Studying Single-period Inventory Problem From The Perspective Of Generalized Parametric Possibility Distribution

Single-period inventory is a classic inventory problem in operation management,and it is also an important issue in the research field of supply chain management.The single-period inventory model,which is abstracted from the single-period inven-tory problem,has a simple structure and can explain a lot of management phenom-ena,so it has received widespread attentions.The market demand information in the single-period inventory model is the important basis for the retailer’s decision-making,and the incomplete demand information will cause great decision deviation.With the development of science and technology,product updates faster and faster.So the rate of information and data statistics often cannot keep up with the rate of product updating.It’s hard to gain the demand information of products in this case.This naturally presents a great challenge to the decision makers of short-life-cycle products.Therefore,the research and development of new uncertain description method for the single-period inventory problem has a great significance in real life.First of all,this thesis proposes a new descriptive method-generalized paramet-ric interval-valued fuzzy variable to characterize the uncertain demand in the single-period inventory problem,where only limited distribution information of uncertain demand is known.Secondly,the proposed uncertain distribution set is applied to describe the fluctuation of nominal probability distribution,and the corresponding distributionally robust single-period inventory model is established.Under decision criteria on the underlining decision-making environment,the robust counterpart of the original fuzzy inventory management problem is formulated.According to the structural characteristics of robust counterpart model,the equivalent mixed integer programmings are derived and a domain-based decomposition algorithm is designed.Thirdly,on the assumption that relevant uncertain demands have variable probabil-ity distributions,this thesis builds two multi-product single-period inventory models under risk neutral and risk aversion criterion,respectively.The corresponding op-timal decision depends on the distribution parameters,so the proposed modeling method is more flexible for practical multi-product single-period inventory prob-lem.At the same time,as an extension of the single-period inventory problem,the necessary and sufficient condition for the coordination of a three level supply chain is derived under the variable possibility distribution of the uncertain market demand.Finally,the effectiveness of the proposed parameter credibilistic optimiza-tion method and the distributionally robust optimization method is illustrated by some application examples.The main contributions of this thesis include the following four aspects:(i)The concept of generalized parametric interval-valued fuzzy variable is proposed,and its selection variable provides a variable parameter method for the description of uncertain information in fuzzy environment.(ii)The uncertain distribution set is presented and the corresponding distributionally robust single-period inventory model is established.To some extent,the optimal decision can resist demand distri-bution uncertainty.(iii)The mean value and two order moment of total profits are derived by multiple Lebesgue-Stieltjes integral.On the assumption that relevant uncertain demands have variable possibility distributions,two multi-product single-period inventory models are built under risk neutral and risk aversion criterion,respectively.(iv)As an extension of the single-period inventory problem,a three level supply chain coordination problem is discussed under the variable possibility distribution of the uncertain market demand.