An analytical study of the Q(s,S) policy applied to the joint replenishment problem

The Q(s,S) control policy for the joint replenishment problem extended to the case of correlation among item-demands

“…He also proposed a generalization of the P(s,S) policy, which he called the Q(s,S) policy, where the review interval is stochastic as described above. For this policy, Nielsen and Larsen (2005) have developed a mathematical model and an algorithm to compute optimal policy variables.…”

“…For instance, for the dataset of Table 1 in Nielsen and Larsen (2005) it can be seen that their computed policy fulfills (19).…”

“…We develop an algorithm to compute an optimal Q(s,S) policy for a compound correlated Poisson process. It is a non-trivial generalization of the work by Nielsen and Larsen (2005). Since not very many have analyzed inventory control problems in the presence of correlated demands this should be considered as the first main contribution of our paper.…”

“…However, our mathematical model can never compute an optimal policy with Q = 1, due to the decomposition approach it applies. Nielsen and Larsen (2005) have received some critical comments on the Q(s,S) policy. Though clearly operational it might not make sense to a practitioner.…”

“…It is a non-trivial generalization of the work by Nielsen and Larsen (2005). We make some numerical analyses on two-item problems where we compare the optimal Q(s,S) policy to the optimal uncoordinated (s,S) policies.…”