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

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The original article was published in Journal of Shipping and Trade 2017 2:3


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. 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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