Steady-state Analysis Of Production Service-inventory Systems With Impatient Customers

Production inventory strategy can effectively balance supply and demand,so it plays an important role in business management.The competitions between enterprises are not only the physical properties of products,but also the service level of products.Therefore,it is necessary to study the performance evaluation of production service-inventory systems and the production control strategy.This paper mainly studies the production service-inventory systems with impatient customers.Firstly,this paper studies a production service-inventory system with impatient customers and infinite waiting space,where the production time obeys the exponential distribution.A level dependent quasi-birth-and-death process is established.Using the method of truncating the tail approximately,the steady-state probability vector and various performance measures are derived.A genetic algorithm and numerical experiment are used for searching optional control strategy.Secondly,a production service-inventory system with impatient customers and finite waiting space is studied.And the production time is subject to exponential distribution.The steady-state probability distribution and some performance measures are obtained by quasi-birth-and-death process and a recursive algorithm.To minimize the expected cost,a inventory optional model is formulated.The inventory model is compared with production inventory systems,which are based on base stock policy and(0,S)strategy,respectively.And this model is analyzed for searching optional control strategy.Finally,this paper studies a production service-inventory system with impatient customers and infinite waiting space,where the production time obeys the mixed exponential distribution.According to the theory of quasi-birth-and-death process,the necessary and sufficient conditions of system's positive recurrence are obtained.By establishing steady-state equilibrium equations,the analytical expressions of the steady-state probability and some performance measures are obtained.A genetic algorithm is used for calculating optional control strategy,and analyzing the effects of parameters on the system cost.