Research on risk-averse newsboy problem and its stochastic approximation method

• 1、Department of Mathematics, Hunan University, Changsha 410082

Abstract：With the digital transformation of the retail industry and the diversified development of commodity categories in recent years, it is of great theoretical and application value to establish a well-planned risk-averse ordering model and design the corresponding numerical algorithm in dealing with market uncertainty and avoiding ordering risks. In this paper, firstly, the stochastic dominance theory is introduced on the basis of the traditional multi-product newsboy model to avoid the ordering risk. By restricting the constraint function, a one-cycle multi-product expected constrained optimal ordering model with second-order stochastic dominance constraint is established and the optimality condition theory of the model is given. Secondly, based on the stochastic approximation method, we design the corresponding stochastic linearization adjacent multiplier algorithm and give the convergence rate of the numerical solution of the algorithm and the high probability guarantee theory of target descent and constraint violation. Finally, taking the tangent plane algorithm as the reference standard, we carried out numerical experiments on product ordering problems with different product category sizes and sample sizes, which confirmed the rationality of the problem model constructed in this paper and the effectiveness of the algorithm design. The experimental results show that compared with the reference algorithm, the stochastic linearization adjacent multiplier algorithm under this model can iterate the better optimal solution.

Keywords： Operational research and cybernetics Newsboy model Second-order stochastic dominance Stochastic approximation