Performance Analysis And Optimization Of Inventory Strategies Of Two-echelon Production-Inventory Queuing Systems

With the diversification of the market development,the influence of supply chain has become more and more extensive,and the links between members of the supply chain have become more and more close.As an important part of the supply chain system,inventory management is the key to improve service quality and save system costs.The two-echelon production inventory queuing system studied in this paper consists of a production center and a distribution center.The optimal inventory level and average costs of the system under different production strategies are considered.The results obtained can provide a basis for decision-makers to make production strategy decisions in practice.Firstly,a two-echelon production inventory queuing system with a production strategy of(rQ,KQ)is studied.The lead time of phase type distribution and backordering are considered in the distribution center.The matrix geometric solution of the steady-state probability distribution of the system is obtained by using the theory of quasi-birth-and-death process.The corresponding performance indexes is given by using the steady-state probability distribution.The optimal inventory strategy and average costs of the system under two production strategies are analyzed and compared by using genetic algorithm.Secondly,a two-echelon production inventory queuing system with a production strategy of(rQ+m,KQ)is studied.Lost sales is considered in the distribution center.Using the theory of quasi-birth-and-death process,the steady-state equilibrium conditions of the system are obtained.By solving the steady-state probability distribution of the modified system model,the product solution of the steady-state probability distribution of the system is obtained,and then the calculation formula of the steady-state performance indexes of the system is given.The optimal inventory strategy and costs of the distribution center,the production center and the system are calculated by using genetic algorithm,and the four production inventory strategies adopted by the system are compared and analyzed by numerical examples.Finally,a two-echelon production inventory queuing system with a production strategy of(rQ+m,KQ)is studied.The server of multiple vacations and backordering are considered in the distribution center.The matrix geometric solution of the steady-state probability distribution of the system is obtained by using the theory of quasi-birth-and-death process.The corresponding performance indexes are given by using the steady-state probability distribution.The influence of inventory parameters on the busy period and the average vacation rate of the server is analyzed by numerical calculation.The optimal inventory strategy and the costs of the system under four production strategies are analyzed and compared by using genetic algorithm.