Critical number policies for inventory models with periodic data

The paper considers an infinite-horizon inventory problem with stochastic demands where the data vary periodically. Karlin shows that a periodic critical-number policy is optimal and presents an algorithm for computing the critical numbers, assuming discounted costs. Here the paper develops an alternative, conceptually simpler approach to these problems. The results include a proof of the optimality of such policies for the average-cost case, and a qualitative description of the behavior of the optimal policy as ‘smoothing’ fluctuations in the data.