A note on the joint replenishment problem under constant demand

This note considers the joint replenishment inventory problem for N items under constant demand. The frequently-used cyclic strategy (T;k1,...,kN) is investigated: a family replenishment is made every T time units and item i is included in each kith replenishment. Goyal proposed a solution to find the global optimum within the class of cyclic strategies. However, it will be shown that the algorithm of Goyal does not always lead to the optimal cyclic strategy. A simple correction is suggested.