A multi-item continuous review inventory system with compound Poisson demands

In this paper, we consider a multi-item continuous review inventory system with compound Poisson demands under a general cost structure. Excess demand is backlogged and a fixed delivery lag is assumed. A new algorithm for computing an exact optimal policy is derived based upon the policy iteration method (PIM) using properties of the optimal policy. This algorithm reduces substantially computation times in both the policy evaluation and the policy improvement routines of the PIM. In fact, numerical examples show that the computation times of the new algorithm are less than three percent of those of the PIM. Moreover, three joint ordering policies – the (s,c,S), the (R,T) and the (Q,S) policies – are compared with the optimal ordering policy computed by the new algorithm. It is shown that the (Q,S) policy is almost best among the three joint ordering policy and gives more than ten percent higher expected cost rate than the optimal ordering policy.