A Queueing-inventory System With Random Discount Opportunities And Retrial Customers

ABSTRACT:In this article, we consider a continuous review queueing-inventory system with random discount opportunities and retrial customers. We all know that the items can always be purchased with the regular order setup and costs. However, when a discount opportunity comes, they can also be purchased with a lower cost. So the paper can simulate the inventory management with discount phenomenon in the real life more accurately. We have the following replenishment policy, which has been shown to be the(r, R, d, D) policy. Under the(r, R, d, D) policy,when the inventory position drops to the level r, an order is placed with the regular costs to increase the inventory position to R; and when a discount opportunity comes and the lever of the inventory is at or below d (d>r), an order is placed with the discount costs to increase the inventory position to D (D> R). In the paper, the system consists of the server, the storehouse, the orbit. And if an arriving customer finds the server idle, the customer obtains service immediately and leaves the system with one item from the inventory after a stochastic time. However, if the server is found busy, the customer will enter into the orbit. But, if an arriving customer finds the server closed, the customer will not enter the system. The system will be closed if and only if there is not item in the inventory.The paper has investigated the following two models. In the first model, the retrial rate of the customer in the orbit is a constant and the items in the storehouse has limitless lifetime. And in the second model, the retrial rate has relationship with the quantity of the customer in the orbit, and the item in the storehouse has a random perishing period. Using the method of matrix analysis in the two models, we obtain the steady joint probability distribution of the number of customers in the orbit and the inventory level for the two models. Various system performance measures in the steady state and the long-run total expected cost rate are got. Finally we illustrate the effect of several parameters on system performance measures and the long-run total expected cost rate via numerical experiments.