Analysis And (s,S) Strategy Optimization Of Production Inventory System Considering Service Time

With the rapid development of the e-commerce and information technologies,competitive modes of modern enterprises have been fundamentally changed.More and more enterprises start to realize that it is not enough to survive from a tough competition while only focusing on the product quality of the products,and it becomes important to pursuit higher profits by the effective combination of products and services.However,even it is quite plenty of research results about traditional production inventory systems,service time as one of the important influence factors was always neglected in the modeling and optimizing procedures.In addition,up to now,the related research results are still very few,because it is relatively complicated to model production inventory system while considering service time.On purpose to study service-oriented production inventory systems,product return,perishable goods,productive facility breakdown,and backorders are considered into systematic control strategy as important influence factors.This study focus on performance analysis and optimization problem of production inventory systems considering service time for building a theoretical method to study production inventory systems considering service time.Through the processes of model building,analytical solution,cost function building,and strategy optimization,it is to form a research method of production inventory systems considering service time based on queue theory.The production inventory system in this paper adopts the production inventory(s,S)strategy,that is,when the inventory level depletes to s,the production process is immediately switched on,and is kept in the on model until the inventory level becomes S.The main research contents are as follows:Firstly,for the case of customers often return products a short time after purchase,a mathematical model is built for production inventory system with service time and product returns.Analytical expressions are deduced for existence conditions of steady solutions,stationary joint probability distribution,and important performance measures by using matrix analysis method.Furthermore,average length of production cycle is calculated byusing phase-type distribution characteristics.To build an average total cost function in a unit time,systematical strategy is optimized to set minimal cost function,and optimal value of inventory strategy is derived from numerical analysis.Secondly,for the case of perishable goods,a mathematical model is built for production inventory system considering service time of perishable goods.The system model is established by using the three-dimensional vector Markov process,and the state transition rate matrix of the system is given.It is proved that the stationary joint probability distribution has a product form under the condition that the probability distribution existence.Some performance measures are further deduced.An average total cost function in a unit time is built,meanwhile,a search algorithm is developed to find optimal strategy by setting minimal cost.Finally,the influence of the different parameters is discussed on performance measures and optimal policy by numerical examples.Thirdly,for practical situations,production facilities may break down or do auxiliary works during idle period.A classical vacation mechanism of queue theory is suitable for modelling such production inventory system.Therefore,a mathematical model of production inventory system considering service time is formulated by adopting a vacation control strategy.Production inventory systems are studied for both single and multiple vacation strategies,and analytical expressions of stationary distributions,existence condition,and performance measures are derived.The numerical examples indicates that the average total cost of multiple vacation control strategy is lower than that of single vacation control strategy under the identical parameters.Finally,for backordering,i.e.,the demand that arrives during the time the inventory is depleted,is back ordered,a mathematical model for production inventory system considering service time and back order is formulated.The equilibrium equation of the system in steady state is given and the existence condition of the stationary distribution is obtained.The analytical expressions of some aggregate probabilities and performance measures of the system are obtained by using the method of probability generating function.An average cost function is established,and the influence of the control variables of s and S on performance measures and average cost are discussed numerically.Moreover the sensitivities of other parameters are investigated and some management revelations areobtained.