A Fully Polynomial-Time Approximation Scheme for Single-Item Stochastic Inventory Control with Discrete Demand

The single-item stochastic inventory control problem is to find an inventory replenishment policy in the presence of independent discrete stochastic demands under periodic review and finite time horizon. In this paper, we prove that this problem is intractable and for any 2 > 0, we design an algorithm with running time polynomial in the size of the problem input and in 1/2, that finds a policy whose value is within a factor (1 + 2) of the value of an optimal policy. In addition, we formally prove that finding an optimal policy is intractable.