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, …, k _N ) is investigated: a family replenishment is made every T time units and item i is included in each k _i th replenishment. Goyal proposed a solution to find the global optimum within the class of cyclic strategies. However, we will show that the algorithm of Goyal does not always lead to the optimal cyclic strategy. A simple correction is suggested.