Optimal inventory control with cyclic fixed order costs

We consider a periodic review single-item inventory model under stochastic demand. Every m periods, in the regular order period, fixed order costs are K. In the periods in-between, the intraperiods, higher fixed order costs of L>K$L>K$ apply. The literature on optimal inventory policies under fixed order costs does not account for these time-dependent fixed order costs. By generalizing existing proofs for optimal inventory policies, we close this gap in inventory theory. The optimal inventory policy is complex in the regular order period and in the intraperiods, a period-dependent (s,S)$(s,S)$ policy is optimal. We describe and prove this optimal policy based on the notion of K-convexity and the optimal ordering behavior in the presence of non-K-convex cost functions. In a numerical study, we find that a major driver of the optimal policy is a forward-buying effect that shifts the probability of ordering from the intraperiods to the regular order period. The cost differences between the optimal and a pure period-dependent (s,S)$(s,S)$ policy are, however, small.