Research On Data-driven Robust Optimization Models And Algorithms Of Newsboy Problems

Newsboy problems are typical stochastic inventory management problems which address how to make optimal inventory or selling strategies for perishable products,and has extensive applications in the fields of operational research,management sciences.The major challenge underlying such problems is to handle uncertainty of demands.In most existing researches,the demand was assumed to conform a given distribution,then a variety of deterministic equivalent formulations were derived to solve the newsboy problem.Recently,some studies pointed out that it is often difficult to know the actual distribution of demands,and in some situations,the demands can not be described by random variables.With the arrival of the era of “Big Data”,in view of theory and applications,it is valuable to study efficient methods which can make optimal decisions directly from sample data without need of assuming that distribution of demands is known.In this thesis,the kernel density estimation method is leveraged to construct the uncertainty set of demand,and construct the robust optimization model for the single-item newsboy problem.The closed-form solutions are obtained by analyzing the properties of the model.Then,impacts of model parameters on the optimal decisions and profit are discussed,and valuable managerial implications are obtained.Then,by considering actual situation of the complementary products,the impacts of prices and the uncertainty of demand,an effective demand function is proposed.Then,a data-driven interval uncertainty set is constructed for describing the uncertain parameters in the demand function,and a data-driven robust optimization model for the newsboy problems with two complementary products is proposed under budget constraints.Owing to non-smoothness of the built model,reformulations of the model are proposed.On the basis of property analysis of the model,an efficient algorithm is developed to solve the original model.Numerical simulation validates the proposed model and its practicability.Sensitivity analyses reveal what are the impacts of the model parameters on optimal decisions and profit,and a plenty of valuable managerial implications are obtained.Finally,a data-driven ellipsoid uncertainty set of uncertain demand parameters is proposed,and a data-driven robust optimization model is constructed to formulate the newsboy problems with two complementary products under budget constraints.According to model properties,smoothing techniques are employed to transform the original model as a series of smooth optimization problems such that they can be solved by the powerful available solver in the sphere of smooth optimization.Effectiveness and robustness of the proposed robust model are both illustrated by numerical simulation,and a plenty of valuable managerial implications are obtained.