Markov Models of Inventory Management Systems with a Positive Service Time

Abstract

Markov models of perishable inventory systems where some customers are withdrawn after completion of the service without buying the stock are studied. It is assumed that the service time and filling supply orders are positive random variables. The inventory replenishment size is a variable and depends on the current inventory level. Exact and approximate methods for calculating the joint distribution of the inventory level and the number of orders in the system are developed. Formulas for calculating the main characteristics of the studied systems are proposed and the problem of their optimization is solved. The high level of accuracy of the proposed formulas is confirmed by the numerical experiments.