Steady-state Analysis Of Inventory System Under Geometric Batch Demand

Based on different vacation strategies and vacation conditions,this paper studies an inventory system model with geometric batch requirements.The steady-state distribution of the system is given using quasi-birth-and-death process and matrix-geometric solution theory.The performance indicators of the queuing inventory system are given,and the cost function of the system is established using the given performance indicators.Finally,in the process of analyzing the cost function,this paper uses genetic algorithms to analyze the parameters such as customer arrival rate and service rate in the system,and the optimal inventory strategy and the corresponding performance index value of the system under different parameters are obtained.The main contents of this paper are as follows:Firstly,this paper studies the inventory system model under the geometric batch demand,where the server takes vacation when the on-hand inventory level is zero,and the forms of server vacation are divided into single vacation and multiple vacation.By using quasi-birth-and-death process and matrix geometric solution theory,the infinitesimal generator matrix and the state transition matrix and the equilibrium condition and the steady-state probability vector and the relevant performance and the cost function of the system is obtained.The sensitivity analysis of the relevant parameters of the cost function is carried out by using genetic algorithm.The optimal inventory strategy of the system and the corresponding performance index value are obtained.Secondly,this paper studies the inventory system model under the geometric batch demand,where the server takes vacation when the number of customers in the system is zero,and the forms of server vacation are divided into single vacation and multiple vacation.By using quasi-birth-and-death process and matrix geometric solution theory,the infinitesimal generator matrix and the state transition matrix and the equilibrium condition and the steady-state probability vector and the relevant performance and the cost function of the system is obtained.The sensitivity analysis of the relevant parameters of the cost function is carried out by using genetic algorithm.The optimal inventory strategy of the system and the corresponding performance index value are obtained.