The Study On Distributionally Robust Multi-Product Newsvendor Problem

The newsvendor problem is an important issue in supply chain management.It plays a key role in some real inventory problems such as perishable goods,fashion and sporting goods,and seasonal products.In today's highly competitive market,due to market demand volatility,enterprises usually face with the shortage or excess of the optimal number of orders.However,unpredictable demand is often considered as a random variable with a deterministic probability distribution.in many cases,it is almost impossible for the decision maker to obtain the proba-bility distribution information accurately.The distributionally robust optimization method can effectively deal with the newsvendor problem of ambiguous probability distribution.At the same time,the existence of uncertain demand will bring certain risk loss.Therefore,the risk preference is important to include in the decision-making process of multi-product newsvendor.In order to obtain the optimal order quantities and weigh the expected profit and risk loss,the decision maker needs to consider both the return and the risk.This paper considers the ran-dom demand with uncertain probability distribution.Using distributionally robust optimization method,this thesis studies the newsvendor problem under risk neutral and risk averseThe main work of this thesis has the following three aspects:Firstly,under the discrete market demand with ambiguous probability distribution,the dis-tributionally robust models under the cap and the cap-and-trade policies are established,respec-tively.The demand distribution information is characterized by Box ambiguity set.After that,in order to further consider the impact of uncertain carbon emissions on the model,we use the Box?Polyhedral and Box?Ball uncertainty sets to describe the uncertain carbon emissions Then we convert the proposed model into a computationally solvable linear programming and second-order cone programmingSecondly,considering the risk loss caused by the uncertainty of market demand,based on the risk aversion criterion,the multi-product dual-sourcing procurement problem under the cap-and-trade policy is studied.The demand probability distribution of discrete market belongs to Box ambiguity set and Polyhedral ambiguity set.Then,the distributionally robust optimization model based on the mean-CVaR criterion is established,and an equivalent mixed integer linear programming model is derived according to the dual theoryFinally,the model is solved by CPLEX software and the nominal optimal solution and the robust optimal solution are compared.We also verify the validity of the model and the model parameters were analyzed.The influence of the carbon policies was analyzed based on the experimental results.