Steady-state Analysis And Optimal Production Policy Of Production-service Inventory System With Two Classes Of Customers

The company’s inventory management is to avoid the occurrence of over-storage and out-of-stock conditions,to provide the best service for users under the constraints of existing resources,and reduce the total cost of the enterprise through reasonable inventory strategies.In the new economic environment,traditional production enterprises need to integrate and develop with emerging service industries.Which requires production companies need to provide product related services when conducting product transactions and provide targeted services according to different customer requirements in order to improve their competitiveness.Therefore,this paper mainly studies the production-service inventory system with two classes of demands.Firstly,we consider the production-service inventory system with two classes of demands,were two methods of replenishment are considered:(1)an internal production under(,)strategy;(2)an external order under(,)strategy.Bright and Taylor’s approximation method for the steady-state distribution of the level dependent quasi-birth-and-death process(LDQBD)is used to solve the steady-state probability vector.The two kinds of production inventory systems with and without external replenishment are compared and analyzed.Secondly,we consider the production-service inventory system with two classes of customers under two production workshops.The production time of two workshops are subject to follow different exponential distributions.The steady-state probability vector is given by using the method of matrix geometric solution and the steady-state performance measures and the total cost function of the system are obtained.The numerical examples are used to analyze the changes of the main performance measures of the system when the parameters take different values.Furthermore,the optimal(,)inventory policy and optimal the total cost of the system are given by genetic algorithm.Finally,we consider the production-service inventory system with two classes of demands.The service time of the first type of customers are subject to follow PH distribution,and the service time of the second type of customers are subject to follow exponentially distributed.The system production under(,,)strategy.It is to add a threshold to control the services of the second type of customers based on the(,)strategy,stop serving the second type of customers when the inventory level is below .The steady-state probability vector is given by using the method of matrix geometric solution.Then,the performance measures and the total cost function are obtained.The effects of parameters on performance measures under three special cases of different PH distributions are compared and analyzed.