Research On Linear Decision-Making Method And Application For Two-Stage Distributionally Robust Stochastic Optimization Problem

Distributionally robust stochastic optimization is a kind of stochastic optimization problem with ambiguity distribution information.This model can effectively describe the uncertain factors in many decision-making problems,such as supply chain management,energy,health care,portfolio,etc,it has attracted many researchers to study.The central idea of this model is to represent uncertainty through an ambiguity set,which is a family of(possibly with infinite)probability distributions known from possible original data or previous structural informations.Modelers choose the best-case from the worst-case decisions.These decisions can provide an effective performance guarantee for all distributions in the ambiguity set,and avoid the robust optimization which is too conservative.For different distributionally robust stochastic optimization problems,different ambiguity sets are constructed and different algorithms are used.How to construct a well-structured ambiguity set and better to solve the distributionally robust stochastic optimization problem has always been the focus and hot issue of distributionally robust stochastic optimization research.This paper mainly considers the research on linear decision-making method and applications for two-stage distributionally robust stochastic optimization problem.The main contents are as follows:In the first part,based on the uncertainty of customer demand,we build a two stage central kitchen of production and distribution model with moment constraints ambiguity set.Under the ambiguity set,the linear decision rule and duality theory are used to convert the central kitchen production and distribution problem into a solvable cone programming problem.The numerical algorithm of the cone programming is applied to solve the equivalent model,and the effectiveness of the model is verified by numerical examples.In the second part,based on the previous research,as for the two-stage distributionally robust stochastic optimization problem with linear recourse,we use the ambiguity set including high-order moment constraints.By introducing the WKS-form ambiguity set,the lifting theorem is used to reduce the dimensionality of the higher-order moment constraints to reduce the complexity of the calculation.It is proved that under the standard set of regularity conditions,this problem can be converted into a cone programming problem that is easy to be solved by using linear decision rules and duality theory.Numerical experiments are given to show the effectiveness of the method.