基于共享不确定性的多阶段生产与库存的鲁棒优化方法

Robust optimization method for multi-stage production and inventory based on shared uncertainty

为解决一类目标和约束同时含有相同不确定性参数的模型求解问题,以多阶段生产与库存问题为研究对象,考虑需求不确定性对市场的影响,为追求利润最大化,提出合理的可调节鲁棒模型,从而得到供应链管理中产量与库存量的最优配比.然而,这样的模型求解往往是NP难题的.考虑在特殊的多面体不确定集下,根据对偶理论将共享不确定性参数的鲁棒优化模型转化为容易求解的问题,并论证其与原问题等价.通过模型分析,本文建立的共享不确定性参数鲁棒优化模型更符合实际意义.数值试验验证了模型的鲁棒性、有效性和灵活性,并能给出更为合理的生产和库存方案,对实际问题具有指导意义.

In order to solve the problem of a class of objective and constraints with the same uncertain parameters,taking the multi-stage production and inventory problem as the research object,considering the influence of demand uncertainty on the market,a reasonable adjustable robust model was proposed to maximize profit,and the optimal ratio of output and inventory in supply chain management was obtained.However,the new model was a NP-hard problem.Considering the special polyhedral uncertainty set,the robust optimization model sharing uncertain parameters was transformed into an easily solved problem according to duality theory,and its equivalence with the original problem was proved.Through the model analysis,the robust optimization model of shared uncertain parameters is more practical.Numerical experiments show that the model is robust,effective and flexible,and can give a more reasonable production and inventory plan,which has guiding significance for practical problems.