Motivated by solving a stylized location problem, the authors develop a light traffic heuristic for an M/G/1 queue with limited inventory that gives rise to a closed form expression for average delay in terms of basic system parameters. Simulation experiments show that the heuristic works well. The inventory operates as follows: the inventory level drops by one unit after each service completion and whenever it drops to a pre-specified level u, an order is placed with replenishment time ¸∼exp(γ). Upon replenishment the inventory is restocked to a pre-specified level s and any arrivals when there is no inventory are placed in queue. Suggestions are given to cover the more general case of a New Better than Used replenishment time distribution. Applications to inventory management problems are also discussed.
