Single-Server Queuing-Inventory Systems with Negative Customers and Catastrophes in the Warehouse

Abstract

In this paper, we studied single-server models of queuing-inventory systems (QIS) with catastrophes in the warehouse part and negative customers (n-customers) in service facility. Consumer customers (c-customers) that arrived to buy inventory can be queued in an infinite buffer. Under catastrophes, all inventory of the system is destroyed but customers in the system (on server or in buffer) are still waiting for replenishment of stocks. Upon arrival of n-customer one c-customer is pushed out, if any. One of two replenishment policies (RP) can be used in the system: either (s,S) or randomized. In the investigated QISs, a hybrid service scheme was used: if upon arrival of the c-customer, the inventory level is zero, then according to the Bernoulli scheme, this customer is either lost (lost sale scheme) or joining the queue (backorder scheme). Mathematical models of the investigated QISs were constructed as two-dimensional Markov chains (2D MC). Ergodicity conditions of the investigated QISs were obtained, and the matrix-analytic method (MAM) was used to calculate the steady-state probabilities of the constructed 2D MCs. Formulas for performance measures were found and the results of numerical experiments are presented.

Keywords

• queuing-inventory system
• catastrophes
• replenishment policies
• matrix-analytic method