Steady State Analysis of Impulse Customers and Cancellation Policy in Queueing-Inventory System

Abstract

This article discusses the queueing-inventory model with a cancellation policy and two classes of customers. The two classes of customers are named ordinary and impulse customers. A customer who does not plan to buy the product when entering the system is called an impulse customer. Suppose the customer enters into the system to buy the product with a plan is called ordinary customer. The system consists of a pool of finite waiting areas of size N and maximum S items in the inventory. The ordinary customer can move to the pooled place if they find that the inventory is empty under the Bernoulli schedule. In such a situation, impulse customers are not allowed to enter into the pooled place. Additionally, the pooled customers buy the product whenever they find positive inventory. If the inventory level falls to s, the replenishment of Q items is to be replaced immediately under the (s, Q) ordering principle. Both arrival streams occur according to the independent Markovian arrival process (MAP), and lead time follows an exponential distribution. In addition, the system allows the cancellation of the purchased item only when there exist fewer than S items in the inventory. Here, the time between two successive cancellations of the purchased item is assumed to be exponentially distributed. The Gaver algorithm is used to obtain the stationary probability vector of the system in the steady-state. Further, the necessary numerical interpretations are investigated to enhance the proposed model.