On queueing-inventory-location problems

A network of queueing-inventory systems is considered where the inventories are replenished by a common central server. Travel times for transport of the items send out from the center and an adaptive dispatching regime to direct transportation towards the locations with queueing-inventory systems are incorporated in the model. The stationary distribution of the system is of product form and is explicitly given. An optimization procedure is developed to find for given locations of the queueing-inventory systems an optimal location for the replenishment center. Optimization is with respect to overall utilization of the resources measured in total throughput of the queueing-inventory systems.