Bottleneck transportation problem

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This is the transportation problem with a traversal time instead of arc cost, and the objective is to minimize the time it takes to satisfy the demands:

\min \left\{ \max \{ t_{ij} : x_{ij} > 0 \} : x \ge 0, \sum_j x_{ij} \le s_i, \sum_i x_{ij} \ge d_j \right\},

where LaTeX: x_{ij} is the flow from source LaTeX: i to destination LaTeX: j, and LaTeX: t_{ij} is the time it takes to ship across arc LaTeX: (i, j) (independent of the quantity shipped).

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