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**A remark on a standard and linear vector network equilibrium problem with capacity constraints.**
*(English)*
Zbl 1175.90068

Summary: (Weak) vector equilibrium principle with capacity constraints is introduced. A necessary condition that a vector minimum cost flow is a vector equilibrium flow with capacity constraints is obtained. When the number of paths connecting with each pair of source and sink is less than or equal to 2, a sufficient condition for a vector minimum cost flow to be a vector equilibrium flow is also obtained. A generalized (weak) vector equilibrium principle is also introduced. Without any additional assumption, a necessary and sufficient condition for a (weak) vector minimum cost flow to be a generalized (weak) vector equilibrium flow is obtained.

### MSC:

90B10 | Deterministic network models in operations research |

90B20 | Traffic problems in operations research |

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\textit{S. J. Li} et al., Eur. J. Oper. Res. 184, No. 1, 13--23 (2008; Zbl 1175.90068)

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