凸概率密度分布簇下的多损失鲁棒优化等价模型及在直营连锁企业中的应用

Equivalent Model of Multi Loss Robust Optimization under Convex Probability Density Distribution Cluster and Its Application in Direct Chain Enterprises

首先,证明了凸概率密度分布簇的单周期期望均值下单损失鲁棒优化等价模型定理,以及凸概率密度分布簇的单周期期望均值下多损失鲁棒优化等价模型。然后,提出了直营连锁企业的产品在凸概率密度分布簇下的期望均值的单周期生产分配供应问题,建立了直营连锁企业的单周期生产分配供应期望均值鲁棒模型,在获得近似周期概率分布簇情形下给出了单周期生产分配供应鲁棒模型,这种近似鲁棒模型等价于一个线性规划问题。最后,通过已知一个产品的4个周期构成的混合分布簇进行了数值实验,数值结果表明了期望均值准则下的生产分配供应鲁棒模型的生产分配供应策略更加稳健。

Firstly,the equivalent model theorem of single period expectation mean and single loss robust optimization for convex probability density distribution cluster is proved.And the equivalent model of multi loss robust optimization under the single period expected mean of convex probability density distribution cluster is also proved.Secondly,the single cycle production allocation supply problem of the expected mean value of the products of the direct chain enterprises under the convex probability density distribution cluster is proposed.A robust model of the expected mean value of single cycle production allocation supply for direct chain enterprises is established.In the case of obtaining approximate periodic probability distribution cluster,a robust model of single period production distribution supply is given,which is equivalent to a linear programming problem.Finally,a numerical experiment is carried out with a known mixed distribution cluster composed of four cycles of a product.The numerical results show that the production allocation and supply strategy of the robust model of production allocation and supply under the expected mean criterion is more robust.