In this paper, we consider a kind of proper efficiency, namely strict efficiency, of a multi-product supply-demand network equilibrium model. We prove that strict equilibrium pattern flows with both a single criterion and multiple criteria are equivalent to vector variational inequalities. In the case of multiple criteria, we provide necessary and sufficient conditions for strict efficiency in terms of vector variational inequalities by using Gerstewitz's function without any convexity assumptions.

中文翻译：

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多产品供求网络均衡模型的严格效率

在本文中，我们考虑了一种多产品供求网络均衡模型的一种适当的效率，即严格效率。我们证明具有单个准则和多个准则的严格平衡模式流等效于向量变分不等式。在有多个标准的情况下，我们通过使用Gerstewitz函数而无需任何凸度假设，就矢量变分不等式而言，为严格效率提供了充分必要的条件。