In mathematical inventory theory the (s, S) ordering policy has played a prominent role. Much work has been expended to determine when some (s, S) policy will be optimal under varying inventory situations. Simple cases exist, however, where no (s, S) policy is optimal. solutions for many of these cases can be viewed as belonging to a more general class of ordering policies, denoted multiple (s, S) policies. A study is made of when such a policy will be optimal.