Can-order policies for coordinated inventory replenishment with Erlang distributed times between ordering

We consider the replenishment of items from the same supplier when the cost of each replenishment order is the sum of a major fixed cost and ordinary item-dependent costs. The items are coordinated by the (s,c,S) policy. A decomposition algorithm is developed to compute the parameters of the policy for each item. The algorithm assumes that the time between ordering is Erlang distributed, with parameters depending on the actual policy. The algorithm is used on various examples and it performs well in comparison with other algorithms. We illustrate that this and related decomposition algorithms do not always converge and the policy identified by the algorithms is not necessarily the best one among the (s,c,S) policies.