This paper considers the coordinated 'periodic-review, order-up-to-level' p
olicy, called. (T, S) policy, for multi-item inventory systems. The mathema
tical model of (T, S) policy for single-item inventory systems is extended
to the more realistic multi-item inventory systems with compound Poisson de
mands, positive replenishment lead times, as well as service level constrai
nts. Numerical comparisons with 'can-order' policy (S, c, s) with different
treatments show that the (T, S) policy outperforms the extensively studied
. (S, c, s) policy. Especially when the lead time is not too short, conside
rable cost reductions can be achieved through an inventory system employing
the (T, S) policy.