3.2 Notations 

In this part, we discuss the sets of subscripts referring to variables in the model. Importer is denoted by \(c\in C,\) with \(C\) being the set of importers. Exporter is indexed by \(m\in M,\) with \(M\) being the set of exporters. In addition, destination port is denoted by \(d\in D(c)\) with \(D(c)\) being the set of destination port of importer \(c\in C.\) The origin port is indicated by \(o\in O(m)\) with \(O(m)\) being the set of origin ports of exporter \(m\in M.\) As each ship is an independent carrier in the shipping market, we can classify the carriers in term of ship sizes. For a certain carrier type (carriers with same ship size), we indicate it by \(k\in K\) with \(K\) being the set of carriers.
   Table 1-3 shows the relevant variables of the importer & exporter, the carrier, and the destination/origin port respectively. Table 4 gives the parameters. In this study, we clarify that a bar on a variable \(x\) (\(\overline{x}\)) indicates that the variable is exogenous.  
Table 1. Variables of importer & exporter
\(Variable\) \(Description\)
\(U_{c}\) Utility of importer \(c\) while trading with different exporters.
\(DC_{c}\) Overall iron ore import volume of importer \(c\) (\(DC_{c}>0\)).
\(I_{c}\) Purchasing budget of importer \(c\).
\(\pi_{m}{}_{c}\) Profits of exporter \(m\) earned by exporting iron ore to importer \(c\).
\(QM_{m}\) Overall export volume of exporter \(m\) (\(QM_{m}>0\)).
\(QTC_{m}\) Iron ore production capacity of exporter \(m\).
\(Q_{m}{}_{c}\) Trade volume between exporter \(m\) and importer \(c\) (\(Q_{m}{}_{c}>0\)).
\(P_{m}{}_{c}\) Import price for iron ores from exporter \(m\) to importer \(c\) (\(P_{m}{}_{c}>0\)).