Applied Mathematics & Information Sciences

Author Country (or Countries)

South Africa


A continuous review of single-product stochastic inventory system is considered in which an adjustable reorder can be placed only after the expiry of a Compulsory Waiting Period (CW P) even if the inventory position of the system demands an earlier placement of a reorder. Compulsory waiting period follows an exponential distribution with mean 1/γ. The maximum capacity of the inventory is M. It is assumed that replenishment is instantaneous. Customers arrive to the inventory system according to a Poisson process with rate λ. There is a single server attached with the inventory and the job of the server is to serve each customer one at a time with one item from the inventory according to First-In-First-Out (FIFO) policy. The server takes a random time to serve each customer and this service time follows an exponential distribution with mean 1/µ. When the server serves a customer, all other customers queueup in a waiting room to meet out the FIFO policy. The capacity of the waiting room is assumed to be M − 1. All arriving demands are assumed to be lost when the waiting room is full. By a numerical illustration, the steady-state joint probability distribution for the number of customers in the queueing system and the number of items in inventory is obtained and performance measures such as stationary mean number of replenishment, mean number of demand satisfied and mean number of demand lost are analysed.

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