基于变分不等式的多商品物流网络优化设计

为优化设计多级多商品流的物流网络，按网络状态把物流网络划分为静态网络和动态网络，分析了静态网络的基础设施建设和动态网络的物流活动问题，构建了可描述不同网络阶段的运营成本和建设成本函数，并且考虑了运营过程带来的环境污染问题，构建了治理费用函数。基于以上函数，建立以供给能力为约束条件，以总成本最小为目标的网络设计和重新设计模型，然后将模型转换为变分不等式问题，证明了所设计模型与变分不等式等价。最后通过算例，运用修正投影算法对模型进行数值演算和验证，得到了最优成本下的设施建设方案和物流组织方案。

Optimization design of multi-commodity logistics network based on variational inequalities

For designing the logistics network of the multi-level and multi-commodity flow, according to network status, the logistics network was divided into static network and dynamic network. This paper analyzed the infrastructure construction of static network and logistics activities of dynamic network. It constructed the operating cost function and construction cost function which can describe the different stages of network. Considering the problem of environmental pollution caused by the operating process, the management cost function was also constructed. Based on the above functions, general logistics network design and re-design optimization models were proposed, whose constraints were supply capacity and goal was minimizing the total cost. The two optimization models were converted to variational inequalities. By the method of modified projection, the paper calculated and verified the model, and obtained the facilities construction program and logistics organization program under the optimal costs.