Abstract
In this paper, we investigate a multi-server retrial inventory-queueing system with two demand classes. The low priority customers are impatient with Bernoulli reneging probabilities. When the inventory level drops to a re-order level a replenishment order is placed at an external supplier. The order is replenished with a randomly positive lead time. Assume the demand arrival is a Markov arrival process (MAP). We propose two modeling approximations for the original two unbounded level problems. After an economic model is formulated we use combined enumerative and quasi-Newton search to heuristically optimize the number of servers, stock and reorder levels, and retrial and service rates such that the average operating cost per unit time is minimized. Numerical examples are provided to illustrate the application.
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