Research On Distributionally Robust Target-oriented Newsvendor Problem Based On CVaR Criterion

The traditional newsvendor model usually takes the maximization of the expected revenue as the objective function,and does not consider the uncertainty of distribution of demand,which is often deviated from the actual decision.This paper studies the newsvendor problem with unknown distribution of demand and adopts CVaR constraint to make it reach the target profit while taking the minimization of risk as the objective function.The uncertainty set was established by partial statistical information of the demand,and the worst case was considered by adopting robust optimization.The model is improved to be suitable for decision-makers with different risk attitudes.In the first part,the model with a single target is considered,and the subproblem of the original problem is transformed into a computable second order cone programming problem by combining the Lagrangian duality theory with the Scarf's method,and then the effective algorithm of the original problem is given by binary method.In the second part,the model with two targets is considered,the subproblem of the original problem is transformed into a computable second-order cone programming problem by Lagrangian duality theory,and the effective algorithm of the original problem is given by Newton iteration method based on the convexity of the feasible region.Finally,the validity of the proposed model is verified through numerical experiments.Compared with the results of maximizing expected profit model and maximizing attainment probability model,it is found that the proposed model has a better effect when the demand is relatively dispersed.