Analysis of a Stochastic Inventory Model on Random Environment with Two Classes of Suppliers and Impulse Customers

Abstract

This paper explores the random environment with two classes of suppliers and impulse customers. The system’s greatest inventory size is S, and it has an infinitely large orbit. In this case, there are two categories of suppliers: temporary suppliers and regular suppliers. Whenever the inventory approaches r, we place on order Q1 (=S−r) unit items to a temporary supplier. Similarly, when the inventory level drops to s (Q1r), we place an order for Q2 (=S−s>s+1) units of items to our regular supplier. Two types of suppliers’ lead times are considered to be exponentially distributed. Here, the customers who arrive from different states of the random environment (RE) are followed by the Markovian arrival process. If there is no inventory in the system when the customer arrives, they are automatically assigned to an orbit. The model was examined in steady state by using the matrix-analytic approach. Finally, the numerical examples for our structural model are discussed.

Keywords

• random environment
• two classes of suppliers
• impulse customers
• Markovian arrival process