Studying Distributionally Robust Newsvendor Problem Based On Conditional Value-at-Risk

The newsvendor problem has been widely used in the real life,and has always been an important issue in the field of supply chain inventory management.The research issue of classic newsvendor problem is mainly to maximize the revenue.However,due to some unpredictable factors(earthquake,economic crisis,etc.),loss averse decision-makers are more concerned with the impact of loss,and legacy loss is a new way to deal with loss in the newsvendor problem.For example,perishable products,seasonal products,fashion and other products with short life cycles or short selling period,their market demand is usually faced with many uncertain-ties.The traditional methods take uncertain parameters as random variables,but sometimes it is difficult for decision maker to predict the exact probability distri-bution of random variables,and distributionally robust optimization can overcome this difficulty.This thesis will apply the distributionally robust optimization theory to establish distributionally robust optimization models for legacy loss of newsven-dor problem under the expectation criterion and conditional value-at-risk(CVaR)criterion.The main work of this thesis is includes the following three aspects.Firstly,when the probability of the discrete demand is described as an ellipsoidal uncertainty set,we establish the legacy loss model of newsvendor based on the expectation criterion and the CVaR criterion,and use distributionally robust optimization theory to give their robust counterpart form.We use the dual theory of conic quadratic programming to transform the proposed optimization model into solvable forms.Secondly,we apply expectation criterion and CVaR criterion to the uncertain newsvendor problem.When the probability of discrete demand is described as a box uncertainty set,a bi-objective mean-CVaR model is established.After that,the bi-objective model is transformed into three single objective models.Using distributionally robust optimization theory,the robust counterparts of three models are given.Then we transform these models into solvable forms by using the duality theory of linear programming.Finally,in the numerical examples,we apply Cplex software to solve various models,compare the nominal optimal solutions with robust optimal solutions of each model,analyze the influence of each parameter on robust optimal solution and legacy loss,and then demonstrate the effectiveness of our distributionally robust optimization model.