Steady-state Analysis Of Production Service-inventory Systems With Perishable Items

For production companies,a reasonable production inventory strategy can reduce their own costs.At present,many companies provide services while providing products to cus-tomers.Therefore,while ensuring the quality of product supply and service,reducing its cost has become an important issue in the management of production inventory.Perishable items have a shorter life,so the life factor must be considered in the management of produc-tion inventory.This paper studies the production service-inventory systems with perishable items.Firstly,the M/M/1 production service-inventory system with perishable items and(s,S)strategy is studied.The steady-state equilibrium equation of the system is established by using Markov theory and the steady-state equilibrium condition is obtained by using the quasi-birth-and-death process theory.The steady-state probability vector is given by using the method of matrix geometric solution.The performance index and cost function are further obtained.The optimal production inventory strategy is obtained by using genetic algorithm.Secondly,the M/M/1 production service-inventory system with perishable items is s-tudied,where two methods of replenishing stocks are considered:(1)an external order under(0,Q)strategy;(2)an internal production under(s,S)strategy.The matrix analysis method is used to prove that the steady-state probability vector of the system has a product solu-tion,and the expressions of important steady-state performance indexes and cost functions are given.The optimal production inventory strategy is analyzed by using genetic algorith-m.The influence of the parameters on the system performance index is examined through numerical examples.Finally,the M/M/1 production service-inventory system with production interruptions for perishable items is studied.Once the inventory level reaches to S,the production facility enters a random vacation.The steady-state equilibrium equation of the system is established by using Markov theory.The matrix analysis method is used to prove that the steady-state probability distribution of the system has a product solution.The performance index and cost function related to the system are obtained.The influence of the parameters on the performance index is analyzed by numerical examples.