Queueing-Inventory System with Two Commodities

A two-commodity inventory system with a single server is considered in this paper. We assume that the capacity of the buffers (to store the two types of commodities) to be finite. Customers (or demands) arrive according to a Poisson Process and the requirement for either type or both type of commodities are modelled using certain probabilities. Customers are lost when their demands are not met due to shortage only at the time of service offerings as opposed to getting lost when the inventory level is zero at the time of arrival. This is to allow the possibility of inventory being replenished prior to offering services to those who arrive when the inventory level is zero. A customer’s demand for both items may be met with only one item should a situation in which there is only one type of inventory is positive and the other is zero at the time of initiating a service occurs. The processing time for meeting the demands are random and modelled using exponential distribution with parameters depending on the type of demands being processed. We adopt (s, S)-type replenishment policy which depends on the type of commodity. Assuming the lead times to be exponentially distributed with parameters depending on the type of commodity, we employ matrix-analytic methods to study the queueing inventory system and report interesting results including an optimization dealing with various costs. © 2018, The Indian Society for Probability and Statistics (ISPS).