  The (R, s, S) is a stochastic inventory control policy widely used by
practitioners. In an inventory system managed according to this policy, the
inventory is reviewed at instant R; if the observed inventory position is lower
than the reorder level s an order is placed. The order's quantity is set to
raise the inventory position to the order-up-to-level S. This paper introduces
a new stochastic dynamic program (SDP) based heuristic to compute the (R, s, S)
policy parameters for the non-stationary stochastic lot-sizing problem with
backlogging of the excessive demand, fixed order and review costs, and linear
holding and penalty costs. In a recent work, Visentin et al. (2021) present an
approach to compute optimal policy parameters under these assumptions. Our
model combines a greedy relaxation of the problem with a modified version of
Scarf's (s, S) SDP. A simple implementation of the model requires a prohibitive
computational effort to compute the parameters. However, we can speed up the
computations by using K-convexity property and memorisation techniques. The
resulting algorithm is considerably faster than the state-of-the-art, extending
its adoptability by practitioners. An extensive computational study compares
our approach with the algorithms available in the literature.
