Research On Performance Analysis And Control Of Queueing-inventory Systems Under The Effect Of Supply-demand And Service

A queueing-inventory system is an integrated system of a queueing system and an inventory system with positive service time.It has a wide application prospect in supply chain systems,production systems,medical service systems,maintenance systems and other fields.The research achievements of queueing-inventory systems during recent years are paticulaly analyzed comprehensively.The performance of queueing-inventory systems affected by three factors including demand,supply and service has been considered,and the optimal control policy of the systems is studied.With the queueing technique,inventory theory,Makovian process,Phase-type distribution theory,linear programming method and other theories and methods,the structural characteristics of the stationary distribution of queue-inventory systems are investigated.The optimal control techniques of different systems are obtained by analyzing the average cost function.The research work of this paper mainly has the following aspects:Firstly,the concept of "batch demands" is introduced for investigating a queueing-inventory system,and the queuing-inventory with geometric batch demands is considered.According to the principle that the demands of a customer are partially satisfied and fully satisfied,we study two queuing-inventory models which are called by ''partial-lost batch demands' ' and ''full-lost batch demands' ' respectively.By using the Markovian queueing theory,the stationary conditions of the two models are given respectively,and it is proved that each model has a staedy-state distribution of product-form.The performance indices of the two systems are given respectively,and the optimal control policies are also discussed by numerical examples.Secondly,a queueing-inventory system with two supply sources is considered.Based on the states of these two sources,and the queuing-inventory model is built by using the vector Markov process.Under the stationary condition,we prove that the steady state distribution has the product form,and the steady state distribution can be decomposed into two stationary distributions of two independent Markovian process,where one distribution is the stationary distribution of the typical M/M/1 queue of the customer,the other distribution is that of the birth-death process of the inventory.With the objective of minimizing the average cost,the algorithmic optimal inventory policy is obtained,and the effects of different parameters on the optimal inventory policy are discussed.Thirdly,a multi-server queueing-inventory system with emergency replenishment is investigated.Assuming that the arrival rate depends on the inventory level,we determine the service rate based the number of servers that work simultaneously,and obtain the stationary condition and the steady state distribution of the queuing-inventory system.By using Phase-type distribution theory,we analyze the emergency replenishment cycle and get the expression of the expectation of the emergency replenishment cycle.The cost function is constructed,and the optimal inventory policy is discussed by numerical experiments.Fourthly,a queueing-inventory system with dynamic variable service rates is proposed.In this system,the service rates come from a set of discrete values,and customers take away the items in the inventory with a certain probability.The objective is to make optimal control of the service rates according to different system states and minimize the total cost.By using the semi-Markov decision process theory,we study the steady state transition equations under the steady decision strategy,and solve the optimal control policy of the service rates with the linear programming theory.Finally,queueing-inventory system theory is applied in maintenance spare parts inventory systems.Taking a large garage in a city as an example,we discuss the application of the theory and method in aforementioned queueing-inventory models respectively.