Research On Several Classes Of Stochastic Inventory Model With Jump Demands And Its' Application

It can more clearly reflect the actual situation when the demand process in inventory system is characterized by a jump stochastic process. Researching on inventory probems with jump demand process can improve the inventory theories, and is also of great practical significance.In this paper, several classes of stochastic inventory problems with jump demand processes, including compound Poisson demand process, compound binomial demand process, dual compound demand process and the Markov-modulated demand process, are considered. Fristly,we established the corresponding mathematical models to various types of inventory problems by minimizing the total cost,or based on strictly controlling the service levels,The purposes aim to obtiane the optimal inventory policy and inventory parameters,to determine the optimal cost function expressions,to determine the distributions of inventory system paremeters.Secondly,we hope to determine the jointly probability density function of partial elasticity of the total cost on order policy parameters.We also hope to prove the optimality of some order policies. Finally, we hope to solve some other actual problems, such as determinning the reasonable scale of foreign exchange reserves problem and so on, by using the ideas and methods of solving the inventory problems with jump demand processes.The contents and the structures of the article are as follows:In chapter 1, we describe the significance of this topic, the basic concepts of inventory problems, and the development of domestic and international status of inventory theory.The whole ideas and and layout of the article are introduced in the end of this chapeter.In chapter 2,the inventory problem with compounde Poisson demand process is discussed,the deterministic inventory ordering policy(Q,T)are obtained,it is consistent with the economic order quantity formula.In addition, the inventory ordering policy(Q,T)is actualy two dimension random variables,when the distribution of (Q,T) is given, the joint probability density function of partial elasticity of the total cost on order quantity and order cycle can be gotten based on the partial elasticity theory.In chapter 3 and 4, the inventory systems with (s,s) ordering policy, compound poission demand process and compound binomial demand process are discussed respectively, the distributions of stock volume, ordering cycle length, stocks are determined by using probability analysis methods. The inventory policy parameters s and S are obtained by minimizing the expected total cost Per unit time.Especially,the concrete steps are given for the inventory systems with compound binomial demand process and random response time which Poisson distribution.Five examples are given when the reaponse time is zero.In chapter 5,we deal with a inventory system that the demand process is the sum of a constant function and a composite Poission jump-diffusion stochastic process.We derive the value function satisfied the Hamilton-Jocobi-Bellman (HJB)equations.Meanwhile,the optimal value function and Optimal ordering policy are obtained by using "guessing" techniques.In chapter 6, The changes in foreign exchange reserves without any state intervention of a country who have achieved the internal and external balance meets the jump diffusion process.We transform the pulse reasonable control problem of the scale of foreign exchange reserves into quasi-variational inequalities and derive the optimal pulse controlled policy satisfying the pulse four parameters structure. The optimal value function is obtained in presence of proportional transaction cost.In chapter 7,we consider the production-inventory design problem of a simple two-stage supply chain with uncertain demand,a centralized inventory policy.We construct a multiobjective programming model based on the service level controlled by the ruin probability of a double risk model.In chapter 8, we study the optimality problem of (s, S) inventory policy of a single-item inventory system with continuous-review, Markov-modulated demand and effective supply rate. Based on the minimum criteria of the total expected operating costs in limited phases, dynamic programming recursive model on inventory cost is constructed and the existence and the optimality of (s,S)policy is proved by using scarf's K-convexity of function.