Open Access

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

Journal of Shipping and Trade20172:4

Received: 15 August 2017

Accepted: 15 August 2017

Published: 28 August 2017

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



Open AccessThis 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.

Authors’ Affiliations

El Esteshary Information Systems(EIS)


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


© The Author(s) 2017