Research On Inventory System With Phase Type Distribution And Optimal Inventory Policy

In this paper,the important factors influencing the inventory service such as the phase type distribution of the lead time and batch demand are put into the inventory system models.Some models that have phase type distribution of lead time,or the batch demand,or the general distribution of lead time are developed,and the models are analyzed and solved.The optimal inventory policy is obtained by numerical examples.Firstly,a lost sales and continuous review inventory system with phase type distribution of lead time and(r,Q)inventory policy is studied.Using the theory of Markov process,the steady state equilibrium equation is established,and the steady probability of the system is obtained.The minimum cost optimization model under certain service level is given.Using numerical example,the optimal inventory policy is calculated,and the sensitivity of the system parameters is analyzed.Secondly,a batch demand and continuous review inventory system with phase type distribution of lead time and(s,S)inventory policy is studied.Using the theory of Markov process,the steady state equilibrium equation is established,and the steady probability of the system is obtained.The inventory control cost function is given.Using numerical example,the optimal inventory policy is calculated,and the sensitivity of the system parameters is analyzed.Finally,a continuous review inventory system with two types of customers and general distribution of lead time and(s,S)inventory policy is studied.Based on the theory of Markov renewal process,the Markov renewal equations are established and the steady-state probability of the system is obtained.In addition,the inventory control cost function is constructed,and the optimal inventory control strategy is calculated by a numerical example.