A Perishable Inventory Model with Bonus Service for Certain Customers, Balking and N + 1 Policy

Abstract

We consider a perishable inventory system with bonus service for certain customers. The maximum inventory level is S. The ordering policy is (0, S) policy and the lead time is zero. The life time of each items is assumed to be exponential. Arrivals of customers follow a Poisson process with parameter λ. Arriving customers form a single waiting line based on the order of their arrivals. The capacity of the waiting line is restricted to M including the one being served. The first N ≥ 1 customers who arrive after the system becomes empty must wait for service to begin. We have assumed that these N customers received an additional service, called bonus service, in addition to the essential service rendered to all customers. The service times are exponentially distributed. An arriving customer who finds the server busy or waiting area size ≥ N, proceeds to the waiting area with probability p and is lost forever with probability (1 − p). The Laplace–Stieltjes transform of the waiting time of the tagged customer is derived. The joint probability distribution of the number of customers in the waiting area and the inventory level is obtained for the steady state case. Some important system performance measures and the long-run total expected cost rate are derived in the steady state.