Hossein Abouee Mehrizi, Baris Balcioglu and Opher Baron. Strategies for an M/G/1 Make-to-Stock Queue Serving Different Markets

Abstract. In this paper, we consider a supplier with a centralized
production facility that caters to demand from distinguishable
markets for a single-type product. We assume that demand from each
market arrives according to a Poisson process and the service times
follow a general distribution. We study two types of
continuously-reviewed inventory systems controlled by a base-stock
policy (a) centralized where the inventory is held at the production
facility, and (b) decentralized where each market has its own
inventory. Such production/inventory systems involve a product
allocation problem as well if different markets are given different
priorities and if dispatching decisions are made at the beginning of
the production or are postponed until the production ends. For the
decentralized priority policy with dispatching decisions postponed,
we provide the exact analysis to find the base-stock levels and the
corresponding cost. Via numerical examples, we demonstrate that
generally this policy significantly outperforms the FCFS policy. For
the centralized systems, we propose two approximations, one for the
inventory rationing problem and one for the strict-priority (SP)
policy from the literature. We numerically show that the inventory
rationing significantly outperforms the SP and the FCFS policies.
Yet, in systems under critical load, we observe that the performance
of the SP and the inventory rationing policies approach that of the
optimal policy in a  make-to-order system serving several classes of
customers.