in S,\mathrm{where}\ {\sum}_{z=3,4}{x}_{igz}^k=1\kern0.5em \mathrm{and}\kern0.5em i\in D, $$


  1. Said El Noshokaty (2017) Shipping Optimisation Systems (SOS): tramp optimisation perspective. J Shipp Trade 2:3.

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Correspondence to Said El Noshokaty.

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The online version of the original article can be found under doi:10.1186/s41072-017-0021-y

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Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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El Noshokaty, S. Erratum to: Shipping Optimisation Systems (SOS): tramp optimisation perspective. J. shipp. trd. 2, 4 (2017).

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