Analysis Of Queueing-Inventory Systems With Batch Demand And Working Vacations

In the process of enterprise operation,it is not only necessary to replenish inventory in time to reduce economic losses caused by customer loss due to inventory shortage,but also to adjust the inventory strategy to improve the service quality while increasing corporate economic benefits of the company by considering the quantity of the customer’s product demands and impatience emotions.This thesis studies queueing-inventory systems with working vacations and customer’s batch demand,and derives the steady-state probability distribution and performance measures of the systems,and optimizes the inventory strategy and the average cost of the systems.Firstly,a queueing-inventory system with customer batch demand,lost sales and multiple working vacations is studied,the server of the system takes vacations when the inventory is zero.Customers arrive according to a Poisson process.The and service time,the replenishment time and the working vacation time all obey exponential distributions,and the batch demands follow a general distribution.By using quasi-birth-death process and matrix geometric solution method,the steady-state conditions and steady-state probability distribution of the system are obtained.Based on the performance measures in steady-state,a long-term average cost function of the system is established.The influence of system parameters on performance measures and optimal inventory strategy and optimal cost are numerically analyzed.Secondly,a queueing-inventory system with batch demand,backordering and multiple working vacations is studied,where the server of the system takes vacations when there are no customers in the system.By using matrix geometric solution method,the steadystate probability vector is obtained.The effect of system parameters on some performance measures of this model and the M/M/1 queueing system with working vacation are analyzed comparatively using numerical examples.Genetic algorithm is applied to obtain the optimal inventory strategy and optimal cost of the system.Finally,a queueing-inventory system with batch demands,impatient customers and multiple working vacations is studied.When the server is in the working vacation period,if the customer waiting in the system during the impatient time of customer is not served,the customer will leave the system.The steady-state probability distribution of the system is obtained by using matrix iteration method,and then the formula of the steady-state performance performances of the system is obtained.Based on these,long-term average cost function of the system is established,and the influence of some system parameters on the performance measures and the optimal strategy is analyzed by numerical examples.