I have been wondering is there any paper that who discuss multi commodity with four index/indices like this formulation below: $$ \begin{gathered} \sum_{k} \sum_{c} F_{j, j, c, k}=1 \quad \forall j \\ \sum_{i} F_{i, j, c, k}=\sum_{i} F_{j, i, c, k} \quad \forall c, j, k \\ \sum_{i, j, c, k} F_{i, j, c, k}=q_{i} \quad \forall i \\ \sum_{i, j, c, k} F_{i, j, c, k} \leq Q * x_{i, j, k} \quad \forall i, j, c, k \end{gathered} $$